Question

Exercise 13-17 A recent article in BusinessWeek 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. Company Sales ($ millions) Earnings ($ millions) Company Sales ($ millions) Earnings ($ millions) Papa John's International $ 86.9 $ 4.7 Checkmate Electronics $ 17.0 $ 4.6 Applied Innovation 19.8 4.4 Royal Grip 12.7 1.7 Integracare 15.9 1.4 M-Wave 15.6 3.7 Wall Data 72.5 8.0 Serving-N-Slide 51.3 8.3 Davidson & Associates 57.0 6.5 Daig 25.2 5.8 Chico's FAS 46.0 4.3 Cobra Golf 66.1 12.1 Click here for the Excel Data File Let sales be the independent variable and earnings be the dependent variable.

(a) Compute the correlation coefficient. (Round your answer to 3 decimal places.) Coefficient of correlation

(b) Compute the coefficient of determination. (Round your answer to 3 decimal places.) Coefficient of determination

(c) Determine the regression equation. (Round your answers to 4 decimal places.) The regression equation, with the coefficients, is Y ˆ Y^ = + X (d) For a small company with $70 million in sales, estimate the earnings. (Round your answer to 4 decimal places.) Estimated earnings $ millions

Answer 1

Calculated Data from the given data 3x = 486 2y- 65.5 Ex2 27147.3 2y2-454.83 2xy- 3195.38 n 12 a) We knowthat coefficient of correlation r- 12.27 1473-4868-12-46583-6ssi:0.6367 12 3195.38-486 12.27 473-48612-454 83-6552 r 0.6367 b) Coefficient of determination, r2- 0.43212 0.4054 c) Regression Equation is Y-2.5141+0.0727X d) When the company has $70 million in sales then the earnings will be Y-2.5141+0.0727(70) Y 7.6031 The estimated earnings is $7.6031 millions

Sales (millions) X Earnings( milliions) Y X2 1 Company 2 Papa john's International 3 Checkmate Electronics 4 Applied Innovation 5 Royal Grip 6 Integracare 7 M-Wave 8 Wall Data 9 Serving-N-Slide 10 Davidson&Associates 11 Daig 12 Chico's FAS 13 Cobra Golf 14 15 16 17 18 19 20 21 Sum 22 Mean 23 24 YA2 86.9 17 19.8 12.7 15.9 15.6 72.5 51.3 57 25.2 4.7 7551.61 408.43 4.6 4.4 392.04 7 161.29 21.59 1.4 252.81 22.26 3.7 243.36 57.72 22.09 21.16 19.36 2.89 1.96 13.69 64 68.89 42.25 33.64 18.49 146.41 78.2 87.12 8 5256.25 8.3 2631.69 425.79 3249 370.5 5.8 635.04 146.16 197.8 12.1 4369.21 799.81 2116 4.3 (E21-(12 B22*C22))/(D21-(12*B22 B22)) 66.1 0.072697 2.514117 C22-(J16 B22) 486 65.5 27147.33195.38 454.83 40.5 5.458333333 Regression Equation is Y-2.514117+0.072697X

SUMMARY OUTPUT Regression Statistics Multiple F 0.636696 R Square 0.405382 Adjusted 0.345921 Standard 2.405447 Observati 12 ANOVA df MS F gnificance F Regressio Residual Total 1 39.44741 39.44741 6.817528 0.025994 10 57.86175 5.786175 11 97.30917 P-value Intercept2.514117 1.324262 1.898504 0.086836 -0.43652 5.4647570.43652 5.464757 X Variable 0.072697 0.027842 2.61104 0.025994 0.010661 0.134733 0.010661 0.134733 Coefficientan dard Err Lower 95%Upper 95%ower 95.09 pper 95.0% t Stat