The following data show the brand, price (S), and the overall score for 6 stereo

Question

The following data show the brand, price (S), 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 trom 0 (lowest) to 100 (highest). The estimated regression equation for these data is 26.108 0.289, wherez price () and vrall score Brand Price score 180 76 160 71 Scullcandy 60 57 Phillips O'Neill Denon 45 25 Round your answers to three decimal places. a. Compute SST, SSR, and SSE. (to 3 decimals) (to 3 decimals) (to 3 decimals) b. Compute the coefficient of determination r Comment on the goodness of fit. The input in the box below will not be graded, but may be revicwed and considered by your instructor. c. What is the value of the sarmple correlation coefficient?

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Score
Independent Variable: Price ($)
Score = 26.107692 + 0.28892308 Price ($)
Sample size: 6
R (correlation coefficient) = 0.86002138
R-sq = 0.73963678
Estimate of error standard deviation: 10.925957

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) SST = 1834

SSR = 1356.494

SSE = 477.506

b) r2 = 0.740

This indicates that 74% of the variation in score can be explained by the price. So, the model seems to be a good fit.

c) r = 0.860

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 26.107692 9.6622241 0 4 2.7020375 0.054 Slope 0.28892308 0.085710259 0 4 3.3709276 0.028

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