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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 displays a section from an educational website providing data on headphones' brands, prices, and scores from Consumer Reports. The page includes a regression equation to explore the relationship between price and overall score. Below is a transcription suitable for an educational context: --- ### Headphone Data Analysis The following dataset presents the brand, price (in dollars), and overall score for six stereo headphones, as tested by Consumer Reports. The scores range from 0 (lowest) to 100 (highest) and reflect sound quality and effectiveness of ambient noise reduction. The estimated regression equation for these data is: \[ \hat{y} = 22.8598 + 0.3214x \] where $ x = \text{price (\$)} $ and $ y = \text{overall score} $. #### Data Table | Brand | Price (\$) | Score | |-----------------|------------|-------| | Bose | 170 | 76 | | Skullcandy | 160 | 71 | | Koss | 85 | 61 | | Phillips/O'Neill| 70 | 56 | | Denon | 70 | 40 | | JVC | 45 | 26 | #### Calculations a. **Compute SST, SSR, and SSE (to 3 decimals).** - SST = ______ - SSR = ______ - SSE = ______ b. **Compute the coefficient of determination $ r^2 $ (to 3 decimals).** - $ r^2 = ______ $ *Comment on the goodness of fit. Hint: If $ r^2 $ is greater than 0.70, the estimated regression equation provides a good fit.* *The least squares line provides a good fit as ______ proportion of the variability in $ y $ has been explained by the least squares line.* c. **Determine the value of the sample correlation coefficient $ r_{xy} $ (to 3 decimals).** - $ r_{xy} = ______ $ --- This educational content helps in understanding statistical relationships and the use of regression in data interpretation.$

Transcribed Image Text:The image displays a section from an educational website providing data on headphones' brands, prices, and scores from Consumer Reports. The page includes a regression equation to explore the relationship between price and overall score. Below is a transcription suitable for an educational context: --- ### Headphone Data Analysis The following dataset presents the brand, price (in dollars), and overall score for six stereo headphones, as tested by Consumer Reports. The scores range from 0 (lowest) to 100 (highest) and reflect sound quality and effectiveness of ambient noise reduction. The estimated regression equation for these data is: \[ \hat{y} = 22.8598 + 0.3214x \] where $ x = \text{price (\$)} $ and $ y = \text{overall score} $. #### Data Table | Brand | Price (\$) | Score | |-----------------|------------|-------| | Bose | 170 | 76 | | Skullcandy | 160 | 71 | | Koss | 85 | 61 | | Phillips/O'Neill| 70 | 56 | | Denon | 70 | 40 | | JVC | 45 | 26 | #### Calculations a. **Compute SST, SSR, and SSE (to 3 decimals).** - SST = ______ - SSR = ______ - SSE = ______ b. **Compute the coefficient of determination $ r^2 $ (to 3 decimals).** - $ r^2 = ______ $ *Comment on the goodness of fit. Hint: If $ r^2 $ is greater than 0.70, the estimated regression equation provides a good fit.* *The least squares line provides a good fit as ______ proportion of the variability in $ y $ has been explained by the least squares line.* c. **Determine the value of the sample correlation coefficient $ r_{xy} $ (to 3 decimals).** - $ r_{xy} = ______ $ --- This educational content helps in understanding statistical relationships and the use of regression in data interpretation.

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