# Regression Analysis

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Can demographic information be helpful in predicting sales at sporting goods stores? The data at left are 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 variables in the data set are:

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, b1, in this problem.

d. Compute the coefficient of determination r2, and interpret its meaning.

e. Construct a 95% confidence interval estimate of the population slope and interpret its meaning.

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The solution provides a detailed Regression Analysis performed in EXCEL and provides students with a clear perspective of the underlying statistical aspects.

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