Response Surfaces, Mixtures, and Ridge Analyses

Marginal interval: coefficient of (β1 - β̂1)²p. 67

Book 25/36Data 1.44

A book error: the coefficient is 1/V(b1) = 36/25 = 1.44, V = 25/36 by (3.12.16), as Design A's 4 is 1/(1/4); the book prints the variance 25/36 itself

Marginal interval: coefficient of (β2 - β̂2)², printed with β1p. 67

Book 25/36Data 1.44

A book error: the coefficient is 1/V(b2) = 36/25 = 1.44, V = 25/36 by (3.12.16); the book prints the variance 25/36 itself, and β1 for β2

Residual: brightness, x1 x4 x6 ---, x2 x3 x5 +-- (run 3)p. 107

Book -3Data 3

A sign slip: run 3's brightness is 37 (Tables 4.4 and 4.6) and its fitted value 34.03, so the residual is +3

Designp. 175

Book 24Data 23

Columns 13 and 16 of Table E5.20 are printed identical, as are their CP (-321) and EF (-23), so the 24 main effects have rank 23; the book's own answer (p. 646) says the two columns are identical and drops 16

Aliases: 124p. 177

Book 124 + 345 + 136 + 2456Data 136, 256, 345

With I = 1235 = 2346 = 1456 the string of 124 is 124 + 345 + 136 + 256 (124 × 1456 = 256); the printed 2456 is not an alias of 124

Aliases: 134p. 177

Book 134 + 245 + 126 + 3456Data 126, 245, 356

With I = 1235 = 2346 = 1456 the string of 134 is 134 + 245 + 126 + 356 (134 × 1456 = 356); the printed 3456 is not an alias of 134

N runs: block (x9, x10, x11) = (-1, -1, +1)p. 181

Book 14Data 15

Table E5.33a as printed puts 15 runs in block (x9, x10, x11) = (-1, -1, +1) and 11 in (-1, +1, +1); the text (p. 181) says 14 and 12; all 58 factorial rows obey x9 = 14, x10 = 16, x11 = 17, so either one centre run's x10 (rows 74 to 79 or 86 to 91) or the text's counts are misprinted

N runs: block (x9, x10, x11) = (-1, +1, +1)p. 181

Book 12Data 11

Table E5.33a as printed puts 15 runs in block (x9, x10, x11) = (-1, -1, +1) and 11 in (-1, +1, +1); the text (p. 181) says 14 and 12; all 58 factorial rows obey x9 = 14, x10 = 16, x11 = 17, so either one centre run's x10 (rows 74 to 79 or 86 to 91) or the text's counts are misprinted

Resolutionp. 186

Book IIIData 4

The generators 1235, 1246 and 1347 give I = 1235 = 1246 = 1347 = 3456 = 2457 = 2367 = 1567, seven words of length four, so the design is of resolution IV, not III (the answer's table titles, p. 655, keep III)

Steepest path: direction vector, x1 elementp. 199

Book 2.8Data 3.8

A misprint: (6.5.8) gives b1 = 3.8 and the book uses 3.8 in (6.5.12) to (6.5.16) and Table 6.5, so the vector is (3.8, 2.6, 1.9)

Sum of squares about zero: ΣY²p. 212

Book 40,260,625Data 40260600

The 27 Y of Table 7.1 give ΣY² = 40,260,624; the book's 40,260,625 is one unit high

Fitted: run 7, second-degree Ŷp. 216

Book 210Data 209

The second-degree fit gives Ŷ = 209.4 at run 7; the book's own residual, -39, agrees with 170 - 209.4, so 210 is a slip

Fitted: run 8, second-degree Ŷp. 216

Book 409Data 410

The second-degree fit gives Ŷ = 409.9 at run 8; the book's own residual, 32, agrees with 442 - 409.9, so 409 is a slip

Coefficient: b0, f = infinity, Box and Behnken (1960a) datap. 227

Book 96.60Data 90.60

Least squares gives β0 = 90.60 (numpy agrees); 96.60 is a misprint, the f = 5, 3 and 1 columns printing 90.59, 90.58 and 90.53

Yates column (4): z'y: 02²3²p. 242

Book -1.560Data -1560.000

Z'y = -1,560; the book prints a decimal point for the thousands comma (columns (7) and (8), -14.44 = -1,560/108 and 22,533 = 1,560²/108, use -1,560)

Coefficient: b0p. 262

Book 1.99Data 199.00

B0 = 199.0, the mean of the three centre runs 211, 184 and 202; 1.99 is a misprint

Extra ss: first orderp. 263

Book 1944.5Data 1994.5

The first-order SS is 12Σb² = 12(0.25² + 7.667² + 8.833² + 5.417²) = 1994.5 from the book's own coefficients; 1944.5 transposes two digits

Extra ms: first orderp. 263

Book 486.13Data 498.62

1994.5/4 = 498.63; the book's 486.13 divides the transposed 1944.5

Extra f: first orderp. 263

Book 2.86Data 2.94

498.63/169.76 = 2.94; the book's 2.86 follows from the transposed 1944.5

Extra ss: second order given b0p. 263

Book 3110.8Data 3060.8

The second-order SS is 3060.8; the book's first- plus second-order 5055.3 is right, and 3110.8 is the remainder after its transposed 1944.5

Extra ms: second order given b0p. 263

Book 311.08Data 306.08

3060.8/10 = 306.08; the book's 311.08 follows from the transposed first-order SS

Extra f: second order given b0p. 263

Book 1.83Data 1.80

306.08/169.76 = 1.80; the book's 1.83 follows from the transposed first-order SS

Ss regression: first orderp. 265

Book 19.99Data 19.94

From the book's own totals coefficients, (Σx² = 20)/2 x (0.0552² + 1.4063² + 0.1155²) = 19.94; 19.99 is a slip (its lack of fit, 47.34, would be 47.40)

Ms regression: first orderp. 265

Book 6.663Data 6.647

19.94/3 = 6.647; the book's 6.663 divides its 19.99

Coefficient: b13, the fit to the totals, inside the bracesp. 265

Book -0.1917Data 0.1917

B13 = Σx1x3T/Σ(x1x3)² = 2.3/12 = +0.1917; the sign is a misprint (the other nine coefficients agree)

Coefficient: first-order model: x1p. 265

Book -0.052Data -0.028

Per observation the coefficient is -0.0276, half the totals-fit coefficient; the book prints the totals-fit number unhalved

Coefficient: first-order model: x2p. 265

Book 1.4063Data 0.7032

Per observation the coefficient is 0.7032, half the totals-fit coefficient; the book prints the totals-fit number unhalved

Coefficient: first-order model: x3p. 265

Book 0.1155Data 0.0577

Per observation the coefficient is 0.0577, half the totals-fit coefficient; the book prints the totals-fit number unhalved

Geometric mean: Yp. 290

Book 562.34Data 563.78

The geometric mean of the 27 runs is 563.78, and the book's own S(lambda) table was worked with it (S(0) = 0.2519 needs 563.78; 562.34 gives 0.2506): 562.34 is a misprint

Ss: mean (zero-degree polynomial)p. 309

Book 27,078.0Data 27080.0

N y-bar^2 = 16 x 41.14^2 = 27,080.0 (41.14 = 658.24/16 exactly); the book prints 27,078.0, 2.0 low, and its total 28,571.2 adds its column with that row

Ss: total, uncorrectedp. 309

Book 28,571.2Data 28573.2

Y'y = 28,573.2; the book's 28,571.2 adds its column, whose mean row is 2.0 low (27,078.0 for 27,080.0)

Checking function: l333p. 317

Book -0.32Data 0.32

X3^(3)'y/16 = 5.12/16 = +0.32 from Table 9.5's column x3^(3) and the data; the book prints -0.32 (its sum of squares 16 l333^2 = 1.6 does not depend on the sign)

Ss: Totalp. 355

Book 50,889.6Data 53589.5

Book misprint: Σy² over the 24 runs is 53,589.47, and the table's own rows give 50,517.6 + 3,072.0 = 53,589.6; the printed total is 50,889.6.

Canonical: approximating form, Ẋ3p. 357

Book 6.53Data 6.81

Book slip: (11.4.10) works with λ3 = -0.0925 where (11.4.6) has -0.0965; with the slope m3'b of the fitted equation the coefficient is 6.80762 (and the constant 52.73, not 57.71).

Eigenvector: row 3 of M', x3p. 360

Book 0.255Data 0.225

Book misprint: the element is 0.225386; with the printed 0.255 the squares of row 3 sum to 1.014, with 0.225 to 0.999.

Canonical: constant of X̃4p. 360

Book -1.684Data 1.683

Book slip: with row 4 signed as (11.5.4) prints it, -m4'xS = 1.68257; the printed constant has the sign of the reversed row.

Canonical: constant of X̃5p. 360

Book 2.408Data -2.370

Book slip: with row 5 signed as (11.5.4) prints it, -m5'xS = -2.36973; the printed 2.408 has the sign of the reversed row and differs in size too.

Sum: y1p. 380

Book 250.9Data 252.7

Book misprint: the y1 column of Table E11.17 sums to 252.7; the printed sum is 250.9.

Coefficient: b1, source 1p. 387

Book 6.23Data -6.23

Book sign error: the fit gives -6.23449, and the answer (p. 704) prints b1 = -6.234; Table E11.22c prints +6.23.

Ridge path: lambda = 4.00: x2p. 395

Book 0.06Data 0.05

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 4.00, (12.3.4) gives (0.017, 0.028) and the table prints about (0.03, 0.06); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 4.00: lambdap. 395

Book 4.00Data 2.44

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 4.00, (12.3.4) gives (0.017, 0.028) and the table prints about (0.03, 0.06); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 3.00: x2p. 395

Book 0.08Data 0.07

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 3.00, (12.3.4) gives (0.025, 0.039) and the table prints about (0.05, 0.08); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 3.00: lambdap. 395

Book 3.00Data 1.84

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 3.00, (12.3.4) gives (0.025, 0.039) and the table prints about (0.05, 0.08); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.60: x2p. 395

Book 0.18Data 0.17

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.60, (12.3.4) gives (0.068, 0.089) and the table prints about (0.14, 0.18); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.60: lambdap. 395

Book 1.60Data 1.13

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.60, (12.3.4) gives (0.068, 0.089) and the table prints about (0.14, 0.18); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.20: x1p. 395

Book 0.25Data 0.26

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.20, (12.3.4) gives (0.124, 0.147) and the table prints about (0.25, 0.29); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.20: x2p. 395

Book 0.29Data 0.28

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.20, (12.3.4) gives (0.124, 0.147) and the table prints about (0.25, 0.29); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.20: lambdap. 395

Book 1.20Data 0.93

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.20, (12.3.4) gives (0.124, 0.147) and the table prints about (0.25, 0.29); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.00: x1p. 395

Book 0.40Data 0.42

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.00, (12.3.4) gives (0.202, 0.223) and the table prints about (0.40, 0.45); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.00: x2p. 395

Book 0.45Data 0.43

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.00, (12.3.4) gives (0.202, 0.223) and the table prints about (0.40, 0.45); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 1.00: lambdap. 395

Book 1.00Data 0.83

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 1.00, (12.3.4) gives (0.202, 0.223) and the table prints about (0.40, 0.45); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.90: x1p. 395

Book 0.58Data 0.60

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.90, (12.3.4) gives (0.290, 0.306) and the table prints about (0.58, 0.61); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.90: x2p. 395

Book 0.61Data 0.59

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.90, (12.3.4) gives (0.290, 0.306) and the table prints about (0.58, 0.61); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.90: lambdap. 395

Book 0.90Data 0.78

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.90, (12.3.4) gives (0.290, 0.306) and the table prints about (0.58, 0.61); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.80: x1p. 395

Book 1.00Data 1.02

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.80, (12.3.4) gives (0.500, 0.500) and the table prints about (1.00, 1.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.80: x2p. 395

Book 1.00Data 0.97

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.80, (12.3.4) gives (0.500, 0.500) and the table prints about (1.00, 1.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.80: lambdap. 395

Book 0.80Data 0.73

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.80, (12.3.4) gives (0.500, 0.500) and the table prints about (1.00, 1.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.78: x1p. 395

Book 1.16Data 1.19

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.78, (12.3.4) gives (0.582, 0.575) and the table prints about (1.16, 1.15); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.78: x2p. 395

Book 1.15Data 1.13

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.78, (12.3.4) gives (0.582, 0.575) and the table prints about (1.16, 1.15); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.78: lambdap. 395

Book 0.78Data 0.72

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.78, (12.3.4) gives (0.582, 0.575) and the table prints about (1.16, 1.15); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.76: x1p. 395

Book 1.39Data 1.41

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.76, (12.3.4) gives (0.694, 0.677) and the table prints about (1.39, 1.35); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.76: x2p. 395

Book 1.35Data 1.33

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.76, (12.3.4) gives (0.694, 0.677) and the table prints about (1.39, 1.35); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.76: lambdap. 395

Book 0.76Data 0.71

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.76, (12.3.4) gives (0.694, 0.677) and the table prints about (1.39, 1.35); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.74: x1p. 395

Book 1.72Data 1.74

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.74, (12.3.4) gives (0.858, 0.826) and the table prints about (1.72, 1.65); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.74: x2p. 395

Book 1.65Data 1.63

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.74, (12.3.4) gives (0.858, 0.826) and the table prints about (1.72, 1.65); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.74: lambdap. 395

Book 0.74Data 0.70

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.74, (12.3.4) gives (0.858, 0.826) and the table prints about (1.72, 1.65); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.72: x1p. 395

Book 2.24Data 2.26

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.72, (12.3.4) gives (1.119, 1.064) and the table prints about (2.24, 2.13); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.72: x2p. 395

Book 2.13Data 2.10

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.72, (12.3.4) gives (1.119, 1.064) and the table prints about (2.24, 2.13); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.72: lambdap. 395

Book 0.72Data 0.69

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.72, (12.3.4) gives (1.119, 1.064) and the table prints about (2.24, 2.13); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.70: x1p. 395

Book 3.20Data 3.23

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.70, (12.3.4) gives (1.600, 1.500) and the table prints about (3.20, 3.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.70: x2p. 395

Book 3.00Data 2.97

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.70, (12.3.4) gives (1.600, 1.500) and the table prints about (3.20, 3.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Ridge path: lambda = 0.70: lambdap. 395

Book 0.70Data 0.68

The table's points are twice Eq. (12.3.4), x = -(1/2)(B - lambda I)^-1 b, the factor 1/2 of (12.2.8) dropped: at lambda = 0.70, (12.3.4) gives (1.600, 1.500) and the table prints about (3.20, 3.00); such points lie near, not on, the path of maximum y-hat of (12.3.1), so on the sphere of the printed R the library's maximum is elsewhere and its multiplier is not the printed lambda

Lack of fit ms: Lack of fitp. 440

Book 29.691Data 29.641

88.923/3 = 29.641; the printed 29.691 is a misprint

Lack of fit f: Lack of fitp. 440

Book 64.86Data 108.92

The book divides 29.641 by its pure error mean square 0.457, itself 1.480/8 too large (the printed runs give 0.2721); 29.641/0.2721 = 108.92

Extra f: Lack of fit, b111p. 440

Book 16.74Data 28.30

The book divides 7.701 by 0.46, its pure error mean square 0.457 rounded, itself 1.480/8 too large; with the printed runs' 0.2721 the ratio is 28.30

Extra f: Lack of fit, b222p. 440

Book 173.17Data 292.72

The book divides 79.656 by 0.46, its pure error mean square 0.457 rounded, itself 1.480/8 too large; with the printed runs' 0.2721 the ratio is 292.72

Extra f: Lack of fit, CCp. 440

Book 3.14Data 5.76

1.567/0.46 = 3.41, printed with its digits transposed as 3.14, and 0.46 is the book's pure error mean square rounded, itself 1.480/8 too large; with the printed runs' 0.2721 the ratio is 5.76

Pure error ss: Pure errorp. 440

Book 3.657Data 2.177

The printed runs give a pure error of 2.177 on 8 df (cube pairs 1.845, star-block centre points 0.332), mean square 0.2721; the book's 3.657 exceeds it by 1.480, as its total 15,069.910 exceeds Sum y^2 = 15,068.430

Pure error ms: Pure errorp. 440

Book 0.457Data 0.272

The printed runs give a pure error of 2.177 on 8 df (cube pairs 1.845, star-block centre points 0.332), mean square 0.2721; the book's 3.657 exceeds it by 1.480, as its total 15,069.910 exceeds Sum y^2 = 15,068.430

Ms residual: s_e^2p. 440

Book 0.457Data 0.272

The printed runs give a pure error of 2.177 on 8 df (cube pairs 1.845, star-block centre points 0.332), mean square 0.2721; the book's 3.657 exceeds it by 1.480, as its total 15,069.910 exceeds Sum y^2 = 15,068.430

Sum of squares: Total, uncorrectedp. 440

Book 15,069.910Data 15068.400

Sum y^2 of the printed runs is 15,068.430; the printed total exceeds it by the 1.480 that the printed pure error exceeds the data's

Pure error ss: transformed predictors: Pure errorp. 444

Book 3.657Data 2.177

The printed runs give a pure error of 2.177 on 8 df (cube pairs 1.845, star-block centre points 0.332), mean square 0.2721; the book's 3.657 exceeds it by 1.480, as its total 15,069.910 exceeds Sum y^2 = 15,068.430; Table 13.9 repeats Table 13.8's figure, and pure error does not depend on the predictors

Pure error ms: transformed predictors: Pure errorp. 444

Book 0.457Data 0.272

The printed runs give a pure error of 2.177 on 8 df (cube pairs 1.845, star-block centre points 0.332), mean square 0.2721; the book's 3.657 exceeds it by 1.480, as its total 15,069.910 exceeds Sum y^2 = 15,068.430; Table 13.9 repeats Table 13.8's figure, and pure error does not depend on the predictors

Sum of squares: transformed predictors: Totalp. 444

Book 15,069.910Data 15068.400

Sum y^2 of the printed runs is 15,068.430; Table 13.9 repeats Table 13.8's total, 1.480 too large like its pure error

Projections: any five factorsp. 500

Book 0Data 21

21 of the 56 five-factor projections, each containing factor 8, cannot fit the full quadratic; with levels 0 and 1 of column 8 swapped every projection fits, so column 8 appears misprinted (in the book or its source)

Ms residual: first-order modelp. 515

Book 0.196Data 0.020

(20.790 - 20.692)/5 = 0.0196 (unrounded 0.01969); the printed 0.196 is a decimal slip

Extra f: H0: β1 = β2 = β3p. 516

Book 0.0155Data 0.7856

The printed 0.0155 is the extra mean square (20.692 - 20.661)/2, not divided by s²; F = 0.0155/0.0197 = 0.79

Sequential ss: z3 after z1 and z2p. 540

Book 16.157Data 16.154

The sequential sum of squares of z3 is 16.154; the book's three values add to 73.028, not the 73.025 it states

Coefficient: x3, special cubicp. 540

Book 3.673Data 35.672

The x3 coefficient of the special cubic in x is 35.673; the printed 3.673 drops a digit

Coefficient: x1·x2·x3, special cubicp. 540

Book −767.62Data 767.624

The x1x2x3 coefficient is +767.62 (6.141/0.2^3); the printed minus sign is a misprint

R squared: the ratio fit, Eq. 18.2.9p. 558

Book 0.9063Data 0.9627

The book prints R² = 0.9063 beside its own 96.3%; the fit gives 0.9627, the 96.3%, so 0.9063 is a misprint

Coefficient: x2·x3p. 560

Book -6202Data -6206

A misprint: the fit gives -6205.9, that is -6206, while the other 14 coefficients of Eq. 18.2.10, up to 1,904,909, agree to the unit

Extra ms: Extra for A (first order)p. 567

Book 2,195Data 2194

A slip: the book prints 2,195 for its own 6,582/3 = 2,194 (2,193.9 from the fit)

Extra f: Extra for A (first order)p. 567

Book 38.51Data 38.48

The book divides its mean square 2,195 (a slip for 2,194) by s² rounded to 57.0, 2,195/57.0 = 38.51; unrounded, 2,193.9/57.016 = 38.48

R squared: model 7p. 569

Book 0.699Data 0.735

The book prints model 7's adjusted R², 1 - (1 - 0.735)(59/52) = 0.699, as its R²; R² is 0.735 (models 5 and 6 print R² itself)

R squared: model 7, in the textp. 570

Book 0.699Data 0.735

The book prints model 7's adjusted R², 1 - (1 - 0.735)(59/52) = 0.699, as its R²; R² is 0.735 (models 5 and 6 print R² itself)

Levels of A: the projected designp. 578

Book 8Data 7

A slip: the 31 points the text lists lie at seven levels of A (0, 1/3, 1/2, 3/5, 2/3, 3/4, 1), as the text itself says later

Mean: x4p. 592

Book 96.170Data 96.172

A slip: the column's 14 values average 96.172 (1,346.403/14), as 100 - 1.830 - 1.906 - 0.092 also gives

Range: x4p. 592

Book 1.300Data 2.600

The book prints half the range: its own Min. and Max give 97.500 - 94.900 = 2.600

Ridge path predicted response: Table 19.2, Path A, λ = ∞: ŷp. 605

Book 6.27Data 6.25

Eq. 19.2.4 gives 6.252 at the focus f = (0.21, 0.21, 0.04, 0.44), the fitted value of run 14; every other ŷ of Table 19.2 agrees with the same equation, so the book's 6.27 is a slip for 6.25

Ridge path predicted response: Table 19.2, Path F, λ = −∞: ŷp. 605

Book 6.27Data 6.25

Eq. 19.2.4 gives 6.252 at the focus f = (0.21, 0.21, 0.04, 0.44), the fitted value of run 14; every other ŷ of Table 19.2 agrees with the same equation, so the book's 6.27 is a slip for 6.25

Coefficient: z2·1, y = θz1 + θ2z2·1p. 631

Book 14.34828Data 14.34830

A book slip: the coefficient of z2·1 is θ̂2 of (b), 14.348267, printed there as 14.34827; here 14.34828

Ss residual: y = θ1z1 + θ2z2p. 631

Book 102Data 107

A book error: S_R = 381592 - 374949.97 - 6535.17 = 106.86; the book prints 102, so its rows fall 5 short of its total, which it calls rounding error

Ms residual: y = θ1z1 + θ2z2p. 631

Book 26Data 27

A book error: s² = 106.86/4 = 26.72; the book's 26 is its residual 102 over 4

Ms residual: s², in units of 100 (MS/100)p. 631

Book 0.26Data 0.27

A book error: s²/100 = 106.86/400 = 0.267, giving a bound of 3.71 (371.0 in the units of the printed quadratic form); the book's 0.26 and 3.61 come from its residual 102

Coding: x2, centrep. 633

Book 1760Data 1750

The levels of X2 are 1000 and 2500 lb (Table E4.9), so the centre is 1750; with 1760 the coded levels would be -1.013 and 0.987

Coefficient: b1p. 635

Book -7.506Data 7.506

A sign slip: b1 is +7.506, half the effect 1 <- 15.01 of Exercise 4.9; the runs at 110 rpm average 37.10 and those at 60 rpm 22.09

Ms regression: first orderp. 636

Book 36.485Data 36.458

109.375/3 = 36.458; the printed 36.485 transposes two digits

Curvature contrast: CC, transformed, response 1 (PDA)p. 637

Book -0.101Data -0.104

The book's -101 does not follow from the printed data: the transformed factorial average 0.12150 less arcsin(0.05^½) = 0.22551 gives 1000 x (-0.10401) = -104.0

Effect: transformed, response 3 (PD), 134p. 637

Book 0.031Data -0.031

A lost minus sign: 1000 times the effect is -31.26, and the same effect untransformed is -1.85 (Table A4.16a)

Effect: transformed, response 3 (PD), 1234p. 637

Book 0.057Data -0.057

A lost minus sign: 1000 times the effect is -57.02, and the same effect untransformed is -4.95 (Table A4.16a)

Effect: transformed, response 4 (R), 124p. 637

Book 0.097Data -0.097

A lost minus sign: 1000 times the effect is -96.61, and the same effect untransformed is -8.03 (Table A4.16a)

Effect: transformed, response 4 (R), 134p. 637

Book 0.147Data -0.147

A lost minus sign: 1000 times the effect is -146.99, and the same effect untransformed is -12.55 (Table A4.16a)

Mean: Ip. 643

Book -106.875Data 106.875

The eight responses of Table E5.15 sum to 855, so the average is +106.875; the mean column is minus the 1234 column, which does not change the average's sign, so the minus sign is a misprint

Effect: 3 - 124p. 643

Book 0.26Data 0.25

The runs of Table E5.15 with x3 = +1 total 428 and those with x3 = -1 total 427, so the 3 - 124 estimate is (428 - 427)/4 = 0.25, not 0.26; the other six estimates reproduce

Effect: 2 + 13p. 643

Book 0.625Data -0.625

Over the 16 readings of Table E5.16, x2 = +1 totals 159 and x2 = -1 totals 164, so the 2 + 13 estimate is (159 - 164)/8 = -0.625; the printed 0.625 has lost its sign

Usable members: without renaming the variablesp. 644

Book -134Data -1256, -135, -2345, -456, 124, 1346, 236

-134 is a word of no member of the family I = ±124 = ±135 = ±236; the members that keep 1, 3 and 5 from all being at + have -135, as Ozzie's I = 124 = -135 = 236 (p. 173) does

Variables transferred to the residual: the eight smallest sums of squaresp. 646

Book 13,075Data 19343

With 3, 5, 6, 11, 19, 21, 22 and 24 transferred the residual is 19,343; the eight smallest sums of squares, CP²/28 from the CP row of Table E5.20, are those of 19, 11, 3, 21, 6, 23, 24 and 5 (86 to 1094), and the table printed (129,730 on 15 df, residual 13,075) is for 23 transferred; 22 (SS 7264, named effective on p. 646) is a misprint for 23

Words of length threep. 648

Book 129 + 789Data 129, 359, 469, 789

The relation of I = 1235 = 1246 = 1347 = 2348 = 129 also holds 359 (1235 × 129) and 469 (1246 × 129): four words of length three, 129, 359, 469 and 789, not two

Aliases: 9p. 648

Book 9 + 12 + 78Data 12, 35, 46, 78

9 = 12 = 35 = 46 = 78 in this design, since 359 and 469 are words of its relation, so 9's string also holds 35 and 46

Aliases: 3, 4, 5, 6p. 648

Book all main effects are estimated clear except for those in the combinationsData 59

3 is aliased with 59, from the word 359 (1235 × 129 = 359, 1246 × 129 = 469), so it is not clear

Aliases: 3, 4, 5, 6p. 648

Book all main effects are estimated clear except for those in the combinationsData 69

4 is aliased with 69, from the word 469 (1235 × 129 = 359, 1246 × 129 = 469), so it is not clear

Aliases: 3, 4, 5, 6p. 648

Book all main effects are estimated clear except for those in the combinationsData 39

5 is aliased with 39, from the word 359 (1235 × 129 = 359, 1246 × 129 = 469), so it is not clear

Aliases: 3, 4, 5, 6p. 648

Book all main effects are estimated clear except for those in the combinationsData 49

6 is aliased with 49, from the word 469 (1235 × 129 = 359, 1246 × 129 = 469), so it is not clear

Coefficient: (a), x1p. 651

Book 505.083Data -571.750

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -571.75; the printed 505.083 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 505.08

Coefficient: (a), x2p. 651

Book -556.083Data 255.417

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 255.42; the printed -556.083 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -556.08

Coefficient: (a), x3p. 651

Book 476.417Data 243.917

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 243.92; the printed 476.417 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 476.42

Coefficient: (a), x4p. 651

Book 0.417Data 18.583

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 18.58; the printed 0.417 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 0.42

Std error: (a), every coefficientp. 651

Book 51.68Data 259.18

The standard error of the four coefficients is 259.18 in Table 5.7's run order and 136.74 in the order the printed coefficients come from; the printed 51.68 is 136.74/√7, the residual variance divided by its 7 df a second time

Coefficient: (b), x1p. 651

Book 505Data -572

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -571.75; the printed 505 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 505.08

Coefficient: (b), x2p. 651

Book -556Data 255

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 255.42; the printed -556 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -556.08

Coefficient: (b), x3p. 651

Book 476Data 244

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 243.92; the printed 476 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 476.42

Coefficient: (b), x4p. 651

Book 0Data 19

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 18.58; the printed 0 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 0.42

Coefficient: (b), x5p. 651

Book 25Data 21

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 20.92; the printed 25 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 25.42

Coefficient: (b), x6p. 651

Book 94Data 137

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 136.58; the printed 94 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 94.25

Coefficient: (b), x7p. 651

Book 62Data -51

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -50.75; the printed 62 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 62.25

Coefficient: (b), x8p. 651

Book 112Data 148

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 147.92; the printed 112 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 111.58

Coefficient: (b), x9p. 651

Book 81Data -92

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -92.08; the printed 81 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 81.42

Coefficient: (b), x10p. 651

Book -269Data -60

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -59.75; the printed -269 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -269.08

Coefficient: (b), x11p. 651

Book 161Data 644

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 643.92; the printed 161 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 161.25

Coefficient: (d), x1p. 652

Book 280Data -818

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -818.17; the printed 280 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 280.33

Coefficient: (d), x2p. 652

Book -556Data 84

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 83.67; the printed -556 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -555.58

Coefficient: (d), x3p. 652

Book 304Data 40

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 40.33; the printed 304 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 304.33

Coefficient: (d), x4p. 652

Book -140Data 177

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 177.33; the printed -140 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -140.42

Coefficient: (d), x1:x2p. 652

Book -225Data -194

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -194.33; the printed -225 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -224.58

Coefficient: (d), x1:x3p. 652

Book -55Data -633

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -633.42; the printed -55 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -55.42

Coefficient: (d), x1:x4p. 652

Book -36Data -121

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -120.92; the printed -36 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -36.17

Coefficient: (d), x2:x3p. 652

Book -253Data 37

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 37.17; the printed -253 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -253.33

Coefficient: (d), x2:x4p. 652

Book -328Data -537

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is -537.33; the printed -328 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give -327.83

Coefficient: (d), x3:x4p. 652

Book 93Data 239

In Table 5.7's printed run order, as the exercise gives the observations, this coefficient is 239.08; the printed 93 reproduces only with observations 2 to 11 on rows 11 to 2 (rows built by moving the first row's signs one place to the left), which give 93.08

Generatorp. 652

Book 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16Data

Every run of Table E5.32 has x1x2x3x4x5 = -1: the fraction is I = -12345, not I = 12345

Resolutionp. 652

Book IVData 5

A 2^(5-1) whose one word, 12345, has five letters is of resolution V, not IV

S²p. 655

Book 5.49Data 5.47

43.775/8 = 5.472, not 5.49; the column sum 43.775, its 8 df and all 16 entries of Table E5.36b reproduce

Nonadditivity ss: S_αp. 659

Book 0.00007Data 0.00003

S_α = 0.00285²/0.2507 = 0.000032 (numpy and the library); the book's 0.00007 uses Σ(q - q̂)² = 0.1366, which is 0.2507 from the q of its own table, and Σ(y - ŷ)q = 0.0030 for 0.00285

Nonadditivity ss: transformation SS (Table 7.6 form)p. 659

Book 0.00007Data 0.00003

S_α = 0.00285²/0.2507 = 0.000032 (numpy and the library); the book's 0.00007 uses Σ(q - q̂)² = 0.1366, which is 0.2507 from the q of its own table, and Σ(y - ŷ)q = 0.0030 for 0.00285

Nonadditivity ms: transformation (one degree of freedom)p. 659

Book 0.00007Data 0.00003

S_α = 0.00285²/0.2507 = 0.000032 (numpy and the library); the book's 0.00007 uses Σ(q - q̂)² = 0.1366, which is 0.2507 from the q of its own table, and Σ(y - ŷ)q = 0.0030 for 0.00285

Nonadditivity f: transformationp. 659

Book 0.01Data 0.00

F = 0.000032/0.007257 = 0.004; the book's 0.01 follows from its S_α = 0.00007, whose Σ(q - q̂)² should be 0.2507

Nonadditivity ss error: adjusted residualp. 659

Book 0.03623Data 0.03628

The adjusted residual is 0.036317 - 0.000032 = 0.03628; the book subtracts its S_α = 0.00007

Nonadditivity ms error: adjusted residualp. 659

Book 0.00725Data 0.00726

0.03628/5 = 0.00726; the book's 0.00725 follows from its S_α = 0.00007

Coefficient: (c), centre of the circle, β2, printed (β2 - 0.2683)²p. 661

Book 0.2683Data -0.2683

B2 = -0.2683, as the book prints it on pp. 657-658, so the circle's centre is β2 = -0.2683 and the term is (β2 + 0.2683)²; the printed minus sign is a slip

Nonadditivity ss: SS(transformation), 1 dfp. 662

Book 83Data 8318

S_α = 8,318 (numpy and the library); the book's 83 is S_α computed for y/10 (83.18), a factor of 100 off

Nonadditivity ss error: SS(adjusted residual)p. 662

Book 76,066Data 67627

The adjusted residual is 75,945 - 8,318 = 67,627; the book's 76,066 is 76,149 - 83, and the second-order residual is 75,945, not 76,149 (the book's own 3^k mean squares sum to 75,943)

Nonadditivity df error: SS(adjusted residual) dfp. 662

Book 17Data 16

The second-order residual has 17 df and the transformation takes one, leaving 16; the book keeps 17

Mean square (z'y)²/z'z: 1p. 662

Book 24,481Data 28481

716²/18 = 28,481; 24,481 is a misprint (the printed root mean square, 169, is the root of 28,481)

Mean square (z'y)²/z'z: 12p. 663

Book 2,607Data 2670

179²/12 = 2,670.1; 2,607 transposes two digits (the printed final column -179 and divisor 12 are right)

Coefficient: b33, second-order modelp. 664

Book 24.28Data -24.28

B33 = -437/18 = -24.28 from the book's own 3^k table, and its b0 = 367.48 needs -24.28; the plus sign is a misprint

Extra f: first orderp. 664

Book 122.0Data 122.9

F = 55,245/449.7 = 122.85; the book's s² = 453 carries its transposed mean square 2,607

Extra ss: second order given b0p. 664

Book 25,275Data 25340

The book adds its mean squares 7,467 + 2,607 + 11,324 + 80 + 261 + 3,536 = 25,275; with 2,670.1 for the transposed 2,607 the second-order SS is 25,339.6

Extra ms: second order given b0p. 664

Book 4,213Data 4223

25,339.6/6 = 4,223.3; the book's 4,213 is its 25,275/6

Extra f: second order given b0p. 664

Book 9.3Data 9.4

4,223.3/449.7 = 9.39; the book's 9.3 is 4,213/453, both carrying the transposed 2,607

Ss residual: residualp. 664

Book 7,709Data 7645

The residual is 7,644.8; the book's 7,709 is the remainder after its 25,275, which adds the transposed 2,607

Ms residual: residualp. 664

Book 453Data 450

7,644.8/17 = 449.7; the book's 453 is 7,709/17

Coefficient: b1, second-order model, all 81 observationsp. 664

Book 131.46Data 177.00

With Table E7.9 as printed (x1 changing fastest) the fit gives b1 = 177.00; the book's equation interchanges x1 and x3, its b1 being the fit's b3

Coefficient: b3, second-order model, all 81 observationsp. 664

Book 177.00Data 131.46

With Table E7.9 as printed (x1 changing fastest) the fit gives b3 = 131.46; the book's equation interchanges x1 and x3, its b3 being the fit's b1

Coefficient: b12, second-order model, all 81 observationsp. 664

Book 43.58Data 66.03

With Table E7.9 as printed (x1 changing fastest) the fit gives b12 = 66.03; the book's equation interchanges x1 and x3, its b12 being the fit's b23

Coefficient: b23, second-order model, all 81 observationsp. 664

Book 66.03Data 43.58

With Table E7.9 as printed (x1 changing fastest) the fit gives b23 = 43.58; the book's equation interchanges x1 and x3, its b23 being the fit's b12

Extra ss: second-order terms given b0p. 664

Book 471,778Data 473039

The second-order SS is 473,039; the book's rows add to 3,271,619 + 471,778 + 295,990 + 244,025 = 4,283,412, 764 short of its own total 4,284,176, so 471,778 is a slip

R squared: second-order modelp. 664

Book 0.8738Data 0.8741

(3,271,619 + 473,039)/4,284,176 = 0.8741; the book's 0.8738 uses its 471,778

Lack of fit ss: lack of fitp. 664

Book 295,990Data 295493

The lack of fit is 539,518 - 244,025 = 295,493; the book's rows do not add to its total (764 short)

Anova sum sq: b11 given b0p. 665

Book 23,053.87Data 23053.40

SS(b11 | b0) = 23,053.36 (numpy and the library); the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova mean sq: b11 given b0p. 665

Book 23,053.87Data 23053.40

The mean square on 1 df is 23,053.36; the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova f: b11 given b0p. 665

Book 102.97Data 103.05

F = 23,053.36/223.72 = 103.05; the book's uses its 23,053.87 and 223.90; the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova sum sq: b22 given b0p. 665

Book 5,827.03Data 5826.78

SS(b22 | b0) = 5,826.78 (numpy and the library); the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova mean sq: b22 given b0p. 665

Book 5,827.03Data 5826.78

The mean square on 1 df is 5,826.78; the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova f: b22 given b0p. 665

Book 26.03Data 26.05

F = 5,826.78/223.72 = 26.05; the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova sum sq: b12p. 665

Book 403.13Data 406.12

SS(b12) = 57²/8 = 406.125 exactly (Σx1x2y = 57); the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova mean sq: b12p. 665

Book 403.13Data 406.12

The mean square on 1 df is 57²/8 = 406.125; the book's partition slips, though its rows still add to the corrected total 32,408.3

Anova f: b12p. 665

Book 1.80Data 1.82

F = 406.125/223.72 = 1.82; the book's partition slips, though its rows still add to the corrected total 32,408.3

Ss residual: residualp. 665

Book 2,686.84Data 2684.60

The residual is 2,684.60; the book's partition slips, though its rows still add to the corrected total 32,408.3

Ms residual: residualp. 665

Book 223.90Data 223.72

S² = 2,684.60/12 = 223.72; the book's partition slips, though its rows still add to the corrected total 32,408.3

Lack of fit ss: lack of fitp. 665

Book 1,085.34Data 1083.10

The lack of fit is 2,684.60 - 1,601.50 = 1,083.10; the book's partition slips, though its rows still add to the corrected total 32,408.3

Lack of fit ms: lack of fitp. 665

Book 361.72Data 361.03

1,083.10/3 = 361.03; the book's partition slips, though its rows still add to the corrected total 32,408.3

Coefficient: b0, (c), second-order modelp. 665

Book 7.5Data 43.5

B0 = 43.5, the mean of the four centre runs; 7.5 is a misprint

Extra f: first orderp. 666

Book 13.53Data 11.26

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so s² = 11.912 and F = 134.08/11.912 = 11.26; the book's 13.53 uses s² = 9.912

Extra f: second order given b0p. 666

Book 18.25Data 15.18

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so s² = 11.912 and F = 180.88/11.912 = 15.18

Lack of fit ss: lack of fitp. 666

Book 42.47Data 54.47

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so the lack of fit, which the book works as a remainder, is 54.47

Lack of fit ms: lack of fitp. 666

Book 14.16Data 18.16

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so the lack-of-fit MS is 54.47/3 = 18.16

Lack of fit f: lack of fitp. 666

Book 2.50Data 3.20

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so F = 18.16/5.667 = 3.20, still below F(3, 3, 0.95) = 9.28

Ss total uncorrected: totalp. 666

Book 16,639.00Data 16651.00

The twelve observations give Σy² = 16,651; the book's 16,639.00 is 12 short (its part (d) total, 40,331, agrees with 16,651), and its lack of fit, worked as a remainder, inherits the slip

Ms residual: residualp. 666

Book 9.912Data 11.912

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so s² = (54.47 + 17.00)/6 = 11.912

Lack of fit f: first-order modelp. 666

Book 17.20Data 17.56

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so F = {(542.63 + 54.47)/6}/5.667 = 17.56; the book also divides by 5.67 rounded

Lack of fit ss: first-order modelp. 666

Book 542.63 + 42.47Data 597.099

The twelve observations give Σy² = 16,651, not the book's 16,639.00, so the first-order model's lack of fit is 542.63 + 54.47 = 597.10

Extra f: nine points: b1, b2p. 668

Book 691.9Data 69.2

F = 81.42/1.176 = 69.24 (the book's own rows give 81.42/1.177 = 69.19); 691.9 misplaces the decimal point

Coefficient: b22, second-order model, all 12 observationsp. 668

Book -16.30Data -16.29

B22 = -16.289 (numpy agrees), which rounds to -16.29; the book's -16.30 is a slip

Coefficient: b12, second-order model, all 12 observationsp. 668

Book -6.00Data 6.00

B12 = (130 - 121 - 110 + 125)/4 = +6.00, and the book's own centre (0.067, -0.051) needs +6 (with -6 it is (0.092, -0.080)); the minus sign is a misprint

Extra ss: b1, b2p. 668

Book 87.90Data 87.91

The first-order SS is 21²/8.5 + 17.5²/8.5 = 87.91; the book's 87.90 is a slip

Extra ms: b1, b2p. 668

Book 43.95Data 43.96

87.91/2 = 43.96; the book's 43.95 halves its 87.90

Extra f: b1, b2p. 668

Book 2.24Data 2.23

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so s² = 19.728 and F = 43.96/19.728 = 2.23

Extra ss: b11, b22, b12 given b0p. 668

Book 3328.62Data 3328.64

The second-order SS is 3,328.64; the book's 3,328.62 is a slip

Extra f: b11, b22, b12 given b0p. 668

Book 56.57Data 56.24

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so F = 1,109.55/19.728 = 56.24

Lack of fit ss: lack of fitp. 668

Book 100.67Data 101.37

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so the lack of fit, a remainder, is 101.37

Lack of fit ms: lack of fitp. 668

Book 33.557Data 33.790

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so the lack-of-fit MS is 101.37/3 = 33.79

Lack of fit f: lack of fitp. 668

Book 5.92Data 5.96

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so F = 33.79/5.667 = 5.96

Ss total: total, correctedp. 668

Book 3534.19Data 3534.92

199,887 - 196,352.08 = 3,534.92; 3,534.19 transposes the last two digits

Ss residual: residualp. 668

Book 117.67Data 118.37

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so the residual is 101.37 + 17.00 = 118.37

Ms residual: residualp. 668

Book 19.612Data 19.728

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so s² = 118.37/6 = 19.728

Ms residual: s²p. 669

Book 19.612Data 19.728

The twelve observations give the corrected total Σy² - (Σy)²/12 = 199,887 - 196,352.08 = 3,534.92, not the book's 3,534.19, so s² = 118.37/6 = 19.728

Ratio: (ŷmax - ŷmin)/(ps²/n)^1/2p. 669

Book 13.70Data 13.65

The book's s² = 19.612 rests on a corrected total of 3,534.19, where the twelve observations give 3,534.92 and s² = 19.728 (see s² above); with it, and the fitted values 150.836 and 107.950, the ratio is 13.65; the book's own numbers give (150.84 - 107.94)/{6(19.612)/12}^1/2 = 13.70

Significance at 5%: lack of fit, all 20 readingsp. 669

Book < 0.05Data 0.78107

With all 20 readings the lack of fit F is (212.5/3)/(2,147.0/11) = 0.36, p = 0.78 (numpy and the library): no lack of fit is exhibited, contrary to the book

Coefficient: b0, reduced first-order modelp. 672

Book 15.8Data 15.7

The first-order intercept is ȳ = 376.8/24 = 15.70; the book repeats the full model's 15.8

Ss residual: first-order modelp. 672

Book 12.359Data 12.328

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: the first-order residual is 387.560 - 375.232 = 12.328

Ms residual: first-order modelp. 672

Book 0.61795Data 0.61642

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: 12.328/20 = 0.6164

Σxi²: each x over the 24 observationsp. 672

Book 16Data 24

Over the 24 observations Σxi² = 8 + 16 = 24, each axial point being run twice; the book's 16 counts each axial point once

Σxi²: each x over the 24 observationsp. 672

Book 16Data 24

Over the 24 observations Σxi² = 8 + 16 = 24, each axial point being run twice; the book's 16 counts each axial point once

Σxi²: each x over the 24 observationsp. 672

Book 16Data 24

Over the 24 observations Σxi² = 8 + 16 = 24, each axial point being run twice; the book's 16 counts each axial point once

Std error: first-order model, b1p. 672

Book 0.20Data 0.16

Se = (0.6164/24)^1/2 = 0.16; the book's 0.20 uses Σxi² = 16 (24 over the 24 observations)

Std error: first-order model, b2p. 672

Book 0.20Data 0.16

Se = (0.6164/24)^1/2 = 0.16; the book's 0.20 uses Σxi² = 16 (24 over the 24 observations)

Std error: first-order model, b3p. 672

Book 0.20Data 0.16

Se = (0.6164/24)^1/2 = 0.16; the book's 0.20 uses Σxi² = 16 (24 over the 24 observations)

Extra ss: first orderp. 672

Book 375.201Data 375.232

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: 375.232

Extra ms: first orderp. 672

Book 125.067Data 125.077

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: MS = 375.232/3 = 125.077

Extra f: first orderp. 672

Book 302.09Data 303.31

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: F = 125.077/0.4124 = 303.3

Extra ss: second order given b0p. 672

Book 6.558Data 6.555

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: the second-order SS is 6.555

Extra f: second order given b0p. 672

Book 2.64Data 2.65

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: F = 1.0925/0.4124 = 2.65

Lack of fit ss: lack of fitp. 672

Book 3.308Data 3.281

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: lack of fit 3.281

Lack of fit ms: lack of fitp. 672

Book 0.661Data 0.656

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: 3.281/5 = 0.656

Lack of fit f: lack of fitp. 672

Book 2.39Data 2.37

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: F = 0.656/0.277 = 2.37

Ms residual: residualp. 673

Book 0.414Data 0.412

The first-order SS is (12.6² + 22.2² + 91.4²)/24 = 375.232 (b1, b2, b3 = 0.525, 0.925, 3.8083 as printed), 0.031 more than the book's 375.201, and the book's remainders inherit the slip: s² = (3.281 + 2.493)/14 = 0.4124

Extra ss: second order given b0, blocks (x 10^3)p. 674

Book 292.4e-3Data 0.268884

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give second order 268.9 (x 10^-3)

Df: second order given b0, blocks (x 10^3)p. 674

Book 7Data 10

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give 10 df for the second-order terms, as Table E7.26b prints

Extra ms: second order given b0, blocks (x 10^3)p. 674

Book 41.77e-3Data 0.0268884

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give 268.9/10 = 26.89 (x 10^-3)

Lack of fit ss: (SS and MS x 10^3)p. 674

Book 43.6e-3Data 0.0670697

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give lack of fit 67.07 (x 10^-3); the book's 292.4 and 43.6 add to the same 336.0

Lack of fit dfp. 674

Book 12Data 9

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give 28 - 16 - 3 = 9 lack-of-fit df, as Table E7.26b prints

Lack of fit ms: (SS and MS x 10^3)p. 674

Book 3.63e-3Data 0.00745219

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give 67.07/9 = 7.452 (x 10^-3)

Lack of fit fp. 674

Book 22.85Data 46.87

The book's own fitted equation (its 16 coefficients agree with the fit) has ten second-order terms; with them numpy and the library give F = 7.452/0.159 = 46.9

Coefficient: b11, ŷ6, second-order modelp. 675

Book 43.81Data 43.84

The fit gives 43.84 (numpy agrees); the book's 43.81 is a slip (the other 82 coefficients and every significance mark agree, so the data are as printed)

Coefficient: b22, ŷ6, second-order modelp. 675

Book 113.3Data 111.3

The fit gives 111.34 (numpy agrees); 113.3 is likely a misprint of 111.3

Coefficient: b0, ŷ6, cubic model with blocksp. 677

Book 15.29Data 14.71

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 14.714

Coefficient: b1, ŷ6, cubic model with blocksp. 677

Book -0.60Data 0.74

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 0.737

Coefficient: b2, ŷ6, cubic model with blocksp. 677

Book -2.21Data -3.54

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives -3.545

Coefficient: b11, ŷ6, cubic model with blocksp. 677

Book 0.97Data 0.47

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 0.469

Coefficient: b22, ŷ6, cubic model with blocksp. 677

Book 5.28Data 4.78

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 4.781

Coefficient: b12, ŷ6, cubic model with blocksp. 677

Book 1.19Data 2.74

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 2.741

Coefficient: b111, ŷ6, cubic model with blocksp. 677

Book 0.29Data -0.45

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives -0.448

Coefficient: b222, ŷ6, cubic model with blocksp. 677

Book -3.93Data -3.19

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives -3.187

Coefficient: b112, ŷ6, cubic model with blocksp. 677

Book -1.63Data 0.83

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 0.825

Coefficient: b122, ŷ6, cubic model with blocksp. 677

Book -0.10Data -2.56

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives -2.556

Coefficient: a1, ŷ6, cubic model with blocksp. 677

Book 0.93Data 2.07

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 2.071

Coefficient: a2, ŷ6, cubic model with blocksp. 677

Book -0.07Data 1.07

Table E7.28 prints y6 = 20.0 for run 2; the book's y6 answer is the fit with 28.0 (numpy: one change of +8.0 at run 2 reproduces all twelve printed y6 coefficients to 0.006); with 20.0 the fit gives 1.071

Lack of fit f: first-order model with blocks, y6, marked bp. 678

Book 110.8Data 119.2

With run 2's y6 at 28.0 numpy gives F = 110.79, as printed; with the 20.0 of Table E7.28, F = 119.2

Lack of fit f: second-order model with blocks, y6, marked bp. 678

Book 21.4Data 36.8

With run 2's y6 at 28.0 numpy gives F = 21.42, as printed; with the 20.0 of Table E7.28, F = 36.8

Lack of fit f: third-order model with blocks, y6p. 678

Book 5.3Data 9.7

With run 2's y6 at 28.0 numpy gives F = 5.29, as printed; with the 20.0 of Table E7.28, F = 9.69

Lack of fit f: third-order model with blocks, y6p. 678

Book > 0.05Data 0.0235466

With the 20.0 of Table E7.28 the third-order lack of fit is significant (p = 0.024); with run 2's y6 at 28.0, F = 5.29 is not, as the book marks it

Ms residual: y2: s2^2p. 679

Book 0.0049Data 0.0048

S2^2 = 0.04797/10 = 0.0048, as the book's own rows give, (0.026 + 0.022)/10; it prints 0.0049

Coefficient: x1:x3p. 679

Book -0.1112Data -0.0471

The x1x3 coefficient of ln y is -0.0471; the book repeats the x1x2 coefficient -0.1112, and its own stationary point (0.693, 0.404, 0.472) needs -0.0471 and -0.0161

Coefficient: x2:x3p. 679

Book -0.1112Data -0.0161

The x2x3 coefficient of ln y is -0.0161; the book repeats the x1x2 coefficient -0.1112, and its own stationary point (0.693, 0.404, 0.472) needs -0.0471 and -0.0161

Std error: b12, b13, b23, s from pure errorp. 680

Book 0.301Data 0.395

With the pure-error s = 1.118 the se is 1.118/8^1/2 = 0.395; the book's 0.301 is 1.273 x 1.118/4.723, but 1.273 comes from the 6 df residual of the plane plus interactions (s = 3.601), not from s = 4.723 (which gives 1.670)

Mean: y-bar_0, the 5 centre runsp. 680

Book 28.2Data 28.5

The five centre runs (29.0, 28.5, 30.0, 27.0, 28.0) average 28.5, as the answer's pure error 5.00 and intercept 29.731 require; the book prints 28.2

Curvature: c = y-bar_f - y-bar_0p. 680

Book 2.3Data 2.0

C = 30.5 - 28.5 = 2.0; the book's 2.3 uses its misprinted centre average 28.2

T value: c over its standard errorp. 680

Book 3.61Data 3.14

C/se = 2.0/0.637 = 3.14; the book's 3.61 is 2.3/0.637, from its misprinted centre average 28.2

Ss total: correctedp. 681

Book 4760.11Data 4750.11

The total corrected SS is 4750.105: the printed rows add to 4750.11, and the answer's 62% needs it; 4760.11 is a misprint

Ss residualp. 682

Book 0.2888915Data 0.2889150

Book misprint: the table's total 9.404509 less its other rows (6.572814, 1.688804, 0.853976) is 0.288915, as the fit gives; the printed 0.2888915 has an extra digit.

Stationary point: (c) x2p. 683

Book 0.515Data 51.500

Book slip: the exercise (p. 367) prints 206x1; the answer's centre (0.2125, 0.515) and ŷS = 75.43775 are those of 2.06x1 (x2S = 2.06/4, ŷS = 75 + 0.43775). With 206x1 as printed the library gives 51.5.

Stationary point: (c) predictedp. 683

Book 75.43775Data 118.77500

Book slip: the exercise (p. 367) prints 206x1; the answer's centre (0.2125, 0.515) and ŷS = 75.43775 are those of 2.06x1 (x2S = 2.06/4, ŷS = 75 + 0.43775). With 206x1 as printed the library gives 118.775.

Coefficient: Y1: b1p. 684

Book 15.493Data 16.494

Book misprint: the fit gives 16.4936, and the answer's own SS(bi) = 9,476.2 needs b1 = 16.49; the printed 15.493 has a wrong first digit.

Coefficient: Y3: b2p. 684

Book 31.4Data -31.4

Book sign error: the fit gives -31.3964, and the answer's own xS = (14.85, -2.17, -18.72) needs b2 = -31.4.

Lack of fit ss: Y3, 5 dfp. 684

Book 1,442.7Data 1422.7

Book misprint: the fit gives 1422.68; with 1,422.7 the four rows sum to the printed total 228,175.0, with the printed 1,442.7 to 228,195.0.

Stationary point: problem 3: x1p. 684

Book 0.901Data 0.910

Book misprint: -½B⁻¹b = (0.9103, 0.7410) for problem 3; the printed 0.901 transposes the digits of 0.910.

Eigenvalue: λ1p. 689

Book -5.520Data -5.521

Book slip: the reduced equation as printed (and the fit) gives eigenvalues -5.5211 and -14.9501, which sum to the trace b11 + b22 = -20.4712; the printed -5.520 and -14.948 sum to -20.468.

Eigenvalue: λ2p. 689

Book -14.948Data -14.950

Book slip: the reduced equation as printed (and the fit) gives eigenvalues -5.5211 and -14.9501, which sum to the trace b11 + b22 = -20.4712; the printed -5.520 and -14.948 sum to -20.468.

Eigenvector: m3, x2p. 691

Book 0.357Data 0.359

Book slip: the fit and the printed equation both give 0.358737 (0.359); the answer prints 0.357.

Eigenvector: m3, x3p. 697

Book -0.3421Data -0.3214

Book misprint: the equation as printed gives -0.321376; the printed -0.3421 transposes the digits of -0.3214 (the column then has unit length).

Lack of fit ss: y1: lofp. 698

Book 4.27Data 3.87

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 3.86976.

Lack of fit df: y1: lofp. 698

Book 15Data 14

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 14.

Lack of fit ms: y1: lofp. 698

Book 0.285Data 0.276

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 0.276411.

Lack of fit f: y1: lofp. 698

Book 2.12Data 1.54

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 1.5368.

Pure error ss: y1: pep. 698

Book 0.67Data 1.08

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 1.07917.

Pure error df: y1: pep. 698

Book 5Data 6

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 6.

Pure error ms: y1: pep. 698

Book 0.134Data 0.180

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. Without them y1's pure error is 0.674 (the printed 0.67); with them 0.179861.

Ratio: y1: (ŷmax - ŷmin)/(ps²/n)^1/2p. 698

Book 22.84Data 22.06

The book takes p = 14, (9.61 - 2.43)/{14(0.247)/35}^1/2 = 22.84; the second-order model in four factors has 15 coefficients (35 runs less the 20 residual df), and with p = 15 the fit gives 22.06

Stationary point: y1: x1p. 698

Book -1.43Data -1.38

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found -1.37829.

Stationary point: y1: x2p. 698

Book 2.67Data 3.24

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found 3.24354.

Stationary point: y1: x3p. 698

Book 0.60Data 6.51

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found 6.51115.

Stationary point: y1: x4p. 698

Book 2.40Data 1.59

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found 1.59454.

Stationary point: y1: predictedp. 698

Book 9.55Data 10.22

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found 10.2184.

Eigenvalue: y1: λ2p. 698

Book -0.19Data -0.07

Book slip: the printed canonical form does not come from the answer's own B (its λ's sum to -0.68, the printed B's trace is -0.512); the fit, whose B agrees with the printed one, gives xS = (-1.378, 3.244, 6.511, 1.595), ŷS = 10.218 and λ = (-0.401, -0.068, -0.025, -0.016). Found -0.0683511.

Lack of fit ss: y2, with run 16: lofp. 699

Book 189.34Data 188.97

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 188.969.

Lack of fit df: y2, with run 16: lofp. 699

Book 15Data 14

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 14.

Lack of fit ms: y2, with run 16: lofp. 699

Book 12.623Data 13.498

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 13.4978.

Lack of fit f: y2, with run 16: lofp. 699

Book 51.73Data 50.78

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 50.7753.

Pure error ss: y2, with run 16: pep. 699

Book 1.22Data 1.59

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 1.595.

Pure error df: y2, with run 16: pep. 699

Book 5Data 6

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 6.

Pure error ms: y2, with run 16: pep. 699

Book 0.244Data 0.266

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 0.265833.

Lack of fit ss: y2, without run 16: lofp. 699

Book 15.54Data 15.16

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 15.1649.

Lack of fit df: y2, without run 16: lofp. 699

Book 14Data 13

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 13.

Lack of fit ms: y2, without run 16: lofp. 699

Book 1.110Data 1.167

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 1.16653.

Lack of fit f: y2, without run 16: lofp. 699

Book 4.55Data 4.39

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 4.38821.

Pure error ss: y2, without run 16: pep. 699

Book 1.22Data 1.59

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 1.595.

Pure error df: y2, without run 16: pep. 699

Book 5Data 6

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 6.

Pure error ms: y2, without run 16: pep. 699

Book 0.244Data 0.266

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. y2's printed 1.22 matches neither 1.19 without them nor 1.595 with them; found 0.265833.

Lack of fit df: y3: lofp. 700

Book 15Data 14

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. For y3 the printed 0.060 is the 6-df value (0.04 without runs 33 and 34), set against 5 df; found 14.

Lack of fit ms: y3: lofp. 700

Book 0.0528Data 0.0566

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. For y3 the printed 0.060 is the 6-df value (0.04 without runs 33 and 34), set against 5 df; found 0.0565858.

Lack of fit f: y3: lofp. 700

Book 4.40Data 5.66

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. For y3 the printed 0.060 is the 6-df value (0.04 without runs 33 and 34), set against 5 df; found 5.65858.

Pure error df: y3: pep. 700

Book 5Data 6

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. For y3 the printed 0.060 is the 6-df value (0.04 without runs 33 and 34), set against 5 df; found 6.

Pure error ms: y3: pep. 700

Book 0.017Data 0.010

Book slip: the answer's pure error has 5 df, leaving out runs 33 and 34, which Table E11.17 prints at the same settings (1.3, -1, 2, 2); with them the library takes 6 df. The printed MS 0.017 is a misprint for 0.012 = 0.060/5, the value its F of 4.40 uses; the library gives 0.060/6 = 0.01.

Stationary point: predictedp. 700

Book 8.20Data 1.80

Book slip: the answer's own printed equation and xS give ŷS = b0 + ½xS'b = 1.79906 (the fit 1.80); the printed 8.20 does not follow.

Eigenvalue: λ4p. 702

Book 0.00000Data -0.00786

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.00785805.

Eigenvalue: λ5p. 702

Book -0.02069Data -0.01282

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.0128243.

Eigenvector: m2, x5p. 702

Book 0.12784Data -0.12780

Book sign error: with the other four elements of row 2 as printed, the authors' equation gives -0.127802.

Eigenvector: m4, x1p. 702

Book 0.53409Data 0.68581

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.685806.

Eigenvector: m4, x2p. 702

Book -0.11307Data 0.08723

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.0872308.

Eigenvector: m4, x3p. 702

Book 0.07621Data -0.48047

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.48047.

Eigenvector: m4, x4p. 702

Book 0.20054Data -0.08525

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.0852509.

Eigenvector: m4, x5p. 702

Book 0.80990Data 0.53286

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.532862.

Eigenvector: m5, x1p. 702

Book 0.24178Data -0.07659

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.0765853.

Eigenvector: m5, x2p. 702

Book -0.19807Data -0.27736

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found -0.277357.

Eigenvector: m5, x3p. 702

Book 0.12837Data 0.43154

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.431538.

Eigenvector: m5, x4p. 702

Book 0.52994Data 0.58210

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.582105.

Eigenvector: m5, x5p. 702

Book 0.77464Data 0.62621

Klein and Marshall's reduction as the book reprints it is wrong in its last two axes: the authors' equation gives the eigenvalues -0.13168, -0.11121, 0.01996, -0.01282 and -0.00786 (the last two sum to the printed -0.02069, but are not 0 and -0.02069), and the printed rows 4 and 5 of M' are not orthogonal (their product is 0.89). Found 0.626209.

Stationary point: ŷ in the plane X̃1 = X̃2 = X̃5 = 0p. 702

Book 1.5029Data 1.0529

Book misprint: the constant is ŷS, printed two lines above as 1.0529 (the authors' equation gives 1.0529); 1.5029 transposes its digits.

Lack of fit msp. 703

Book 363Data 366

Book misprint: 2,198/6 = 366.3 and the fit gives 366.417; the table prints 363.

Lack of fit fp. 703

Book 8.07Data 8.06

Follows the misprinted mean square: 363/45 = 8.07; the fit gives 366.42/45.47 = 8.05902.

Stationary point: yield: predictedp. 703

Book -85.25Data 97.45

Book slip: the exercise's yield equation gives ŷS = b0 + ½XS'b = 97.4536 at the printed XS (1.15, 1.10, 1.11, 0.49, 0.68), with the printed eigenvalues; the answer prints -85.25.

Canonical: yield: constant of X̃1p. 703

Book 0.09Data 1.88

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 1.8803.

Canonical: yield: constant of X̃2p. 703

Book 1.38Data -0.29

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is -0.286862.

Eigenvector: yield: m3, X5p. 703

Book 0.53Data 0.57

Book misprint: the yield equation gives 0.567288, which rounds to 0.57; the matrix prints 0.53.

Canonical: yield: constant of X̃3p. 703

Book 0.71Data -0.18

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is -0.183732.

Canonical: yield: constant of X̃4p. 703

Book 0.68Data -0.50

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is -0.502585.

Canonical: yield: constant of X̃5p. 703

Book -1.25Data 0.75

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 0.751074.

Extra ms: first orderp. 704

Book 186.46Data 186.48

Book slip: 559.43/3 = 186.48, and the fit gives 186.477; the answer prints 186.46.

Stationary point: purity: predictedp. 704

Book 68.97Data 68.07

Book slip: the exercise's purity equation gives ŷS = 68.0697 at the printed XS, with the printed eigenvalues; the answer prints 68.97.

Canonical: purity: constant of X̃1p. 704

Book -1.03Data 1.93

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 1.93096.

Canonical: purity: constant of X̃2p. 704

Book 1.24Data 0.05

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 0.0474314.

Canonical: purity: constant of X̃3p. 704

Book 0.63Data -1.02

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is -1.02209.

Canonical: purity: constant of X̃4p. 704

Book 0.78Data 0.55

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 0.549163.

Canonical: purity: constant of X̃5p. 704

Book 1.72Data 1.22

Book slip: the printed matrix holds the eigenvectors as its columns (checked element by element) but X̃ = (matrix)X + c applies it by rows, and the printed constants are -(matrix)XS row-wise (numpy: yield 0.10, 1.38, 0.71, 0.68, -1.21; purity -1.04, 1.24, 0.63, 0.77, 1.72); -mi'XS with the columns is 1.22065.

Stationary point: Calciump. 706

Book 0.777619Data 0.787500

Book slip: the answer's own printed equation (and the fit) gives xS = (0.7875, -0.1423) and ŷS = 9.135, with the printed eigenvalues; found 0.7875.

Stationary point: Phosphorusp. 706

Book -0.144422Data -0.142343

Book slip: the answer's own printed equation (and the fit) gives xS = (0.7875, -0.1423) and ŷS = 9.135, with the printed eigenvalues; found -0.142343.

Stationary point: predictedp. 706

Book 9.268Data 9.135

Book slip: the answer's own printed equation (and the fit) gives xS = (0.7875, -0.1423) and ŷS = 9.135, with the printed eigenvalues; found 9.13533.

Stationary point: Calcium, actualp. 706

Book 47Data 5

Book misprint: 3.75 + 1.25x1S = 4.73437 from the fit (4.72 from the answer's own x1S); the printed 47 has lost its decimal point.

Coefficient: quadratic: Interceptp. 706

Book -307.73Data -165.07

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives -165.068 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: quadratic: x1p. 706

Book 126.38Data 59.86

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives 59.8592 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: quadratic: x2p. 706

Book 98.847Data 61.732

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives 61.732 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: cubic: Interceptp. 706

Book -165.07Data -307.73

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives -307.732 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: cubic: x1p. 706

Book 59.859Data 126.376

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives 126.376 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: cubic: x2p. 706

Book 61.732Data 98.847

Book slip: the intercept and linear coefficients of the two printed equations are interchanged; the fit gives 98.8468 here, the value printed in the other equation (quadratic -165.07, 59.859, 61.732; cubic -307.73, 126.38, 98.847).

Coefficient: cubic: x2²p. 706

Book -6.533Data -6.347

Book slip: the cubic's x2² coefficient is -6.34733; the printed -6.533 is the quadratic's.

Coefficient: cubic: x1²x2p. 706

Book -0.4188Data 0.2998

Book slip: the printed third-order coefficients are rotated: the fit gives x1²x2 0.2998, x1x2² 1.3508 and x2³ -0.4188, printed as -0.4188, 0.2998 and 1.3508; found 0.299807.

Coefficient: cubic: x1x2²p. 706

Book 0.2998Data 1.3509

Book slip: the printed third-order coefficients are rotated: the fit gives x1²x2 0.2998, x1x2² 1.3508 and x2³ -0.4188, printed as -0.4188, 0.2998 and 1.3508; found 1.35085.

Coefficient: cubic: x2³p. 706

Book 1.3508Data -0.4188

Book slip: the printed third-order coefficients are rotated: the fit gives x1²x2 0.2998, x1x2² 1.3508 and x2³ -0.4188, printed as -0.4188, 0.2998 and 1.3508; found -0.418795.

Extra ms: cubic: first order|b0p. 707

Book 779.5Data 729.3

Book misprint: 1,459/2 = 729.5, and the fit gives 729.283; the table prints 779.5.

Extra f: cubic: first order|b0p. 707

Book 17.6Data 16.4

Follows the misprinted mean square: 779.5/44.4 = 17.6; the fit gives 729.28/44.39 = 16.4304.

Classification: y1p. 707

Book maximumData saddle_point

Book slip: Table E11.25c's y1 coefficients give B with eigenvalues -0.298 and +0.029 (det < 0), a saddle centred at (8.2, 10.7), outside the region; the library says saddle_point, not a maximum.

Classification: y4p. 707

Book minimumData saddle_point

Book slip: Table E11.25c's y4 coefficients give B with eigenvalues -0.017 and +0.067 (det < 0), a saddle centred at (2.79, 3.35), outside the region; the library says saddle_point, not a minimum.

Canonical: model III: eigenvalue 1 of Bp. 710

Book -0.544Data -0.545

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the eigenvalues are -0.5443 and -0.1887

Canonical: model III: eigenvalue 2 of Bp. 710

Book -0.189Data -0.188

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the eigenvalues are -0.5443 and -0.1887

Stationary point: model III: N^1/2p. 710

Book 19.9624Data 20.0761

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the stationary point is (19.9624, 18.3725) exactly

Stationary point: model III: P^1/2p. 710

Book 18.3725Data 18.4696

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the stationary point is (19.9624, 18.3725) exactly

Stationary point: model III: Np. 710

Book 398Data 403

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the stationary point has N = 19.9624^2 = 398.5

Stationary point: model III: Pp. 710

Book 338Data 341

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the stationary point has P = 18.3725^2 = 337.55

Stationary point: model III: y-hat at the maximump. 710

Book 147.3Data 148.1

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the maximum is 147.30

Ridge path: model III: lambda where the path leaves the regionp. 710

Book 0.0207Data 0.0217

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the multiplier on the sphere N + P = 599 is 0.02063, and Eq. (12.2.8) at lambda = 0.0207 puts the path at (N, P) = (319.9, 278.7)

Ridge path: model III: y-hat where the path leaves the regionp. 710

Book 145.95Data 146.59

The answer's model III numbers follow b12 = 0.3410 for N^1/2 P^1/2, not the exercise's printed 0.34310 (solving 2Bx = -b at the printed stationary point gives b12/2 = 0.17050 and 0.17051 from its two rows); with 0.3410 the maximum on the sphere N + P = 599 is 145.96, and Eq. (12.2.8) at lambda = 0.0207 gives 145.95

Ridge path: lambda = 100: x6p. 710

Book -0.233Data -0.223

Eq. (12.2.8) at lambda = 100 gives x6 = -0.2226 (the library on the printed sphere -0.2225); the printed -0.233 is a misprint of -0.223

Ridge path: full quadratic, lambda = 0.57: x1p. 712

Book 0.979Data 0.978

The row's R, 0.979, is the radius of (0.977, -0.051, -0.011); Eq. (12.2.8) at lambda = 0.57 gives x1 = 0.977 and the library on the printed sphere 0.9776: the printed 0.979 is a misprint of 0.977

Ridge path: path 4, lambda = -100: x2p. 713

Book 0.001Data -0.001

Eq. (12.2.8) at lambda = -100 gives (-0.0005, -0.0010), and the library on the sphere R = 0.001 gives x2 = -0.0009: x2 is -0.001, the printed minus sign missing

Ridge path: y2, lambda = 0: x2p. 714

Book 0.261Data 0.260

The stationary point of the y2 surface is (-0.574, 0.260), as Table 11.25d prints it; the printed 0.261 is one unit high

Ridge path: y3, lambda = -0.3: lambdap. 714

Book -0.3Data -0.0

The row's point lies on the path at lambda = -0.030 (a maximum path needs lambda above the largest eigenvalue, -0.0787); the printed -0.3 is a misprint of -0.03

Ridge path: y3, lambda = -0.4: lambdap. 714

Book -0.4Data -0.0

The row's point lies on the path at lambda = -0.040 (a maximum path needs lambda above the largest eigenvalue, -0.0787); the printed -0.4 is a misprint of -0.04

Ridge path: lambda = 50: lambdap. 714

Book 50Data 80

The row's point (1.719, -1.356, 0.171), R = 2.196, y-hat = 975 lies on the path at lambda = 80.0; at lambda = 50 Eq. (12.2.8) puts the path at R = 5.906: the printed 50 is a misprint of 80

Ridge path: lambda = -0.1: x1p. 715

Book -0.767Data -0.770

The row's R, 0.829, is the radius of (-0.770, -0.051, -0.303), and Eq. (12.2.8) at lambda = -0.1 gives x1 = -0.770; the printed -0.767 is a misprint of -0.770

Coefficient: B-form b, x1p. 719

Book -6.902Data -6.906

B1 is -6.90625 (the fitted equation prints -6.9062); the printed -6.902 is a misprint of -6.906

Coefficient: B[1,1]p. 719

Book 0.285Data -0.285

B11 is -0.2847 (the fitted equation prints -0.285); the minus sign of B[1,1] is missing

Canonical: eigenvalue 1 of Bp. 719

Book -3.64Data -3.55

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Canonical: eigenvalue 2 of Bp. 719

Book -0.66Data -0.56

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Canonical: eigenvalue 3 of Bp. 719

Book 3.14Data 3.48

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 10: x1p. 720

Book -0.44Data -0.43

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 10: x2p. 720

Book -0.03Data -0.02

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 10: x3p. 720

Book 0.41Data 0.42

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 6: x1p. 720

Book -0.99Data -0.95

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 6: x2p. 720

Book -0.07Data -0.06

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 6: x3p. 720

Book 1.04Data 1.06

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 6: y-hatp. 720

Book 49.8Data 50.2

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.5: x1p. 720

Book -1.18Data -1.14

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.5: x2p. 720

Book -0.08Data -0.07

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.5: x3p. 720

Book 1.27Data 1.31

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.5: y-hatp. 720

Book 55.3Data 56.2

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.5: lambdap. 720

Book 5.5Data 5.8

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.4: x1p. 720

Book -1.23Data -1.19

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.4: x2p. 720

Book -0.08Data -0.07

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.4: x3p. 720

Book 1.33Data 1.38

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.4: y-hatp. 720

Book 56.7Data 57.8

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.4: lambdap. 720

Book 5.4Data 5.7

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.3: x1p. 720

Book -1.29Data -1.24

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.3: x2p. 720

Book -0.09Data -0.07

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.3: x3p. 720

Book 1.39Data 1.44

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.3: y-hatp. 720

Book 58.4Data 59.5

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.3: lambdap. 720

Book 5.3Data 5.6

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.19: x1p. 720

Book -1.35Data -1.30

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.19: x2p. 720

Book -0.09Data -0.08

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.19: x3p. 720

Book 1.47Data 1.52

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.19: y-hatp. 720

Book 60.5Data 61.6

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Ridge path: lambda = 5.19: lambdap. 720

Book 5.19Data 5.50

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Optimum: optimum response on or in a sphere of radius 2p. 720

Book 60.5Data 61.6

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Optimum: its coded point: x1p. 720

Book -1.35Data -1.30

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Optimum: its coded point: x2p. 720

Book -0.09Data -0.08

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Optimum: its coded point: x3p. 720

Book 1.47Data 1.52

The answer's eigenvalues and ridge table follow a surface with b33 about 1.17 in place of the fitted b33 = 1.690 it prints (b33 = 1.17 gives eigenvalues -3.638, -0.656, 3.143 and the table's points to within a unit in the last digit); the printed surface, which the data reproduce, has eigenvalues -3.550, -0.561, 3.481 and on the sphere R = 2 its maximum is 61.64 at (-1.296, -0.075, 1.521), lambda = 5.50

Coefficient: y1: B[1,3]p. 720

Book 4.1935Data 4.1937

B13/2 = 8.3875/2 = 4.19375; the printed 4.1935 drops the digit 7

Coefficient: y1: B[2,3]p. 720

Book 9.2685Data 9.2688

B23/2 = 18.5375/2 = 9.26875; the printed 9.2685 drops the digit 7

R squared: y1p. 720

Book 0.910Data 0.900

The R^2 of the two responses are swapped: the fit of y1 gives 0.900 and that of y2 0.910

Ridge path: y1, lambda = -10.5: lambdap. 720

Book -10.5Data -10.1

The row's point lies on the path at lambda = -10.05 (the rows run -10.1, -10.05, -10.01, -10 as R grows); the printed -10.5, here and in the text, is a misprint of -10.05

Coefficient: y2: b, x2p. 721

Book -6.984Data -6.948

The fit gives b2 = -6.948, and Table E12.11c follows -6.948; the printed -6.984 transposes two digits

R squared: y2p. 721

Book 0.900Data 0.910

The R^2 of the two responses are swapped: the fit of y2 gives 0.910 and that of y1 0.900

Lack of fit msp. 722

Book 51,851Data 10370

The printed mean square is the sum of squares undivided by its 5 df; 51,850.5/5 = 10,370.1

Lack of fit fp. 722

Book 2.72Data 2.18

The printed F is 51,851/19,067, the sums of squares undivided by their df; with the mean squares, 10,370.1/4,766.7 = 2.18 on 5 and 4 df

Pure error msp. 722

Book 19,067Data 4767

The printed mean square is the sum of squares undivided by its 4 df; 19,066.7/4 = 4,766.7

Coefficient: x1x3p. 731

Book −4Data 4

Table E16.5's y = 7 at (0.5, 0, 0.5) gives b13 = 4(7) - 2(6 + 6) = +4; the printed -4 has the wrong sign

Prediction: ŷ at the centroid (1/3, 1/3, 1/3)p. 731

Book 7.11Data 8.00

With b13 = +4 the centroid prediction is 8 + (-4 + 4 + 0)/9 = 8; the printed 8 - 8/9 = 7.11 carries the sign slip in b13

Coefficient: x1x2(x1 − x2)p. 731

Book −54Data -6.69182e-15

The exact fit gives 0 for x1x2(x1 - x2); with the printed -54 the equation predicts 3 and 13 at (2/3, 1/3, 0) and (1/3, 2/3, 0), where Table E16.6 has 7 and 9

Pseudocomponents: run 6: water, alcohol, ureap. 733

Row 6 of Table E17.5a prints the percentages 0, 3, 3 instead of the pseudocomponents 0, 0.5, 0.5

Coefficient: E19.1c: x4p. 736

Book 3.67Data 3.66

The fit of Eq. (E19.1c) gives 3.6633, which rounds to 3.66; the book's 3.67 is the x4 coefficient of Eq. (E19.1a), 3.6656, carried over

Ridge path predicted response: second table of Exercise 19.7, (b) Path of minimum response, λ = −∞: ŷp. 742

Book 20.69Data 21.08

The refitted model predicts 21.08 at the centroid; the book repeats 20.69, the full model's value, from the first table, and the second table's other rows agree with the refitted model