Multiple Regression 2. Solving for and b. The weight for predictor x j will be a function of: The correlation x j and y. The extent to which x j ’s relationship with y is redundant with other predictors relationships with y (collinearity).
The Xj predictor is not related to Y when the other predictors are held constant.
Regression diagnostics check on these assumptions
1. Distance -- detects outliers in the dependent variable and assumption violations -- primary measure is the residual (Y-Y^) or standardized residual (i.e., put in terms of z scores) or studentized residual (i.e., put in terms of t-scores)
2. Leverage -- identifies potential outliers in the independent variables -- primary measure is the leverage statistic or “hat” diagnostic
3. Influence -- combines distance and leverage to identify unusually influential observations (i.e., observations or cases that have a big influence on the MR equation) -- the measure we will use is Cook’s D