The following data show the brand, price (S), 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 reductio cores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 23.2437 +0.3176x, wherez-price ($) and yoverall score. Price ($) Score 180 76 Brand Bose Scullcandy Koss 150 71 85 61 Phillips/O'Neill 70 57 Denon 70 JVC 45 25 1. Compute SST, SSR, and SSE (to 3 decimals). X EST= 1834 SSR = 1356.49 X SSE= 477.506 Compute the coefficient of determination (to 3 decimals). X 0.740 Comment on the goodness of fit. Hint: If 2 is greater than 0.70, the estimated regression equation provides a good fit. The least squares line provided ✓a good fit as a large ✓✓ proportion of the variability in has been explained by the least squares line. What is the value of the sample correlation coefficient (to 3 decimals)? Ky =0.860

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Exercise 14.18 Algo (Coefficient of Determination)
Question 8 of 10.
Hint(s) Check My Work
The following data show the brand, price (8), 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 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 23.2437 +0.3176z, where - price ($) and yoverall score.
Price ($)
Score
Brand
Bose
180
76
150
71
Scullcandy
Koss
85
61
Phillips/O'Neill
70
57
Denon
70
40
JVC
45
25
a. Compute SST, SSR, and SSE (to 3 decimals).
X
SST =
1834
SSR = 1356.49 *
SSE = 477.506 X
b. Compute the coefficient of determination 2 (to 3 decimals).
*
-0.740
Comment on the goodness of fit. Hint: If ² is greater than 0.70, the estimated regression equation provides a good fit.
The least squares line provided
✓✓✓ a good fit as a large
V
proportion of the variability in y has been explained by the least squares line.
c. What is the value of the sample correlation coefficient (to 3 decimals)?
Txy = 0.860
* Hide Feedback
Hint(s) Check My Work
Partially Correct
Transcribed Image Text:Exercise 14.18 Algo (Coefficient of Determination) Question 8 of 10. Hint(s) Check My Work The following data show the brand, price (8), 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 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 23.2437 +0.3176z, where - price ($) and yoverall score. Price ($) Score Brand Bose 180 76 150 71 Scullcandy Koss 85 61 Phillips/O'Neill 70 57 Denon 70 40 JVC 45 25 a. Compute SST, SSR, and SSE (to 3 decimals). X SST = 1834 SSR = 1356.49 * SSE = 477.506 X b. Compute the coefficient of determination 2 (to 3 decimals). * -0.740 Comment on the goodness of fit. Hint: If ² is greater than 0.70, the estimated regression equation provides a good fit. The least squares line provided ✓✓✓ a good fit as a large V proportion of the variability in y has been explained by the least squares line. c. What is the value of the sample correlation coefficient (to 3 decimals)? Txy = 0.860 * Hide Feedback Hint(s) Check My Work Partially Correct
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