Question:
An analyst regressed $Y$ on $X_1$ and $X_2$. If she later noticed that $X_1=5X_2$, then which assumption of the classical linear regression model was violated?
An analyst regressed $Y$ on $X_1$ and $X_2$. If she later noticed that $X_1=5X_2$, then which assumption of the classical linear regression model was violated?
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Exact linear dependence among regressors (e.g., $X_1=aX_2$) \Rightarrow perfect multicollinearity \Rightarrow OLS coefficients are not uniquely estimable.
Updated On: Sep 1, 2025
- Homoscedasticity
- No Perfect Multicollinearity
- No Autocorrelation
- Linearity in parameters
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The Correct Option is B
Solution and Explanation
Since $X_1=5X_2$, the regressors are in an exact linear relationship (one is a constant multiple of the other). This violates the assumption of no perfect multicollinearity—columns of the design matrix must be linearly independent for OLS to yield unique estimates. Therefore, option \fbox{(B)} is correct.
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