The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is 9 20.987 +0.340x, where x price ($) and y = overall score. Brand Price ($) Score A 180 78 B 150 73 C 95 59 D 70 56 E 70 38 F 35 26 Squares), SSR (Regression Sum of Squares), and SSE (Error Sum of Squares). (Round your answers. three decimal places.) (a) Compute SST (Total Sum 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. 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. 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.

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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$### Regression Analysis of Stereo Headphones Data The following data show the brand, price ($), 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 $\hat{y} = 20.987 + 0.340x$, where $ x $ = price ($) and $ y $ = overall score. #### Data Table: | Brand | Price ($) | Score | |-------|----------:|------:| | A | 180 | 78 | | B | 150 | 73 | | C | 95 | 59 | | D | 70 | 56 | | E | 70 | 38 | | F | 35 | 26 | #### Tasks: (a) **Compute Total Sum of Squares (SST), Regression Sum of Squares (SSR), and Error Sum of Squares (SSE).** Round your answers to three decimal places. - **SST =** - **SSR =** - **SSE =** (b) **Compute the coefficient of determination $\mathbf{r^2}$.** Round your answer to three decimal places. - $\mathbf{r^2 =}$ 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 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 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 least squares line provided a good fit as a large proportion of the variability in $ y $ has been explained by the least squares line.$

Transcribed Image Text:### Regression Analysis of Stereo Headphones Data 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 $\hat{y} = 20.987 + 0.340x$, where $ x $ = price ($) and $ y $ = overall score. #### Data Table: | Brand | Price ($) | Score | |-------|----------:|------:| | A | 180 | 78 | | B | 150 | 73 | | C | 95 | 59 | | D | 70 | 56 | | E | 70 | 38 | | F | 35 | 26 | #### Tasks: (a) **Compute Total Sum of Squares (SST), Regression Sum of Squares (SSR), and Error Sum of Squares (SSE).** Round your answers to three decimal places. - **SST =** - **SSR =** - **SSE =** (b) **Compute the coefficient of determination $\mathbf{r^2}$.** Round your answer to three decimal places. - $\mathbf{r^2 =}$ 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 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 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 least squares line provided a good fit as a large proportion of the variability in $ y $ has been explained by the least squares line.

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