The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 23.462 + 0.315x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 74 B 150 73 C 95 59 D 70 58 E 70 42 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST=SSR=SSE= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.
The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. 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 ŷ = 23.462 + 0.315x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 74 B 150 73 C 95 59 D 70 58 E 70 42 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST=SSR=SSE= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is
ŷ = 23.462 + 0.315x,
where x = price ($) and y = overall score.Brand | Price ($) | Score |
---|---|---|
A | 180 | 74 |
B | 150 | 73 |
C | 95 | 59 |
D | 70 | 58 |
E | 70 | 42 |
F | 35 | 24 |
(a)
Compute SST, SSR, and SSE. (Round your answers to three decimal places.)
SST=SSR=SSE=
(b)
Compute the coefficient of determination
r2.
(Round your answer to three decimal places.)r2
= Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)
The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.
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