# sol4 - Stat 201A HW4 Solution 1(a The defining relation is...

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Stat 201A HW4 Solution 1. (a) The deﬁning relation is I=ABCD and the resolution is IV. The alias structure is A = BCD, B = ACD, C = ABD, D = ABC, E = ABCDE, AB = CD, AC = BD, AD = BC, AE = BCDE, BE = ACDE, CE = ABDE, DE = ABCE, ABE = CDE, ACE = BDE, ADE = BCE. (b) We can include one efect in each alias set. A halF-normal plot suggests that A, B, E, BE are signiﬁcant and D is marginal. The regression summary is lm(formula = height ~ (A + B + C + D + A:B + A:C + A:D) * E, data = dat2) Estimate Std. Error t value Pr(>|t|) (Intercept) 7.625625 0.020205 377.411 < 2e-16 *** A 0.121042 0.020205 5.991 1.12e-06 *** B -0.081875 0.020205 -4.052 0.000302 *** C -0.024792 0.020205 -1.227 0.228774 D 0.045625 0.020205 2.258 0.030893 * E -0.119375 0.020205 -5.908 1.42e-06 *** A:B -0.014792 0.020205 -0.732 0.469451 A:C 0.000625 0.020205 0.031 0.975515 A:D -0.011458 0.020205 -0.567 0.574603 A:E 0.031875 0.020205 1.578 0.124500 B:E 0.076458 0.020205 3.784 0.000640 *** C:E -0.016458 0.020205 -0.815 0.421343 D:E 0.019792 0.020205 0.980 0.334662 A:B:E 0.001042 0.020205 0.052 0.959204 A:C:E 0.009792 0.020205 0.485 0.631251 A:D:E -0.029792 0.020205 -1.474 0.150128 Residual standard error: 0.14 on 32 degrees of freedom Multiple R-Squared: 0.7831,Adjusted R-squared: 0.6814 The p-values conﬁrms that A, B, E, BE are very signiﬁcant and D is signiﬁcant at 5% level but not 1% level. ±rom (a), we know none oF these efects is aliased with other main efects or two-Factor interactions, so we conclude that A, B, E and possibly D inﬂuence the mean Free height. (c) There is nothing unusual about the residuals plots.

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## This note was uploaded on 11/24/2010 for the course STAT 201a taught by Professor Wu during the Spring '10 term at Pasadena City College.

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sol4 - Stat 201A HW4 Solution 1(a The defining relation is...

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