The Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The data contained in the file named TireRatings show survey results for 68 all-season tires (Tire Rack website, March 21, 2012). Performance traits are rated using the following 10-point scale.

The values for the variable labeled Wet are the average of the ratings for each tire's wet traction performance and the values for the variable labeled Noise are the average of the ratings for the noise level generated by each tire. Respondents were also asked whether they would buy the tire again using the following 10-point scale:

The values for the variable labeled Buy Again are the average of the buy-again responses. For the purposes of this exercise, we created the following binary dependent variable:

Thus, if Purchase = 1, the respondent would probably or definitely buy the tire again.
a. Write the logistic regression equation relating x1 = Wet performance rating and x2 = Noise performance rating to y = Purchase.
b. Use Minitab to compute the estimated logit.
c. Use the estimated logit to compute an estimate of the probability that a customer will probably or definitely purchase a particular tire again with a Wet performance rating of 8 and a Noise performance rating of 8.
d. Suppose that the Wet and Noise performance ratings were 7. How does that affect the probability that a customer will probably or definitely purchase a particular tire again with these performance ratings?
e. If you were the CEO of a tire company, what do the results for parts (c) and (d) tell you?

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Excellent Good Fair Unacceptable Superior 10 4 Definitely 10 Probably Possibly bably Not | Definitely Not 1 if the value of the Buy-Again variable is 7 or greater 0 if the value of the Buy-Again variable is less than 7 Purchase-