The Tire Rack, America's leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 being the highest rating) for 18 maximum performance summer tires. The variable Steering rates, the tire's steering responsiveness, Tread Wear rates, quickness of wear based on the driver's expectations, and Buy Again rates the driver's overall tire satisfaction and desire to purchase the same tire again. Values shown below are averages as obtained from surveys.

Table 4

Sample of Ratings of Eighteen Maximum Performance Summer Tires.

Tire

Steering

Treadwear

Buy Again

Goodyear Assurance TripleTred

8.9

8.5

8.1

Michelin HydroEdge

8.9

9.0

8.3

Michelin Harmony

8.3

8.8

8.2

Dunlop SP 60

8.2

8.5

7.9

Goodyear Assurance ComforTred

7.9

7.7

7.1

Yokohama Y372

8.4

8.2

8.9

Yokohama Aegis LS4

7.9

7.0

7.1

Kumho Power Star 758

7.9

7.9

8.3

Goodyear Assurance

7.6

5.8

4.5

Hankook H406

7.8

6.8

6.2

Michelin Energy LX4

7.4

5.7

4.8

Michelin MX4

7.0

6.5

5.3

Michelin Symmetry

6.9

5.7

4.2

Kumho 722

7.2

6.6

5.0

Dunlop SP 40 A/S

6.2

4.2

3.4

Bridgestone Insignia SE20

5.7

5.5

3.6

Goodyear Integrity

5.7

5.4

2.9

Dunlop SP20 FE

5.7

5.0

3.3

Use the data provided in Table 4 to answer the following questions:

1. Provide descriptive statistics of the data.
2. Develop two simple regression models that can be used to predict the Buy Again rating given the Steering Rating in one and the Tread Wear rating in the other. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use = .05. Include all phases of assessment of the model.
3. Develop a multiple regression model that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
4. Does combining the two independent variables improve coefficient of determination? Please explain.
5. Choose a combination of steering and treadwear not given in the above table and find the expected Buy Again for this combination.