For the house data in Table 4.1, the average selling price is ̄y = 447.0. Imagine that you do not know the size of any house, so you predict the selling price of each of them to be 447.0. This is equivalent to using the line y = ̄y for prediction.

a. Compute the residual for each point using the line y = ̄y.

b. Compute the sum of squared residuals for the line y = ̄y.

c. Compute the residual for each point using the least-squares regression line.

d. Compute the sum of squared residuals for the least-squares regression line.

e. Determine how much better the least-squares predictions are by computing the difference Decrease in sum of squared residuals

f. Compute the ratio

g. Show that the ratio obtained in part

(f) is equal to the coefficient of determination.

= (Sum of squared residuals for y = y) -(Sum of squared residuals for regression line)