The regression model has the response ~ terms form, where response is the response vector, and terms is a series of terms that specifies a predictor. We can illustrate a simple regression model with the formula y=α+βx, where α is the intercept while the slope, β, describes the change in y when x changes. By using the least squares method, we can estimate and (where indicates the mean value of y and denotes the mean value of x).

To perform linear regression, we first prepare the data that has a linear relationship between the predictor variable and response variable. In this example, we load Anscombe's quartet dataset from the package car. Within the dataset, the x and y1 variables have a linear relationship, and we prepare a scatter plot of these variables. To generate the regression line, we use the lm function to generate a model of the two variables. Furthermore, we use abline to plot a regression line on the plot. As per the previous screenshot, the regression line illustrates the linear relationship of x and y1 variables. We can see that the coefficient of the fitted model shows the intercept equals 3.0001 and coefficient equals 0.5001. As a result, we can use the intercept and coefficient to infer the response value. For example, we can infer the response value when x at 3 is equal to 4.5103 (3 * 0.5001 + 3.0001).