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Regression Analysis Part B Calculation Procedures

Regression Analysis Part B Calculation Procedures. Read Chapters 3, 4 and 5 of Forecasting and Time Series, An Applied Approach. Regression Analysis Modules. Part A – Basic Model & Parameter Estimation Part B – Calculation Procedures

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Regression Analysis Part B Calculation Procedures

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  1. RegressionAnalysisPart BCalculation Procedures Read Chapters 3, 4 and 5 of Forecasting and Time Series, An Applied Approach.

  2. Regression Analysis Modules 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 R

  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. Univariate Regression Data

  5. Manual Calculations Univariate Case

  6. Excel, Data Analysis Calculations Univariate Case

  7. Excel, Data Analysis Calculations Univariate Case (continued)

  8. SPSS Data Analysis Calculations Univariate Case SPSS: Analyze/Regression/Linear/

  9. SPSS Data Analysis Calculations Univariate Case (continued)

  10. Multivariate Regression Data

  11. Manual Calculations Multivariate Case (1 of 4)

  12. Manual Calculations Multivariate Case (2 of 4) Shift + Control then Enter

  13. Manual Calculations Multivariate Case (3 of 4) Shift + Control then Enter Shift + Control then Enter

  14. Manual Calculations Multivariate Case (4 of 4) Shift + Control then Enter

  15. Excel, Data Analysis Calculations Multivariate Case

  16. Excel, Data Analysis Calculations Multivariate Case (continued)

  17. SPSS Data Analysis Calculations Multivariate Case SPSS: Analyze/Regression/Linear/

  18. SPSS Data Analysis Calculations Multivariate Case (continued)

  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. 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. How large will a correlation be when there is a multicollinearity condition? Skip says: r > .98 may be a problem. Textbook says: r > .90 may be a problem.

  22. Test for Multicollinearity by VIF in SPSS SPSS: Analysis / Regression / Linear • Potential multicollinearity: • If largest Rj2 > .9 • If largest VIFj > 10 • If Mean VIF >>> 1

  23. Verification of Calculated VIF Values

  24. Calculated VIF Values if only Excel is Available The R2 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. Calculated the R2 for each of the independent variables.

  26. Calculated the R2(continued) These are the desired R2 ‘s

  27. Calculated the R2(continued) CONCLUSION The VIFs are the diagonals of the C-Inverse matrix (see previous slide).

  28. Verification of the R2 Calculations Individual regression fits.

  29. Verification of the R2 Calculations (continued) From SPSS output.

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