ABSTRACT
Most regression models in practice involve multiple predictors, that is, multiple regression models. The model benefits from new predictor variables that are relevant correlate much with Y, and unique, and do not correlate much with the other predictors. Predictor accuracy can increase, and an understanding of the variable relations can improve by adding predictor variables to the regression model. The meaning of the slope coefficients changes in the multiple regression model from the single predictor model. The partial slope coefficients in multiple regression represent the effect on the response as a unit increase in the predictor variable with the value of all other predictor variables held constant, statistical control. Multiple regression models can improve fit, but sometimes fit can be too good if it does not generalize to new data, evidence of an overfit model. An important aspect of multiple regression is model selection, choosing the most appropriate but parsimonious set of predictor variables. The regression model can integrate one-way ANOVA and a continuous predictor variable by including a grouping variable to investigate group differences in the presence of a continuous predictor, called the analysis of covariance or ANCOVA.
