Which of the following is a main linear regression assumption?

• A. Linearity
• B. Heteroscedasticity
• C. Autocorrelation
• D. Multicollinearity

Answer: (A)

Linearity is the fundamental assumption because ordinary least squares regression relies on the idea that the expected value of the outcome changes in a straight-line (linear) way as the predictors change. In practical terms, the model assumes the outcome is a linear function of the predictors (for multiple predictors, a hyperplane in the predictor space), with the effect of each predictor captured by a constant slope. If the true relationship is curved or involves complex interactions that a simple linear form can’t capture, the model’s predictions and inferences become biased or misleading unless you transform the data or use a nonlinear approach.

The other options describe issues that can undermine the analysis but aren’t the defining assumption. Heteroscedasticity refers to non-constant error variance across levels of the predicted value and primarily affects the reliability of standard errors and tests. Autocorrelation means residuals are correlated across observations, common in time-series data and also affecting standard errors. Multicollinearity happens when predictors are highly correlated, making it hard to disentangle their individual effects and inflating variance estimates.