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.
DA0-001 Analyzing and Modeling Data Practice Question
This DA0-001 practice question tests your understanding of analyzing and modeling data. Read the scenario carefully and evaluate each option against the stated constraints before committing to an answer. After answering, compare your reasoning against the explanation and wrong-answer breakdown below. Once you have made your selection, read the full explanation to reinforce the concept and understand why each distractor is designed to mislead on exam day.
In multiple linear regression, which TWO assumptions are critical for unbiased coefficient estimates? (Choose two.)
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 between predictors and the response. Homoscedasticity (D) ensures that the variance of errors is constant across all levels of the predictors, which is necessary for the Gauss-Markov theorem to hold and for ordinary least squares (OLS) estimates to be unbiased.
Key principle: Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
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
Nonlinear relationships can bias coefficient estimates.
Related concept
Read the scenario before looking for a memorised answer.
✗
Large sample size
Why it's wrong here
Large sample size supports normality assumption but is not an assumption of the model itself.
✗
Normality of errors
Why it's wrong here
Normality is not required for unbiased coefficient estimates; it matters for inference in small samples.
✓
Homoscedasticity: errors have constant variance
Why this is correct
Heteroscedasticity leads to inefficient estimates and invalid confidence intervals.
Related concept
Read the scenario before looking for a memorised answer.
✗
Independence of errors
Why it's wrong here
Independence is critical, but it is often assumed from study design; not typically checked by residual plots.
Common exam traps
Common exam trap: answer the scenario, not the keyword
CompTIA often tests the distinction between assumptions required for unbiasedness (linearity and homoscedasticity) versus those needed for efficiency or inference (normality, independence, large sample size), causing candidates to mistakenly select normality or independence as critical for unbiased coefficients.
Detailed technical explanation
How to think about this question
Under the hood, the Gauss-Markov theorem states that OLS estimators are the Best Linear Unbiased Estimators (BLUE) when the errors have zero mean conditional on the predictors (linearity) and constant variance (homoscedasticity). In practice, if homoscedasticity is violated (heteroscedasticity), coefficient estimates remain unbiased but their standard errors are biased, leading to incorrect t-statistics and confidence intervals. A real-world scenario is modeling housing prices with square footage and number of bedrooms; if the variance of errors increases with house size (heteroscedasticity), the coefficient for square footage is still unbiased, but its significance test may be misleading.
KKey Concepts to Remember
Read the scenario before looking for a memorised answer.
Find the constraint that changes the correct option.
Eliminate answers that are true in general but not in this case.
TExam Day Tips
→Watch for words such as best, first, most likely and least administrative effort.
→Review why wrong options are wrong, not only why the correct option is correct.
Key takeaway
Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Real-world example
How this comes up in practice
A practitioner preparing for the DA0-001 exam encounters this exact type of scenario on the job. The correct answer here is not the most general option — it is the best answer for the specific constraint described. Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option. Real exam questions reward reading the full scenario before eliminating options, because the constraint defines which answer fits.
What to study next
Got this wrong? Here's your next step.
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
Analyzing and Modeling Data — This question tests Analyzing and Modeling Data — Read the scenario before looking for a memorised answer..
What is the correct answer to this question?
The correct answer is: 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 between predictors and the response. Homoscedasticity (D) ensures that the variance of errors is constant across all levels of the predictors, which is necessary for the Gauss-Markov theorem to hold and for ordinary least squares (OLS) estimates to be unbiased.
What should I do if I get this DA0-001 question wrong?
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
What is the key concept behind this question?
Read the scenario before looking for a memorised answer.
About these practice questions
Courseiva creates original exam-style practice questions with explanations and wrong-answer analysis. It does not publish real exam questions, exam dumps, or protected exam content. Learn why practice questions differ from exam dumps →
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 C: Linear regression assumes that the relationship between the independent and dependent variables is linear (option C). This means the model expects that a unit change in the predictor results in a constant change in the outcome, which is the core assumption for ordinary least squares (OLS) estimation to produce unbiased coefficients.
Last reviewed: Jun 30, 2026
Question Discussion
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