{Exercise 14.18} The following data show the brand, price ($), and the overall s

Question

{Exercise 14.18}

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is  = 23.097 + 0.319x, where x = price ($) and y = overall score.

Round your answers to three decimal places.

a. Compute SST, SSR, and SSE.

b. Compute the coefficient of determination r2. Comment on the goodness of fit.

r2 =  

c. What is the value of the sample correlation coefficient?

r =  

Brand Price Score Bose 180 75 Scullcandy 150 72 Koss 95 61 Phillips/O'Neill 70 57 Denon 60 40 JVC 45 25

Explanation / Answer

From Excel

a)

b)

coefficient of determination r2 =0.79

Hence we can say that 79% of variation explained in score is due to price.

c) Correlation coefficient is 0.89

SUMMARY OUTPUT Regression Statistics Multiple R 0.89066 R Square 0.793276 Adjusted R Square 0.741595 Standard Error 9.788596 Observations 6 ANOVA df SS MS F Significance F Regression 1 1470.734 1470.734 15.34946 0.017279 Residual 4 383.2664 95.81661 Total 5 1854 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 23.09689 9.07075 2.546304 0.063554 -2.08755 48.28133 -2.08755 48.28133 Price 0.319031 0.08143 3.917839 0.017279 0.092944 0.545118 0.092944 0.545118

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