The most obvious plot to study for a linear regression model, you guessed it, is the regression itself. If we plot the predicted values vs the real values we can see how close they are to our reference line of 45° (intercept = 0, slope = 1). If we’d had a very sparse plot where we can see no clear tendency over that line, then we have a bad regression. On the other hand, if we have all our points over the line, I bet you gave the model your wished results!
Then, the Adjusted R2 on the plot gives us an easy parameter for us to compare models and how well did it fits our reference line. The nearer this value gets to 1, the better. Without getting too technical, if you add more and more useless variables to a model, this value will decrease; but, if you add useful variables, the Adjusted R-Squared will improve.
We also get the RMSE and MAE (Root-Mean Squared Error and Mean Absolute Error) for our regression’s results. MAE measures the average magnitude of the errors in a set of predictions, without considering their direction. On the other side we have RMSE, which is a quadratic scoring rule that also measures the average magnitude of the error. It’s the square root of the average of squared differences between prediction and actual observation. Both metrics can range from 0 to ∞ and are indifferent to the direction of errors. They are negatively-oriented scores, which means lower values are better.
I like this approach to explaining models.