1. Regression Analysis Part B Calculation Procedures Read Chapters 3, 4 and 5 of Forecasting and Time Series, An Applied Approach.

2. L01B MGS 8110 - Regression - Calculations 2 Part A – Basic Model & Parameter Estimation Part B – Calculation Procedures Part C – Inference: Confidence Intervals & Hypothesis Testing Part D – Goodness of Fit Part E – Model Building Part F – Transformed Variables Part G – Standardized Variables Part H – Dummy Variables Part I – Eliminating Intercept Part J - Outliers Part K – Regression Example #1 Part L – Regression Example #2 Part N – Non-linear Regression Part P – Non-linear Example Regression Analysis Modules 

3. L01B MGS 8110 - Regression - Calculations 3 Alternative Calculation Procedures -Manual - use Excel and type in the formulas and intermediate steps. -Use the Data Analysis option of Excel. -Use SPSS statistical software program.

4. L01B MGS 8110 - Regression - Calculations 4 Univariate Regression Data

5. L01B MGS 8110 - Regression - Calculations 5 Manual Calculations Univariate Case

6. L01B MGS 8110 - Regression - Calculations 6 Excel, Data Analysis Calculations Univariate Case

7. L01B MGS 8110 - Regression - Calculations 7 Excel, Data Analysis Calculations Univariate Case(continued)

8. L01B MGS 8110 - Regression - Calculations 8 SPSS Data Analysis Calculations Univariate Case SPSS: Analyze/Regression/Linear/

9. L01B MGS 8110 - Regression - Calculations 9 SPSS Data Analysis Calculations Univariate Case(continued)

10. L01B MGS 8110 - Regression - Calculations 10 Multivariate Regression Data

11. L01B MGS 8110 - Regression - Calculations 11 Manual Calculations Multivariate Case (1 of 4)

12. L01B MGS 8110 - Regression - Calculations 12 Manual Calculations Multivariate Case (2 of 4) Shift + Control then Enter

13. L01B MGS 8110 - Regression - Calculations 13 Manual Calculations Multivariate Case (3 of 4) Shift + Control then Enter

14. L01B MGS 8110 - Regression - Calculations 14 Manual Calculations Multivariate Case (4 of 4) Shift + Control then Enter

15. L01B MGS 8110 - Regression - Calculations 15 Excel, Data Analysis Calculations Multivariate Case

16. L01B MGS 8110 - Regression - Calculations 16 Excel, Data Analysis Calculations Multivariate Case (continued)

17. L01B MGS 8110 - Regression - Calculations 17 SPSS Data Analysis Calculations Multivariate Case SPSS: Analyze/Regression/Linear/

18. L01B MGS 8110 - Regression - Calculations 18 SPSS Data Analysis Calculations Multivariate Case (continued)

19. L01B MGS 8110 - Regression - Calculations 19 Test for Multicollinearity by Correlation Analysis in Excel High correlation between dependent variable and the independent variables is desirable. High correlation between the independent variables is an undesirable. A potential multicollinearity condition. Excel: TOOLS / DATA ANALYSIS / Correlation

20. L01B MGS 8110 - Regression - Calculations 20 Test for Multicollinearity by Correlation Analysis in SPSS High correlation between dependent variable and the independent variables is desirable. High correlation between the independent variables is an undesirable, multicollinearity condition. SPSS: Analysis / Correlate / Bivariate

21. L01B MGS 8110 - Regression - Calculations 21 How large will a correlation be when there is a multicollinearity condition? Skip says:  >.98 may be a problem. Textbook says:  >.90 may be a problem.

22. L01B MGS 8110 - Regression - Calculations 22 Test for Multicollinearity by VIF in SPSS SPSS: Analysis / Regression / Linear Potential multicollinearity: –If largest R j 2 >.9 –If largest VIF j > 10 –If Mean VIF >>> 1

23. L01B MGS 8110 - Regression - Calculations 23 Verification of Calculated VIF Values

24. L01B MGS 8110 - Regression - Calculations 24 Calculated VIF Values if only Excel is Available The R 2 for each of the independent variables versus all of the remaining independent variables is needed to calculate the VIF’s. That is, “p” linear regression would need to be calculated. There is a useful trick that can be used to avoid doing the “p” regressions. The procedure is described in the next slides.

25. L01B MGS 8110 - Regression - Calculations 25 Calculated the R 2 for each of the independent variables.

26. L01B MGS 8110 - Regression - Calculations 26 Calculated the R 2 (continued) These are the desired R 2 ‘s

27. L01B MGS 8110 - Regression - Calculations 27 Calculated the R 2 (continued) CONCLUSION The VIFs are the diagonals of the C- Inverse matrix (see previous slide).

28. L01B MGS 8110 - Regression - Calculations 28 Verification of the R 2 Calculations Individual regression fits.

29. L01B MGS 8110 - Regression - Calculations 29 Verification of the R 2 Calculations (continued) From SPSS output.