Minitab homework

The data set is about earnings per hours. The variable definitions are:

Obs: 526

1. wage average hourly earnings

2. educ years of education

3. exper years potential experience

4. tenure years with current employer

5. nonwhite =1 if nonwhite

6. female =1 if female

7. married =1 if married

8. numdep number of dependents

9. smsa =1 if live in SMSA

10. northcen =1 if live in north central U.S

11. south =1 if live in southern region

12. west =1 if live in western region

13. construc =1 if work in construc. indus.

14. ndurman =1 if in nondur. manuf. indus.

15. trcommpu =1 if in trans, commun, pub ut

16. trade =1 if in wholesale or retail

17. services =1 if in services indus.

18. profserv =1 if in prof. serv. indus.

19. profocc =1 if in profess. occupation

20. clerocc =1 if in clerical occupation

21. servocc =1 if in service occupation

22. lwage log(wage)

23. expersq exper^2

24. tenursq tenure^2

1. Compute a correlation matrix for the following variables: wage, years of education, years of potential experience, years with current employer, female, married, and number of dependents. The dependent variable is return on equity. (20 points). 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 “lwage” on years of education, year of potential experience, years with current employer, female, married, and number of dependents. Note that female and married are categorical variables or qualitative variables. Use the output to answer the questions below. (40 points). Copy and paste the regression output from Minitab to this part of your Word document.

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 at the 5% significance level.

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 at the 1%, 5% and 10% significance levels.

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. Given the regression output in question 2, drop numdep because it has the smallest t-value and run the regression again. Use this regression model, the one that includes only significant variables, to evaluate the multiple regression assumptions. (40 points) Copy and paste the regression outputs from Minitab to this part of your Word document.

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.

3.5. 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 “lwage” on years of education, years potential experience, years with current employer, female, and married. (20 points) Copy and paste the regression outputs from Minitab to this part of your Word document.

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. Use the regression output in question 3 to write out the estimated regression model. This is the regression output that has only significant variables. (You may use the equation below). (30 points)

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

5.2. What would be predicted value of wage if educ=11, exper=2 , tenure=0, female=1 and married=0? Compute “log(wage)” first and then get “wage”. (Use the entire coefficients and round your answer to 2 decimal places.)

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

5.4. Read section 1.7 in chapter 1 and 3.14 in chapter 3 to answer this question on ethics and statistics. Using a scale from 0 to 10, please rate the importance of using statistics with integrity and honesty when collecting, organizing, summarizing, analyzing, and interpreting data as well as reporting results. Zero being the lowest value and 10 the highest value.

1 ____ , 2 _____ , 3 _____ , 4 ______ , 5 _____ , 6_____ , 7 _____ , 8 _____ , 9 ______ , 10 _____

5.5. Using a scale from 0 to 10, please rate the knowledge of Minitab you had before taking this class. Zero being the lowest value and 10 the highest value.

0____, 1 ____ , 2 _____ , 3 _____ , 4 ______ , 5 _____ , 6_____ , 7 _____ , 8 _____ , 9 ______ , 10 _____

5.6. Using a scale from 0 to 10, please rate the knowledge of Minitab you have after the work you have done in this class during this semester. Zero being the lowest value and 10 the highest value.

0 ____ , 1 ____ , 2 _____ , 3 _____ , 4 ______ , 5 _____ , 6_____ , 7 _____ , 8 _____ , 9 ______ , 10 _____