The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 20.455 + 0.335x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 78 B 150 69 95 59 D 70 56 70 38 F 35 24 (a) Compute SST (Total Sum of Squares), SR (Regression Sum of Squares), and SSE (Error Sum of Squares). (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination 2. (Round your answer to three decimal places.) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O 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. O 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. O 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. O 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.

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:The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 20.455 + 0.335x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 78 В 150 69 C 95 59 70 56 E 70 38 F 35 24 (a) Compute SST (Total Sum of Squares), SSR (Regression Sum of Squares), and SSE (Error Sum of Squares). (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination r. (Round your answer to three decimal places.) 12 = 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 did not provide 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.

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