Multiple Linear Regression

Purpose To analyze the relationship between a single dependent variable and several independent variables

Key terms Bivariate Partial Correlation: Simple correlation between two variables after the effects of all other variables is removed Correlation: how a change in one variable affects another variable Strength Direction Dependent variable: criterion Independent variable: predictor

Key terms Regression variate: a linear combination of the independent variables used to attempt to predict the dependent variable Beta coefficient: standardized regression coefficient that allows for a direct comparison between variables as to their relative explanatory power of the dependent variable

Key Terms Correlation Coefficient R: degree to which two or more predictors are related to the criterion. Measure applied to the variate. Coefficient of determination R square: Measure of the proportion of the variance of the criterion that is explained by the predictors. Measure applied to the variate.

Key terms Residual Variance and R-square. This value is immediately interpretable in the following manner. If we have an R-square of 0.4 then we know that the variability of the Y values around the regression line is times the original variance; in other words we have explained 40% of the original variability, and are left with 60% residual variability. Ideally, we would like to explain most if not all of the original variability. The R-square value is an indicator of how well the model fits the data (e.g., an R-square close to 1.0 indicates that we have accounted for almost all of the variability with the variables specified in the model).

Steps First interpret the variate. If the variate is NOT significant, stop. If it is significant, then you can interpret the Betas and R square values. Use the Betas to answer your hypotheses.