An analyst regressed on and . If she later noticed that , then which of the following assumptions of the classical linear regression model was violated?
Tap an option to check your answer.
1 mark, −0.333EconometricsClassical assumptions and their violationsMulticollinearityEasyabout 1 min
GATE 2023 Question 32: Classical assumptions and their violations
Answer and worked solution
Answer: (B)
If exactly, then and are perfectly linearly related — one regressor is an exact linear function of the other, with no independent variation between them.
This is precisely the definition of perfect multicollinearity, which violates the classical linear regression assumption that no exact linear relationship exists among the regressors. In this situation, OLS cannot even uniquely estimate separate coefficients for and (the design matrix becomes singular).
Homoscedasticity, no autocorrelation, and linearity in parameters are unrelated assumptions concerning the error term's variance, correlation structure, and the functional form, respectively — none of these are implicated by a relationship between the regressors themselves.
Therefore the answer is (B) No Perfect Multicollinearity.
The trap: (A) Homoscedasticity
Students who are less confident distinguishing the CLRM assumptions sometimes default to 'homoscedasticity' as a catch-all guess for 'something went wrong with the regression,' without specifically recognizing that a stated exact linear relationship between two regressors is the textbook signature of multicollinearity, not a variance-related issue.
Plain-text version
An analyst regressed Y on X₁ and X₂. If she later noticed that X₁=5X₂, then which of the following assumptions of the classical linear regression model was violated? (A) Homoscedasticity (B) No Perfect Multicollinearity (C) No Autocorrelation (D) Linearity in parameters
Also written as: An analyst regressed Y on X_1 and X_2. If she later noticed that X_1=5X_2, then which of the following assumptions of the classical linear regression model was violated?
Classical assumptions and their violations has come up 26 times in 7 exams since 2011.
What this question tests
This question is on Multicollinearity, part of Classical assumptions and their violations in Econometrics.
Highly correlated regressors: symptoms, consequences and the perfect case.
TestStop has 8 past-paper questions on this subtopic.
Question from the GATE 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.