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 represents 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 65

a. Set up the design matrix.

b. Run the analysis of covariance.