What is the mathematical formula for multiple linear regression?

• A. y = m1x1 + m2x2 + ... + mnxn + b
• B. y = a1x1 + a2x2 + ... + anxn + c
• C. y = m1x1 + b
• D. y = m1x1^2 + m2x2^2 + ... + mnxn^2 + b

Answer: (A)

Multiple linear regression models the expected value of the dependent variable as a linear combination of several independent variables, with one coefficient for each variable and an intercept. The standard form is ŷ = β0 + β1 x1 + β2 x2 + ... + βn xn, which is linear in the parameters βi.

The given expression y = m1 x1 + m2 x2 + ... + mn xn + b matches this structure: each feature x_i is multiplied by its coefficient m_i, and there is an intercept b. This is exactly how multiple linear regression is typically written, just with common parameter names.

Other forms either rename the coefficients (which is mathematically equivalent) or introduce different terms. The version with squares of the predictors would correspond to a nonlinear or polynomial model unless those squared terms are treated as separate features, which goes beyond the standard multiple linear regression setup. In practice, a noise term ε is also included, so the full model is y = β0 + β1 x1 + ... + βn xn + ε, but the core idea remains the same.