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The following data show the brand, price , and the overall score for six stereo headphones that were tested by Consumer Reports ( Consumer Reports

The following data show the brand, price , and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from (lowest) to (highest). The estimated regression equation for these data is , where and .

Brand Price ($) Score
Bose 180 76
Scullcandy 160 71
Koss 95 62
Phillips/O'Neill 70 56
Denon 70 40
JVC 25 25

a. Compute , , and (to decimals).

SST =
SSR =
SSE =

b. Compute the coefficient of determination (to decimals).

Comment on the goodness of fit. Hint: If is greater than , the estimated regression equation provides a good fit.

The least squares line - Select your answer - provided did not provide Item 5 a good fit as - Select your answer - a large a small Item 6 proportion of the variability in has been explained by the least squares line.

c. What is the value of the sample correlation coefficient (to decimals)?

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