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 = 23.528 + 0.315x,

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

Brand	Price ($)	Score
A	180	76
B	150	71
C	95	59
D	70	56
E	70	42
F	35	26

(a)

Compute SST (Total Sum of Squares), SSR (Regression Sum of Squares), and SSE (Error Sum of Squares). (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 large proportion of the variability in y has been explained by the least squares line

.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 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.

Answer 1

The statistical software output for this problem is :

(a)

SST= 1724

SSR= 1480.738

SSE= 243.263

(b)

coefficient of determination = 0.859

.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.