Key Assumptions for Unbiased Regression Coefficients
In multiple linear regression, which TWO assumptions are critical for unbiased coefficient estimates? (Choose two.)
Quick Answer
The answer is linearity and homoscedasticity, as these two assumptions are critical for unbiased coefficient estimates in multiple linear regression. Linearity ensures that the model correctly captures the relationship between each predictor and the response variable, meaning the expected value of the error term is zero across all predictor values, which is a core requirement for ordinary least squares (OLS) estimates to be unbiased. Homoscedasticity, or constant variance of the errors, is equally essential because it satisfies the Gauss-Markov theorem, guaranteeing that OLS estimators are the best linear unbiased estimators (BLUE). On the CompTIA Data+ DA0-001 exam, this concept often appears in questions testing your understanding of regression diagnostics, with a common trap being the assumption that normality of errors is required for unbiasedness—it is not, only for inference. A helpful memory tip is to think of “L and H” for Linearity and Homoscedasticity: without them, your coefficients are biased, no matter how large your sample.
⚠ Common exam trap
The exam often tests the distinction between assumptions for unbiasedness (linearity and independence) versus those for efficiency (homoscedasticity) or inference (normality). Candidates may incorrectly select homoscedasticity as critical for unbiased coefficient estimates.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
Linearity: the relationship between predictors and response is linear
For unbiased coefficient estimates in multiple linear regression, the linearity assumption (A) ensures that the model correctly specifies the functional form, and the independence of errors assumption (E) ensures that errors are uncorrelated, both of which are required for ordinary least squares (OLS) estimates to be unbiased. Homoscedasticity (D) is not required for unbiasedness but for efficiency (Gauss-Markov theorem).
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
Linearity: the relationship between predictors and response is linear
Why this is correct
Correct. Linearity is required for unbiasedness because if the relationship is misspecified, OLS estimates will be biased.
- ✗
Large sample size
Why it's wrong here
Incorrect. Large sample size is not an assumption; it affects asymptotic properties but not unbiasedness in finite samples.
- ✗
Normality of errors
Why it's wrong here
Incorrect. Normality of errors is not required for unbiasedness; it is needed for exact inference in small samples.
- ✗
Homoscedasticity: errors have constant variance
Why it's wrong here
Incorrect. Homoscedasticity is required for efficiency and for the standard errors to be valid, but not for unbiasedness.
- ✓
Independence of errors
Why this is correct
Correct. Independence of errors is required for unbiasedness; without it, OLS estimates can be biased.
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Same concept, more angles
1 more way this is tested on DA0-002
These questions test the same concept from different angles. Work through them to make sure you can recognise it however the exam phrases it.
Variation 1. Which TWO of the following are common assumptions of linear regression?
medium- ✓ A.Independence of observations
- B.No multicollinearity
- ✓ C.Linearity of the relationship
- D.Normality of the dependent variable
- E.Homoscedasticity
Why A: Linear regression relies on several assumptions for valid OLS estimation. Two fundamental assumptions are independence of observations (option A), meaning the residuals are independent, and linearity of the relationship (option C), meaning the model correctly specifies a linear relationship between predictors and outcome. While homoscedasticity (equal variance of residuals) is also an important assumption, it is not listed as one of the two most common assumptions in this context. Options B and D are incorrect: no multicollinearity applies only to multiple regression, and normality of the dependent variable is not required; rather, normality of residuals is needed for hypothesis testing.
JA
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This DA0-002 practice question is part of Courseiva's free CompTIA certification practice question bank. Courseiva provides original exam-style practice questions with explanations, topic-based practice, mock exams, readiness tracking, and study analytics to help learners prepare for the DA0-002 exam.