Definition

Multiple Regression (MR) evaluates the relationship between a continuous response variable (Y) and two or more independent explanatory variables (Xs) by determining an equation to estimate the outcome of interest from knowledge of the multiple input variables.

Application

MR results in an equation (called the regression equation or model) of the form:

Y = b_{0}+ b_{1}X_{1} + b_{2}X_{2} + .... + ε

where

Y = the response (output) variable of interest

And the b_{i}’s are the regression coefficients:

b_{0} = the mean of Y when all the Xs are set to zero

b_{1} = the change in the mean of Y for a one unit increase in the value of X_{1} (holding all other Xs constant)

b_{2} = the change in the mean of Y for a one unit increase in the value of X_{2} (holding all other Xs constant)

…. and so on …..

ε = the random error term

See Also

Regression Analysis

Regression Coefficient