Consider the Sherwin-Williams Company example discussed in this chapter (see Table 4.1). 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 0.05 level of significance) that there is no relationship (i.e., 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 0.05 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.