e following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is 9 = 22.458194 +0.325418x, where x price ($) and y= overall score. Brand Price ($) Score A 78 69 B с с D E F 180 150 95 70 70 35 63 56 38 26 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST - SSR- SSE - (b) Compute the coefficient of determination 2. (Round your answer to three decimal places.) 2. 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 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 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. (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

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 ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.458194 + 0.325418x, where x = price ($) and y = overall score. SSR = SSE = Brand Price ($) A = B C D E F 180 150 95 70 70 35 Score 78 69 63 56 38 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = 26 (b) Compute the coefficient of determination r2. (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 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 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. 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. (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

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