Answered: The following data show the brand,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

(c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

[Input box for the answer]

$The data provided represents the brand, price in dollars, and overall score of six stereo headphones evaluated by a magazine. The overall score evaluates factors such as sound quality and effectiveness of ambient noise reduction, rated on a scale from 0 (lowest) to 100 (highest). The estimated regression equation for this dataset is given by: \[ \hat{y} = 21.588629 + 0.334114x \] where $ x $ represents the price in dollars, and $ \hat{y} $ is the overall score. ### Data Table: | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 78 | | B | 150 | 71 | | C | 95 | 59 | | D | 70 | 58 | | E | 70 | 40 | | F | 35 | 24 | ### Questions: #### (a) Compute SST, SSR, and SSE. (Round your 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 your answer to three decimal places.) - $ r^2 = $ ___ This exercise involves computing statistical measures to evaluate how well the regression equation fits the data. SST measures the total variability in the scores, SSR measures the variability explained by the model, and SSE measures the unexplained variability. The coefficient of determination $ r^2 $ indicates the proportion of variance in the scores that is predictable from the price.$

Transcribed Image Text:The data provided represents the brand, price in dollars, and overall score of six stereo headphones evaluated by a magazine. The overall score evaluates factors such as sound quality and effectiveness of ambient noise reduction, rated on a scale from 0 (lowest) to 100 (highest). The estimated regression equation for this dataset is given by: \[ \hat{y} = 21.588629 + 0.334114x \] where $ x $ represents the price in dollars, and $ \hat{y} $ is the overall score. ### Data Table: | Brand | Price ($) | Score | |-------|-----------|-------| | A | 180 | 78 | | B | 150 | 71 | | C | 95 | 59 | | D | 70 | 58 | | E | 70 | 40 | | F | 35 | 24 | ### Questions: #### (a) Compute SST, SSR, and SSE. (Round your 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 your answer to three decimal places.) - $ r^2 = $ ___ This exercise involves computing statistical measures to evaluate how well the regression equation fits the data. SST measures the total variability in the scores, SSR measures the variability explained by the model, and SSE measures the unexplained variability. The coefficient of determination $ r^2 $ indicates the proportion of variance in the scores that is predictable from the price.

Expert Solution