DA0-002 Independence of observations Practice Question
Which TWO of the following are common assumptions of linear regression?
⚠ Common exam trap
Candidates often confuse homoscedasticity as an assumption that must be strictly satisfied, but it is actually a requirement for efficiency of OLS estimators. However, in many definitions, independence and linearity are considered the primary assumptions.
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
✓
Independence of observations
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.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
Independence of observations
Why this is correct
Correct. Independence of observations is a key assumption of linear regression; violations can lead to biased standard errors.
- ✗
No multicollinearity
Why it's wrong here
Incorrect. No multicollinearity is an assumption for multiple regression, not for simple linear regression, and even in multiple regression it is not always considered a 'common' assumption in the same sense.
- ✓
Linearity of the relationship
Why this is correct
Correct. Linearity is a fundamental assumption; the model must correctly specify a linear relationship.
- ✗
Normality of the dependent variable
Why it's wrong here
Incorrect. Linear regression assumes normality of residuals, not the dependent variable.
- ✗
Homoscedasticity
Why it's wrong here
Incorrect. Although homoscedasticity is an important assumption for unbiased standard errors, it is not selected here as it is often not considered one of the most common assumptions for basic linear regression.
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