The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest) The estimated regression equation for these data is ý = 21.656 + 0.333x, where x = price ($) and y = overall score. Brand Price ($) Score 180 76 B 150 73 95 61 D 70 54 70 42 35 24 (a) Compute SST, SSR, and SS. (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 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 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 large 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. (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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$The image contains a dataset and several related questions regarding linear regression analysis for educational purposes. The dataset and questions are presented as follows: ### Dataset A table displays information about six brands of stereo headphones, detailing their price in dollars and overall score based on sound quality and noise reduction. The score ranges from 0 (lowest) to 100 (highest). | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 76 | | B | 150 | 73 | | C | 95 | 61 | | D | 70 | 54 | | E | 40 | 35 | | F | 25 | 24 | The estimated regression equation provided is $ \hat{y} = 21.656 + 0.333x $, where $ x $ = price ($) and $ y $ = overall score. ### Questions #### (a) Compute SST, SSR, and SSE - Instructions are to round answers to three decimal places. - **SST**: Total Sum of Squares - **SSR**: Regression Sum of Squares - **SSE**: Error Sum of Squares #### (b) Compute the coefficient of determination $ r^2 $ - Round the answer to three decimal places. - **Comment on the goodness of fit**: Consider a proportion large if it is at least 0.55. - Options to select from: 1. 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. 2. 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. #### (c) What is the value of the sample correlation coefficient $ r $? - Round your answer to three decimal places. This exercise aims to teach students how to conduct regression analysis, interpret the results, and assess the fit of a regression model.$

Transcribed Image Text:The image contains a dataset and several related questions regarding linear regression analysis for educational purposes. The dataset and questions are presented as follows: ### Dataset A table displays information about six brands of stereo headphones, detailing their price in dollars and overall score based on sound quality and noise reduction. The score ranges from 0 (lowest) to 100 (highest). | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 76 | | B | 150 | 73 | | C | 95 | 61 | | D | 70 | 54 | | E | 40 | 35 | | F | 25 | 24 | The estimated regression equation provided is $ \hat{y} = 21.656 + 0.333x $, where $ x $ = price ($) and $ y $ = overall score. ### Questions #### (a) Compute SST, SSR, and SSE - Instructions are to round answers to three decimal places. - **SST**: Total Sum of Squares - **SSR**: Regression Sum of Squares - **SSE**: Error Sum of Squares #### (b) Compute the coefficient of determination $ r^2 $ - Round the answer to three decimal places. - **Comment on the goodness of fit**: Consider a proportion large if it is at least 0.55. - Options to select from: 1. 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. 2. 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. #### (c) What is the value of the sample correlation coefficient $ r $? - Round your answer to three decimal places. This exercise aims to teach students how to conduct regression analysis, interpret the results, and assess the fit of a regression model.

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