SOLVED: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 devel- oped for each treadmill tested. In general, a higher overall score indicates better perfor- mance. The following data show the price, the quality rating, and overall score for the 24 treadmills (Consumer Reports, February 2006) . \begin{array}{l}{\text { a. Use these data to develop an estimated regression equation that could be used to esti- }} \\ {\text { mate the overall score given the price. }} \\ {\text { b. Use } a=.05 \text { to test for overall significance. }}\end{array} \begin{array}{l}{\text { c. To incorporate the effect of quality, a categonical variable with three levels, we used two }} \\ {\text { dummy variables, Quality-E and Quality-VG. Each variable is coded } 0 \text { or } 1 \text { as follows. }}\end{array} Quality-E =\left\{\begin{array}{l}{1 \text { if quality rating is excellent }} \\ {0 \text { otherwise }}\end{array}\right. Quality-VG =\left\{\begin{array}{l}{1 \text { if quality rating is very good }} \\ {0 \text { otherwise }}\end{array}\right. Develop an estimated regression equation that could be used to estimate the overall score given the price and the quality rating. \begin{array}{l}{\text { d. For the estimated regression equation developed in part (c), test for overall signifi- }} \\ {\text { cance using } \alpha=.10 .}\end{array} \begin{array}{l}{\text { e. For the estimated regression equation developed in part (c), use the } t \text { test to determine }} \\ {\text { the significance of each independent variable. Use } \alpha=.10 \text { . }}\end{array} \begin{array}{l}{\text { f. Predict the overall score for a treadmill with a price of } \ 2000 \text { and a good quality rating. }} \\ {\text { How much would the prediction change if the quality rating were very good? Explain. }}\end{array}