The regression model has the income ~ prestige + women form, where income is the response vector, and prestige and women specifies a predictor. We can illustrate a simple regression model in the formula y=α+β₁x₁ + β₂x₂, where α is the intercept while the slope, β₁ and β₂, 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 x₁ and x₂).

In this example, we load the Prestige dataset from the car package. To generate the regression line, we use the lm function to generate a model of the three variables. Further, we use scatter3d to plot a regression line in a 3d plot.