E1 Findings

The adjusted R2 of the untransformed model was 66.8%, compared to 71.1% in the reported model. This result indicates that the natural log transformation of the dependent variable is associated with an increase in explanatory power of the model. The intercept term is negative (-7.497) in the untransformed model, compared to a positive intercept (1.75895) in the reported model.

The untransformed model meets fewer regression assumptions compared to the reported model. The normal probability plot (Figure E1 below) of the standardised residuals suggests that hourly salary does not meet the assumption of coming from a normal distribution. The scatter plot of studentised residuals versus standardised predicted values (Figure E2) suggests that the assumption of a linear relationship between hourly wages and the matrix of predictor variables, and the assumption that hourly wages has a constant variance, were not met. Heteroscedasticity is evident in Figure E2, with the residuals fanning out as the standardised, predicted value of hourly salary increases.

Figure E1. Normal Probability Plot of the Untransformed Model

Figure E2. Residuals Plot of the Untransformed Model

The one-sample Kolmogorov-Smirnov test for goodness-of-fit produced a test statistic of 11.852 (p < .001). This test statistic is over twice the size of that produced for the reported model (5.577, p < .001) and strongly suggests that the residuals from the untransformed model have an even worse fit with the normal distribution. The largest Cook's D statistic was 0.29 compared to only 0.24 for the reported model, and the Durbin-Watson statistic was 2.0 (the same as for the reported model).

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