Model Assessment and Comparison in Multiple Linear Regression

Once the model is built, you would want to assess it in terms of its predictive powers. For multiple linear regression, you may build more than one model with different combinations of the independent variables. In such a case, you would also need to compare these models with one another to check which one yields optimal results. 

Let’s hear more on this from Rahim.

Now, for the assessment, you have a lot of new considerations to make. Besides, selecting the best model to obtain decent predictions is quite subjective. You need to maintain a balance between keeping the model simple and explaining the highest variance (which means that you would want to keep as many variables as possible). You can do this using the key idea that a model can be penalised for keeping a large number of predictor variables. 

Hence, there are two new parameters that come into the picture:

                                                              $Adjusted$ $R^2=1-\frac{(1-R^2)(N-1)}{N-p-1}$

                                                                  $AIC=n\times log\left(\frac{RSS}{n}\right)+2p$

Here, $n$ is the sample size, meaning the number of rows you would have in the data set, and $p$ is the number of predictor variables.

Additional reading

• AIC- Akaike Information Criterion
• BIC- Bayesian Information Criterion
• Mallows' CP