Multiple Regression

Multiple Regression

1. We would use Multiple Regression if we have 2 or more predictors to explain an outcome

2. ·

3. Assumptions

   • Independence
   • Linearity
   • Bivariate Normality
   • Homoscedasticity
   • Non-multicollinearity
     • No highly correlated predictors

4. Test of Significance

   • R^2 is the effect of our regression
   • Larger N can lead to smaller denominator
   • F is t^2

5. MR might not have been significant because:

   • Small sample size (low power)
   • Effects too small (look for better predictors)
   • Inappropriate inclusion of predictors (IV's)
   • Poor operationalisation (e.g., DV)
   • Model does not apply to this population but may be useful in another

6. Predictors

   • May be useful because:
     • It is theoretically relevant to Y
     • It is correlated with Y
     • It is uniquely predictive of Y
   • Unique contribution of a predictor depends on other predictors
     • It decreases when more predictors are used in the equation
     • It decreases when there is another predictor that makes a similar contribution

7. Tolerance

   • Tolerance of X, in a set of predictors represents the proportion of X that is unique

8. Semi-Partial Correlation (sr)

   • Is a measure of the unique contribution of X1 to the prediction of Y
   • It is the correlation between X1 and Y when effects of all other Xs are 'partialed' or removed from X1
   • (sr)^2 is the proportion of (the whole of) Y that is uniquely predicted by X1

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