Which of the following assumptions do we need to check to make sure our regression is appropriate?

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When evaluating whether a regression model is appropriate, we examine the assumptions that underpin the method and its diagnostics.
Option A: 'Errors should not be normally distributed.' In ordinary least squares (OLS) regression, normality of the error terms is not required for the unbiasedness or consistency of the coefficient estimates. It matters primarily for making exact inferences (e.g., small-sample t-tests). In large samples, the central limit theorem often makes normality less critical. Therefore this is not a general necessity to check for model adequacy, though it can affect inference.
Option B: 'Homoscedasticity.' This is the assumption that the error variance is constant across all levels of the predictor(s). It is a core requirement for valid standard errors, t-tests, and F-tests in OLS. If heteroscedasticity is present, standard errors may be biased, leading to unreliable inference, so checking for homoscedasticity is important to ensure regression appropriateness.
Option C: 'Heteroscedasticity.' By definition, heteroscedasticity is the violation of the homoscedasticity assumption. While detecting heteroscedasticity is important, stating it as something we need to check as an assumption itself can be confusing: we check for it to decide if the homoscedasticity assumption holds or if remedies are needed. As a standalone assumption to require, it is not the assumption we intend to verify as part of the model’s proper specification; rather, it is a potential issue to diagnose.
Option D: 'Both A and B are correct.' Since A is not a required assumption for the core validity of the regression estimates (though relevant for inference in small samples), pairing A with B as jointly correct is inaccurate. The most precise required assumption among the options is B, while A's role is conditional and not a blanket requirement for regression adequacy.
In summary, among the choices, the one that aligns with a fundamental assumption necessary for standard regression inferences is homoscedasticity, as it directly affects the reliability of standard errors and tests; the other options either describe nonessential conditions or misstate the relationships between concepts.

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Which of the following assumptions do we need to check to make sure our regression is appropriate?

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