What is the name of the statistical model described by Y = BX + E, where Y is the outcome vector, X is the predictor matrix, B are coefficients, and E are errors?

• A. Nonlinear model
• B. Exponential model
• C. Linear model
• D. Polynomial model

Answer: (C)

This form is a linear model because the outcome is built as a straight linear combination of the predictors, with an additive error term. The coefficients multiply each predictor and are summed, so the model’s prediction is a linear function of X (the parameters B determine the slope for each predictor). The error term E accounts for whatever random variation is not captured by the linear relationship. An exponential model would involve a non-linear transformation like an exponent, and a polynomial model would add higher-order terms of X; neither changes the fact that the given equation expresses a linear relationship in the predictors. Therefore, the correct label is a linear model.