## Interpreting Regression Coefficients in Simple Regression

How are the regression coefficients interpreted in simple regression?

The simple regression model is

The formula for Regression Coefficients in Simple Regression Models is:

$$b = \frac{n\Sigma XY – \Sigma X \Sigma Y}{n \Sigma X^2 – (\Sigma X)^2}$$

$$a = \bar{Y} – b \bar{X}$$

The basic or unstandardized regression coefficient is interpreted as the predicted change in $Y$ (i.e., the dependent variable abbreviated as DV) given a one-unit change in $X$ (i.e., the independent variable abbreviated as IV). It is in the same units as the dependent variable.

• Note that there is another form of the regression coefficient that is important: the standardized regression coefficient. The standardized coefficient varies from –1.00 to +1.00 just like a simple correlation coefficient;
• If the regression coefficient is in standardized units, then in simple regression the regression coefficient is the same thing as the correlation coefficient.