Chapter 14.3, Problem 22E

Refer to exercise 5 where the following data were used to investigate whether higher prices are generally associated with higher ratings for elliptical trainers (Consumer Reports, February 2008).

Brand and Model	Price ($)	Rating
Precor 5.31	3700	87
Keys Fitness CG2	2500	84
Octane Fitness Q37e	2800	82
LifeFitness X1 Basic	1900	74
NordicTrack AudioStrider 990	1000	73
Schwinn 430	800	69
Vision Fitness X6100	1700	68
ProForm XP 520 Razor	600	55

With x = price ($) and y = rating, the estimated regression equation is $\hat{y}=58.158+.008449x$. For these data, SSE = 173.88.

1. a. Compute the coefficient of determination r².
2. b. Did the estimated regression equation provide a good fit? Explain.
3. c. What is the value of the sample correlation coefficient? Does it reflect a strong or weak relationship between price and rating?