Part VII: Multiple Regression (MR)
Overview of Multiple Regression
| Uses of MR | Questions Addressed by MR |
 
 
Multiple Regression is a "general linear model" with a wide range of applications. It is basically an extension of the bivariate correlation and simple regression analysis. The primary uses of MR are as follows:
  • Prediction of a continuous Y with several continuous X variables: Unlike ordinary bivariate regression, MR allows the use of an entire set of variables to predict another.
  • Use of categorical variables in prediction: Through the technique of dummy coding, categorical variables (such as marital status or treatment group) can be used in addition to continuous variables.
  • Calculation of the unequal n ANOVA problem: Disproportional cell size in any factorial ANOVA design produces a correlation among the independent variables. MR estimates effects and interactions in this situation by the use of dummy codes.
  • Model nonlinear relationships between Y and a set of X: By the addition of "polynomial" terms (e.g. quadratic, cubic, trends) into the equation, relationships that do not meet the linear assumptions can be analyzed.
 
 
In the above uses of multiple regression, several questions can be asked about the set of variables used in the analysis. For instance:
  • How well does the set of predictors estimate Y? Multiple Regression can provide you with the proportion of criterion variance accounted for by the set of predictors.
  • What is the relative contribution of each variable in predicting Y? Being able to answer this question is an advantage for Multiple Regression over other techniques. This ability exists because Multiple Regression takes into account correlations between predictor variables.
  • What is the incremental validity of each predictor over every other? In other words, does the addition of a new predictor significantly enhance our predictive abilities?
  • What is the best subset of predictor variables from the overall set? By dividing the total predicted variance into variance uniquely predicted by each variable, Multiple Regression offers several techniques for deciding which is the single best predictor.