# Question: Consumer Reports provided extensive testing and ratings for 24 treadmills

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.

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.

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