Two Predictors, One Outcome

Simple regression fits a line to one predictor. Multiple regression extends it to two or more: ŷ = b₀ + b₁X₁ + b₂X₂, where each coefficient measures that predictor's effect with the others held constant. This multiple regression calculator fits the two-predictor model by least squares.

The Normal Equations

Least squares leads to a small linear system — the normal equations — built from sums, sums of squares, and cross-products of the data. The calculator assembles the 3×3 system and solves it with Gaussian elimination, giving the exact coefficients in one pass.

Reading the Fit

R² reports how much of the outcome's variance the model explains; the predicted-vs-actual scatter makes the fit visual — points hugging the diagonal mean good predictions. Use the equation to forecast y for new combinations of X₁ and X₂.