Sales and profits. A business analyst was interested in the relationship between a company’s sales and its profits. She collected data (in millions of dollars) from a random sample of Fortune 500 companies and created the regression analysis and summary statistics shown.

The assumptions for regression inference appeared to be satisfied.

Profits Sales Dependent variable is Profits Count 79 79 R-squared = 66.2% s = 466.2 Mean 209.839 4178.29 Variable Coefficient SE(Coeff)
Variance 635,172 49,163,000 Intercept -176.644 61.16 Std Dev 796.977 7011.63 Sales 0.092498 0.0075

a) Is there a statistically significant association between sales and profits? Test an appropriate hypothesis and state your conclusion in context.

b) Do you think that a company’s sales serve as a useful predictor of its profits? Use the values of both R2 and s in your explanation.