A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.
Sales Earnings Sales Earnings
Company ($ millions) ($ millions) Company ($ millions) ($millions)
Papa John's International $89.2 $4.9 Checkmate Electronics $17.5 $ 2.6
Applied Innovation 18.6 4.4 Royal Grip 11.9 1.7
Integracare 18.2 1.3 M-Wave 19.6 3.5
Wall Data 71.7 8.0 Serving-N-Slide 51.2 8.2
Davidson Associates 58.6 6.6 Daig 28.6 6.0
Chico's Fas 46.8 4.1 Cobra Golf 69.2 12.8
Let sales be the independent variable and earnings be the dependent variable. Each question must be answered in its entirety.
a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Interpret your findings in parts b and c.
e. Determine the regression equation.
f. For a small company with $50.0 million in sales, estimate the earnings
This solution draws out the scatter diagram for the question and then determines the coefficient of correlation and coefficient of determination. It also estimates the earnings for a small company. This solution is provided in both a Word file and an Excel file.