Troubleshooting
Problem
I have run a linear regression with 2 predictors and noticed two surprising results. 1. Although the correlations among the 2 predictors (X and W, say) and the dependent variable are positive, the sign of the regression coefficient for X is negative and its standardized coefficient is much larger than the standardized coefficient when X is the only predictor. 2. The squared multiple correlation (R^2) for the two-predictor models is larger than the sum of the two R^2s for the simple regressions with each of these predictors as the sole predictor. The presence of W seems to enhance the predictive power of X. I thought that the presence of 2 correlated predictors would reduce the predictive value of each of them.
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Historical Number
42165
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Modified date:
16 April 2020
UID
swg21479993