Describe how multicollinearity can have adverse effects in constructing the regression model, how it is identified, and how normality of residuals is verified.

You have learned about the multiple linear regression, and now please answer the following questions in detail by applying the knowledge that you have gained from readings and lectures. It is important to include hypothetical examples whenever applicable.

· Explain the multiple linear regression model, the independent variables and the dependent variable, assumptions of the model, objectives, and the approach taken to construct the model, and using the model for prediction.

· Explain the analysis of variance (ANOVA) test on significance of the regression and how the result of this test is interpreted; discuss the hypotheses on coefficients of the regression and how the results of testing these hypotheses are interpreted about significance of these coefficients; include both unidirectional and bidirectional situations the coefficient of determination, adjusted coefficient of determination, and their significance.

· Describe how multicollinearity can have adverse effects in constructing the regression model, how it is identified, and how normality of residuals is verified.

Question 2:

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 ɑ = .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 ɑ = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
  4. Does combining the two independent variables improve the 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.

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