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.