Business and Economic Statistic exam

Test policies (please read):

• By signing this test you agree that you are using an exact Word version of the PDF version of the test posted on D2L.

• By signing this test you agree to work independently. However, if the instructor finds out that you have received help, you and the helper will get zero credits on this test.

• You can use the class notes and the textbook to answer the questions.

• You must use MINITAB to do the required analysis.

• If you have a computer that uses a Mac operating system, I recommend that you use the computers in the computer lab. The student is responsible for submitting a file that can be managed with Microsoft operating system. If I cannot open your files due to a different computer operating system, you will get zero credits.

• The Minitab project is 50 percent of the grade of the final exam grade, the other 50 percent comes from the answers to the questions.

• Please use your name to name your files.

• Do not change the format of the test.

• You will receive an email to confirm that you have submitted your test.

Instructions (please read):

• Write your name on the header. This is your signature.

• To do the multiple regression analyses, use the MLB_1 data set that is posted on D2L.

• Import the data from Excel to Minitab.

• Follow the instructions for each question.

• Save your Minitab project. You must submit it with your test (Word file).

• Read Chapters 13 and 14 as well as the Lab guide.

• If you have questions related to using Minitab, feel free to ask.

• Do not wait until the last day.

• Do not use your D2L email because the files could be too big and the message could not be delivered; use your MSU email or personal email.

• Copy and paste your Minitab output to the appropriate place in your Word document.

The data set is about Major League Baseball. The variable definitions are:

1. salary 1993 season salary
2. teamsal team payroll
3. nl =1 if national league
4. years years in major leagues
5. games career games played
6. atbats career at bats
7. runs career runs scored
8. hits career hits
9. doubles career doubles
10. triples career triples
11. hruns career home runs
12. rbis career runs batted in
13. bavg career batting average
14. bb career walks
15. so career strike outs
16. sbases career stolen bases
17. fldperc career fielding perc
18. frstbase =1 if first base
19. scndbase =1 if second base
20. shrtstop =1 if shortstop
21. thrdbase =1 if third base
22. outfield =1 if outfield
23. catcher =1 if catcher
24. yrsallst years as all-star
25. hispan =1 if hispanic
26. black =1 if black
27. whitepop white pop. in city
28. blackpop black pop. in city
29. hisppop hispanic pop. in city
30. pcinc city per capita income
31. gamesyr games per year in league
32. hrunsyr home runs per year
33. atbatsyr at bats per year
34. allstar perc. of years an all-star
35. slugavg career slugging average
36. rbisyr rbis per year
37. sbasesyr stolen bases per year
38. runsyr runs scored per year
39. percwhte percent white in city
40. percblck percent black in city
41. perchisp percent hispanic in city
42. blckpb black*percblck
43. hispph hispan*perchisp
44. whtepw white*percwhte
45. blckph black*perchisp
46. hisppb hispan*percblck
47. lsalary log(salary)

1. Compute a correlation matrix for the following variables lsalary, years, gamesyr, bavg, hrunsyr, rbisyr, games, hits, hispan and black. The dependent variable is lsalary. Copy and paste the correlation matrix from Minitab to this part of your Word document.

1.1. Explain the meaning of each correlation coefficient between the dependent variable and the independent variables. These are the values in the first column of the correlation matrix.

1.2. Given the correlation coefficients among the independent variables, explain whether there is a multicollinearity problem.

2. Run the regression of lsalary on years, gamesyr, bavg, hrunsyr, rbisyr, games, hits, hispan and black. Note that hispan and black are qualitatively variables. Copy and paste the regression output from Minitab to this part of your Word document. Use the output to answer the questions below.

2.1. Regarding the ANOVA table.

2.1.1. What are the degrees of freedom for the regression?
2.1.2. What are the degrees of freedom for the error?
2.1.3. What are the formula and value for the regression sum of squares?
2.1.4. What are the formula and value for the residual sum of squares?

2.2. Compute the multiple standard error of the estimate. What does this value mean?

2.3. Compute the coefficients of determinations R2 and adjusted R2. Interpret these coefficients.

2.4. Conduct a global test.

What kind of test statistic and distribution are we using for this test?
Is this a one-tailed or two-tailed test, explain?
What is your conclusion given this test?

2.5. Conduct a test of hypothesis for each explanatory variable coefficient.

What kind of test statistic and distribution are we using for this test?
Is this a one-tailed or two-tailed test, explain?
What is your conclusion given these tests?
Do you have to drop any variable, explain?

3. Use the regression model that includes only significant variables to evaluate the multiple regression assumptions.

3.1. Linearity assumption. Use the appropriate graphs and explain them. Copy and paste the graphs from Minitab to this part of your Word document.

3.2. Variation in the residuals. Use the appropriate graphs and explain them. Copy and paste the graphs from Minitab to this part of your Word document.

3.3. Distribution of residuals. Use the appropriate graphs and explain them. Copy and paste the graphs from Minitab to this part of your Word document.

3.4. Multicollinearity.

3.4.1. Compute the VIF values for the explanatory variables simultaneously and explain your results. Copy and paste the output from Minitab to this part of your Word document.

3.4.2. If you have multicollinearity problems drop the variable with the highest VIF, run the regression again, and explain your results. Copy and paste the output from Minitab to this part of your Word document.

3.5. Independent observations. Use the appropriate graphs and explain them. Copy and paste the graphs from Minitab to this part of your Word document

4. Run a stepwise regression of lsalary on years and gamesyr (only the significant variables that do not have multicollinearity problem as shown in question 3.4.2).

Explains how this method works.

Why do the coefficients of determination increase as the method is adding variables?
Why does the multiple standard error of the estimate decrease as the method is adding variables?

5. Write out the estimated regression model that includes only the significant variables as suggested in question 4 (you may want to use the equation below).

5.1. What does the coefficient on each explanatory variable mean, explain?

5.2. What would be predicted value of salary years=25, gamesyr=150? (Round your answers to 2 decimal places.)

5.3. What is the method used to compute the regression coefficients, and what does it do?

Attachment:- mlb_1_1.xlsx