16.14 If you have access to SAS, use that program to analyze the data in Exercise 16.7.
Add /SS1 SS2 SS3 SS4 to the end of your Model command and show that
a. Type I sums of squares adjust each term in the model only for those that come earlier in
the model statement.
b. Type II sums of squares adjust main effects only for other main effect variables, while
adjusting the interaction for each of the main effects.
c. Type III sums of squares adjust each term for all other terms in the model.
d. Type IV sums of squares in this case are equal to the Type II sums of squares.
16.15 In studying the energy consumption of families, we have broken them into three groups.
Group 1 consists of those who have enrolled in a time-of-day electrical-rate system (the
charge per kilowatt-hour of electricity is higher during peak demand times of the day). Group 2
is made up of those who inquired into such a system but did not use it, and Group 3 repre-
sents those who have shown no interest in the system. We record the amount of the electrical
bill per month for each household as our dependent variable (Y). As a covariate, we take the
electrical bill for that household for the same month last year (C). The data follow:
Group 1 Group 2 Group 3
YC Y C Y C
58 75 60 70 75 80
25 40 30 25 60 55
50 68 55 65 70 73
40 62 50 50 65 61
55 67 45 55 55 65a. Set up the design matrix.
b. Run the analysis of covariance.16.16 To refine the experiment described in Exercise 16.15, a psychologist added an additional set
of households to each group. This group had a special meter installed to show them exactly
how fast their electric bill was increasing. (The amount-to-date was displayed on the meter.)
The data follow; the nonmetered data are the same as those in Exercise 16.15.
YCYCY C
Nonmetered 58 75 60 70 75 80
25 40 30 25 60 55
50 68 55 65 70 73
40 62 50 50 65 61
55 67 45 55 55 65Metered 25 42 40 55 55 56
38 64 47 52 62 74
46 70 56 68 57 60
50 67 28 30 50 68
55 75 55 72 70 76a. Run the analysis of covariance on these data—after first checking the assumption of
homogeneity of regression.
b. Draw the appropriate conclusions.16.17 Compute the adjusted means for the data in Exercise 16.16.
Exercises 625