40 Algorithms Every Programmer Should Know

Multiple regression

The fact is that most real-world analyses have more than one independent variable. Multiple regression is an extension of simple linear regression. The key difference is that there are additional beta coefficients for the additional predictor variables. When training a model, the goal is to find the beta coefficients that minimize the errors of the linear equation. Let's try to mathematically formulate the relationship between the dependent variable and the set of independent variables (features).

Similar to a simple linear equation, the dependent variable, y, is quantified as the sum of an intercept term plus the product of the β coefficients multiplied by the x value for each of the i features:

y = α + β ₁ x ₁ + β