Figure 1.2: Multiple Linear Regression

Multiple Linear Regression

When introducing additional independent variables to our dataset, our mathematical model expands into higher dimensions. Instead of finding a line of best fit for a single variable (x), we are now finding the plane of best fit for two variables (x₁ and x₂). The core principle of Ordinary Least Squares (OLS) remains identical: the model seeks the plane that minimizes the sum of the squared vertical residuals (the dashed red lines) between the observed data and the surface of the plane.

Figure 1.2: A 3D spatial visualization of the multiple regression model ŷ = β₀ + β₁x₁ + β₂x₂. The dependent variable (y) is predicted by evaluating the coordinates on the translucent regression plane.