Financial Risk Manager Part 1
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When does a set of data termed as homoscedastic?
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NNikitesh
A
The variance of the errors is the same across all the observations
B
The observations are iid random variables
C
The variance of the errors varies with the independent variables
D
None of the above
Explanation:
Explanation
Homoscedasticity is a key assumption in regression analysis where the variance of the error terms (residuals) is constant across all levels of the independent variables. This means:
- Constant variance: The spread of residuals should be roughly the same for all predicted values
- No pattern in residuals: When plotting residuals against predicted values, there should be no funnel shape or systematic pattern
- Contrast with heteroscedasticity: When variance changes with independent variables (option C), it's called heteroscedasticity
Why other options are incorrect:
- Option B: IID (independent and identically distributed) is a broader concept that includes more assumptions than just homoscedasticity
- Option C: This describes heteroscedasticity, the opposite of homoscedasticity
- Option D: Incorrect because option A is the correct definition
Homoscedasticity is important because when this assumption is violated, ordinary least squares (OLS) estimators are still unbiased but no longer have minimum variance among all linear unbiased estimators.
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