The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.391 + 0.326x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 71 C 95 63 D 70 56 E 70 40 F 35 24 #1) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = #2) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = #2a) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) A) 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. B) 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) 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. D) 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. #3) 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 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

ŷ = 22.391 + 0.326x,

where x = price ($) and y = overall score.

Brand	Price ($)	Score
A	180	76
B	150	71
C	95	63
D	70	56
E	70	40
F	35	24

#1) Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

SST =

SSR =

SSE =

#2) Compute the coefficient of determination r².
(Round your answer to three decimal places.) r²=

#2a) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

A) 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.

B) 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) 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.

D) 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.

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

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