Linear regression with continuous predictors

Let's start with an actual and illuminating example of confounding. Consider that we would like to predict the amount of air pollution based on the size of the city (measured in population size as thousand of habitants). Air pollution is measured by the sulfur dioxide (SO2) concentration in the air, in milligrams per cubic meter. We will use the US air pollution data set (Hand and others 1994) from the gamlss.data package:

> library(gamlss.data)
> data(usair)

Model interpretation

Let's draw our very first linear regression model by building a formula. The lm function from the stats package is used to fit linear models, which is an important tool for regression modeling:

> model.0 <- lm(y ~ x3, data = usair)
> summary(model.0)

Residuals:
    Min      1Q  Median      3Q     Max 
-32.545 -14.456  -4.019  11.019  72.549 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 17.868316   4.713844   3.791 0...