What a coefficient?

Regression analysis generates an equation to describe the statistical relationship between one or more predictor variables and the response variable. After you use Minitab Statistical Software to fit a regression model, and verify the fit by checking the residual plots, you’ll want to interpret the results. In this post, I’ll show you how to interpret the p-values and coefficients that appear in the output for linear regression analysis.

How Do I Interpret the P-Values in Linear Regression Analysis?

The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.

Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.

In the output below, we can see that the predictor variables of South and North are significant because both of their p-values are 0.000. However, the p-value for East (0.092) is greater than the common alpha level of 0.05, which indicates that it is not statistically significant.

Typically, you use the coefficient p-values to determine which terms to keep in the regression model. In the model above, we should consider removing East.

How Do I Interpret the Regression Coefficients for Linear Relationships?

Regression coefficients represent the mean change in the response variable for one unit of change in the predictor variable while holding other predictors in the model constant. This statistical control that regression provides is important because it isolates the role of one variable from all of the others in the model.