Diagnosing the need for WLS

  1. To run an initial Linear Regression analysis, from the menus choose:

    Analyze > Regression > Linear...

    Note: This feature requires the Statistics Base option.

    Figure 1. Linear Regression main dialog box
    Linear Regression main dialog box
  2. Select Adjusted Cost of Construction as the dependent variable.
  3. Select Square Footage through Years of Experience of Architect as independent variables.
  4. Click Plots.
    Figure 2. Plots dialog box
    Plots dialog box
  5. Select *ZRESID as the Y variable.
  6. Select *ZPRED as the X variable.
  7. Click Continue.
  8. Click Save in the Linear Regression dialog box.
    Figure 3. Save dialog box
    Save dialog box
  9. Select Standardized in the Residuals group.
  10. Click Continue.
  11. Click OK in the Linear Regression dialog box.
Figure 4. Model Summary
Model Summary

At first, the resulting OLS model appears to be reasonable. The model summary reports an R2 of 0.662.

Figure 5. Coefficients
Coefficients

The significance values for the estimates of the Square Footage and Indoor/Outdoor Mall coefficients are both less than 0.05, indicating that their effects are not due to chance. Somewhat surprisingly, the coefficient for architect's experience is not significant.

Figure 6. Plot of standardized residuals vs. standardized predicted vales
Plot of standardized residuals vs. standardized predicted vales

However, the scatterplot of standardized residuals versus standardized predicted values shows heteroscedasticity; that is, the variance of the residuals is not constant across values of the predicted values. In this plot, the spread of the residuals increases with increasing predicted values. This violates the assumptions of the OLS model, so you will need to compute a WLS model in order to obtain valid estimates.

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