Consumer Reports provided extensive testing and ratings for 24 treadmills. An overall score, based primarily on ease of use, ergonomics, exercise range, and quality, was developed for each treadmill tested. In general, a higher overall score indicates better performance. The following data show the price, the quality rating, and overall score for the 24 treadmills (Consumer Reports, February 2006).

a. Use these data to develop an estimated regression equation that could be used to estimate the overall score given the price.
b. Use α = .05 to test for overall significance.
c. To incorporate the effect of quality, a categorical variable with three levels, we used two dummy variables: Quality-E and Quality-VG. Each variable was coded 0 or 1 as follows.

Develop an estimated regression equation that could be used to estimate the overall score given the price and the quality rating.
d. For the estimated regression equation developed in part (c), test for overall significance using α = .10.
e. For the estimated regression equation developed in part (c), use the t test to determine the significance of each independent variable. Use α = .10.
f. Develop a standardized residual plot. Does the pattern of the residual plot appear to be reasonable?
g. Do the data contain any outliers or influential observations?
h. Estimate the overall score for a treadmill with a price of $2000 and a good quality rating. How much would the estimate change if the quality rating were very good? Explain.

Brand & Model Landice L7 NordicTrack S3000 SportsArt 3110 Quality Score rice 2900 3500 2900 3500 2300 2000 3000 1300 3200 1600 1300 1500 2600 600 1800 1700 1600 Very good Excellent Excellent Excellent Excellent Excellent Very good Very good Very good Very good Excellent 85 True Z4 HRC Vision Fitness T9500 Precor M 9.31 Vision Fitness T9200 Star Trac TR901 Trimline T350HR Schwinn 820p Bowflex 7-Series NordicTrack S1900 Horizon Fitness PST8 Horizon Fitness 5.2T Evo by Smooth Fitness FX30 ProForm 1000S Horizon Fitness CST4.5 81 79 72 72 Very good Very good Very good Very good Very good Verv good 83 83 82 80 75 75 74 1200 1600 1000 1400 1000 600 Very good Very good Keys Fitness 320t Smooth Fitness 7.1HR Pro NordicTrack C2300 Spirit Inspire ProForm 750 Image 19.0 R 70 Very good 67 Good l if quality rating is excellent 0 otherwise ifquality rating is very good 0 otherwise Quality-E= Quality-VG