What are the key assumptions of linear regression?

• A. Linearity, independence, homoscedasticity, normality of residuals, and no multicollinearity
• B. Linearity, independence, heteroscedasticity, non-normal residuals, and no multicollinearity
• C. Linearity, independence, constant residuals, and normality of predictors
• D. Linearity only; no other assumptions required

Answer: (A)

Linear regression relies on a specific set of assumptions about how the data relate to the model and how the residuals behave. The relationship between the predictors and the outcome should be linear, so the expected value of the outcome given the predictors is described by a straight-line (or plane in multiple dimensions) in the parameterized form. Observations must be independent, meaning one case does not provide information about another. The residuals—the differences between observed and predicted values—should have constant variance across all levels of the fitted values (homoscedasticity). The residuals should be approximately normally distributed, which supports valid confidence intervals and hypothesis tests for the coefficients, especially with smaller samples. Finally, the predictor variables should not be excessively correlated with each other (no multicollinearity); high correlation among predictors makes coefficient estimates unstable and inflates standard errors.

These conditions together explain why this set of assumptions is the correct one. The other options mix up heteroscedasticity for homoscedasticity, claim normality of predictors (which isn’t an assumption), or state that linearity is the only requirement, all of which misstate what linear regression needs for reliable estimates and inference.