A recent article in BusinessWeek listed the “Best Small Companies.” We are inter

Question

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.

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 __________

(d) For a small company with $50 million in sales, estimate the earnings. (Round your answer to 4 decimal places.) Estimated earnings $ millions

Company Sales
($ millions) Earnings
($ millions) Company Sales
($ millions) Earnings
($ millions) Papa John's International $ 86.2 $ 5.0 Checkmate Electronics $ 17.1 $ 2.6 Applied Innovation 19.4 4.4 Royal Grip 13.3 1.7 Integracare 18.5 1.3 M-Wave 16.2 3.6 Wall Data 70.2 7.9 Serving-N-Slide 54.8 8.3 Davidson & Associates 55.1 6.5 Daig 29.2 6.1 Chico's FAS 46.1 4.2 Cobra Golf 67.4 10.0

Explanation / Answer

a) r = [nxy - xy]/sqrt[(nx2 - (x)2)(ny2 - (y)2)] = 0.7218

b) R2 = 0.72182 = 0.521

c) Mean(X) = 41.125
Mean(Y) = 5.133
SD(X) = 25.35799
SD(Y) = 2.711032

slope = r*SD(Y)/SD(X) = 0.0772

intercept = 5.133 - 0.07717*41.125 = 1.9593

earnings = 0.0772*sales + 1.9593

d) earnings = 0.0772*50 + 1.9593 = 5.8193(in millions of $)

Company Sales Earnings ($ millions),X ($ millions),Y X*Y X^2 Y^2 Papa John's International 86.2 5 431 7430.44 25 Applied Innovation 19.4 4.4 85.36 376.36 19.36 Integracare 18.5 1.3 24.05 342.25 1.69 Wall Data 70.2 7.9 554.58 4928.04 62.41 Davidson & Associates 55.1 6.5 358.15 3036.01 42.25 Chico's FAS 46.1 4.2 193.62 2125.21 17.64 Checkmate Electronics 17.1 2.6 44.46 292.41 6.76 Royal Grip 13.3 1.7 22.61 176.89 2.89 M-Wave 16.2 3.6 58.32 262.44 12.96 Serving-N-Slide 54.8 8.3 454.84 3003.04 68.89 Daig 29.2 6.1 178.12 852.64 37.21 Cobra Golf 67.4 10 674 4542.76 100 Total 493.5 61.6 2648.11 27368.49 397.06

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