Question

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 = 23.462 + 0.315x,

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

Brand	Price ($)	Score
A	180	74
B	150	73
C	95	59
D	70	58
E	70	42
F	35	24

(a)

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

SST=

SSR=

SSE=

(b)

Compute the coefficient of determination r².

(Round your answer to three decimal places.)

r²

=

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 provided 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 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.

(c)

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

Answer 1

The statistical software output for this problem is :

(a)

SST= 1840

SSR=1487.039

SSE= 352.962

(b)

r ² = 0.808

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.

(c)

sample correlation coefficient = 0.899