In multiple regression, we are interested in testing the impact of several predictors on a criterion, instead of just one in simple regression. Here, the value of the observations can be computed as the intercept plus the slope coefficient multiplied by the predictor value (for each predictor) plus the residuals.

The analysis estimates the unique contribution of the predictors to the criterion—that is, each obtained slope coefficient value (there is one for each predictor) and the intercepts that are controlled for the influence of the other predictors on the criterion. We are not going to detail the calculation of the slope and intercept for multiple regression as this involves more complex explanations than for simple regression and will not add much to your understanding; most of what we have seen (except the calculation of the coefficients and degrees of freedom) remains valid for multiple regression. We will now directly skip to a more practical section.