# Multivariate regression analysis

In this section we will learn how to run a regression analysis with more than one independent variables.

Almost all social phenomena have more than one cause. To control, statistically, for all possible causes social scientists employ multinomial regression analysis.

The multivariate regression model is the following:

$Y_{i}=\alpha+\beta_{1}X_{i}+ \beta_{2}Z_{i}+ u_{i}$

The interpretation of the slope coefficients for the multivariate- in this case three variable model- is similar to the bivariate model but with one major difference. The coefficient $\beta_{1}$ represents the effect of X on Y while keeping Z (the third variable) constant. The same will hold if we had a model with four variables.