Question

# The following data show the brand, price (\$), and the overall score for six stereo headphones...

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 = 23.127 + 0.319x,

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

Brand Price (\$) Score
A 180 74
B 150 73
C 95 61
D 70 56
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.

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 small 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.

(c)

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

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