Question

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is  ŷ = 19.786 + 0.342x, where x = price ($) and y = overall score.

Brand	Price ($)	Score
A	180	76
B	150	73
C	95	59
D	70	54
E	70	38
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.)

a) 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.

b) 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) 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.

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

Answer 1