Refer to the analysis of covariance model ????i = ????0 + ????1xi1 + ????2xi2 for quantitative x1 and binary x2 for two groups, with xi2 = 0 for group 1 and xi2 = 1 for group 2. Denote the sample means on x1 and y by (x̄

(1)

1 , ȳ(1)) for group 1 and

(x̄

(2)

1 , ȳ(2)) for group 2. Show that the least squares fit corresponds to parallel lines for the two groups, which pass through these points. (At the overall x̄1, the fitted values ????̂

0 + ????̂

1x̄1 and ????̂

0 + ????̂

1x̄1 + ????̂

2 are called adjusted means of y.)