In this episode of Office Hours Dan extends his prior introduction of the linear regression model to show how the model is fit to sample data using ordinary least squares estimation. Dan’s presentation is less mathematical and more conceptual, and attempts to provide some insight into what happens behind-the-scenes when estimating a regression model in practice...

Dan begins by reviewing the three parameters that define a one-predictor regression model: the intercept, slope, and residual variance. He then describes the analytic goal of obtaining optimal estimates of these parameters from the sample data. He uses graphical representations to highlight the goal of calculating sample estimates that result in the smallest possible sum of squared residuals. This episode establishes several basic principles that will be revisited in the following two episodes on inference.