# Regression analysis with standardized variables

Chapter

## Abstract

The standardization of both the dependent and independent variables in regression analysis leads to a number of important results. To begin with, the regression coefficient between two standardized variables is equal to the covariance of the standardized variables. This result can be seen from the following equation for the regression coefficient:
$$b_{yx}^* = \frac{{Cov\left( {z_y ,z_x } \right)}} {{Var\left( {z_x } \right)}} = \frac{{Cov\left( {z_y ,z_x } \right)}} {1} = Cov\left( {z_y ,z_x } \right)$$
In order to avoid confusion, the standardized regression coefficient, b*yX, is denoted with an asterisk in order to distinguish it from the unstandardized regression coefficient, byx. Moreover, the standardized regression coefficient for the regression of variable y on variable x is equal to the standardized regression coefficient for the regression of variable x on variable y such that:
$$b_{yx}^* = b_{xy}^*$$

These two standardized regression coefficients are equal to one another because the covariances in their numerators are the same and the variances in their denominators are both equal to one.

## Keywords

Regression Analysis Regression Coefficient Standardize Score Dard Deviation Standardize Variable