Multiple linear regression model
In the The simple linear regression model section, we considered an almost (un)realistic problem of having only one predictor. We need to extend the model for the practical problems when one has more than a single predictor. In Example 3.2.9. Octane rating of gasoline blends, we had a graphical study of mileage as a function of various vehicle variables. In this section, we will build a multiple linear regression model for the mileage.
If we have X 1, X 2, …, X p independent sets of variables that have a linear effect on the dependent variable Y, the multiple linear regression model is given by the following equation:
This model is similar to the simple linear regression model, and we have the same interpretation as earlier. Here, we have additional independent variables in X
1, …, X
p and their effect on the regressand Y respectively through the additional regression parameters 
. Now suppose we have n pairs of random observations 
for understanding the multiple...
