Can demographic information be helpful in predicting sales at sporting goods stores? The file contains the monthly sales totals from a random sample of 38 stores in a large chain of nationwide sporting goods stores. All stores in the franchise, and thus within the sample, are approximately the same size and carry the same merchandise. The county or, in some cases, counties in which the store draws the majority of its customers is referred to here as the customer base. For each of the 38 stores, demographic information about the customer base is provided. The data are real, but the name of the franchise is not used, at the request of the company. The data set contains the following variables:
Sales-Latest one-month sales total (dollars)
Age-Median age of customer base (years)
HS-Percentage of customer base with a high school diploma
College-Percentage of customer base with a college diploma
Growth-Annual population growth rate of customer base over the past 10 years
Income-Median family income of customer base (dollars)
a. Construct a scatter plot, using sales as the dependent variable and median family income as the independent variable. Discuss the scatter plot.
b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
c. Interpret the meaning of the Y intercept, b0, and the slope, , in this problem.
d. Compute the coefficient of determination, r2, and interpret its meaning.
e. Perform a residual analysis on your results and determine the adequacy of the fit of the model.
f. At the 0.05 level of significance, is there evidence of a linear relationship between the independent variable and the dependent variable?
g. Construct a 95% confidence interval estimate of the population slope and interpret its meaning.