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Multiple Regression Analysis

1. Multiple Regression Analysis. Model:. Multiple Regression Analysis. Adjusted Coefficient of Determination. Multiple Regression Analysis. Analysis of Variance and F Statistic. Problems in Regression Analysis. Multicollinearity: Two or more explanatory variables are highly correlated.

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Multiple Regression Analysis

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  1. 1

  2. Multiple Regression Analysis Model:

  3. Multiple Regression Analysis Adjusted Coefficient of Determination

  4. Multiple Regression Analysis Analysis of Variance and F Statistic

  5. Problems in Regression Analysis • Multicollinearity: Two or more explanatory variables are highly correlated. • Heteroskedasticity: Variance of error term is not independent of the Y variable. • Autocorrelation: Consecutive error terms are correlated.

  6. Durbin-Watson Statistic Test for Autocorrelation If d = 2, autocorrelation is absent.

  7. Steps in Demand Estimation • Model Specification: Identify Variables • Collect Data • Specify Functional Form • Estimate Function • Test the Results

  8. Functional Form Specifications Linear Function: Power Function: Estimation Format:

  9. Chapter 4 Appendix

  10. Getting Started • Install the Analysis ToolPak add-in from the Excel installation media if it has not already been installed • Attach the Analysis ToolPak add-in • From the menu, select Tools and then Add-Ins... • When the Add-Ins dialog appears, select Analysis ToolPak and then click OK.

  11. Entering Data • Data on each variable must be entered in a separate column • Label the top of each column with a symbol or brief description to identify the variable • Multiple regression analysis requires that all data on independent variables be in adjacent columns

  12. Example Data

  13. Running the Regression • Select the Regression tool from the Analysis ToolPak dialog • From the menu, select Tools and then Data Analysis... • On the Data Analysis dialog, scroll down the list of Analysis Tools, select Regression, and then click OK • The Regression tool dialog will then be displayed

  14. Select the Data Ranges • Type in the data range for the Y variable or select the range on the worksheet • Type in the data range for the X variable(s) or select the range on the worksheet • If your ranges include the data labels (recommended) then check the labels option

  15. Select an Output Option • Output to a selected range • Selection is the upper left corner of the output range • Output to a new worksheet • Optionally enter a name for the worksheet • Output to a new workbook • And then click OK

  16. Regression Output

  17. Multiple Regression Data

  18. Regression Output

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