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
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Exercise 14.18 Algo (Coefficient of Determination)
Question 8 of 10.
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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
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