Multiple regression

More often than not, we want to include not just one, but multiple predictors (independent variables) in our predictive models. Luckily, linear regression can easily accommodate us! The technique? Multiple regression.

By giving each predictor its very own beta coefficient in a linear model, the target variable gets informed by a weighted sum of its predictors. For example, a multiple regression using two predictor variables looks like this:

Now, instead of estimating two coefficients ( b₀ and  b₁), we are estimating three: the intercept, the slope of the first predictor, and the slope of the second predictor.

Before explaining further, let's perform a multiple regression predicting gas mileage from weight and horsepower, using the following code:

  model <- lm(mpg ~ wt + hp, data=mtcars) 
  summary(model) 
   
  Call: 

  lm(formula = mpg ~ wt + hp, data = mtcars) 
   
  Residuals: 
     Min     1Q Median     3Q    Max  
  -3.941 -1.600 -0.182  1.050  5.854  
   
  Coefficients...