Consider the Sherwin-Williams Company example (see Table). Suppose one is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable.
a. Determine the estimated regression line.
b. Give an economic interpretation of the estimated intercept (a) and slope (b) coefficients.
c. Test the hypothesis (at the .05 level of significance) that there is no relationship (that is, β = 0) between the variables.
d. Calculate the coefficient of determination.
e. Perform an analysis of variance on the regression, including an F-test of the overall significance of the results (at the .05 level).
f. Based on the regression model, determine the best estimate of paint sales in a sales region where the selling price is $14.50. Construct an approximate 95 percent prediction interval.
g. Determine the price elasticity of demand at a selling price of$14.50.

SHERWIN-WILLIAMS COMPANY DATA SALES REGION GALLONS) SALES (Y) (x 1,000 PROMOTIONAL EXPENDITURES (A) (x$1,000) DISPOSABLE INCOME (M) (x $1,000) SELLING PRICE (P) (S/GALLON) 15.00 13.50 16.50 14.50 17.00 16.00 13.00 18.00 12.00 15.50 160 220 140 190 130 160 200 150 210 190 150 160 50 190 90 19.0 175 14.0 21.0 15.5 14.5 21.5 18.0 18.5 140 110 200 100 10