Financial Risk Manager Part 1
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Which of the following statements regarding linear regression is incorrect?
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NNikitesh
A
Homoskedasticity occurs when the variance of the residuals is constant across all observations.
B
Heteroskedasticity occurs when the variance of the residuals, commonly known as error terms, is not the same across all observations in the sample.
C
If residual terms are correlated with each other, this can lead to serial correlation.
D
Heteroskedasticity does not lead to problems with inference and estimation.
Explanation:
Explanation:
Statement D is incorrect because heteroskedasticity does indeed lead to problems with inference and estimation.
Key points:
- Heteroskedasticity refers to the situation where the variance of the residuals (error terms) is not constant across observations.
- Impact of Heteroskedasticity:
- While the coefficient estimates remain unbiased, the standard errors become biased and inconsistent.
- This leads to incorrect statistical inferences - hypothesis tests (t-tests, F-tests) become unreliable.
- Confidence intervals and p-values become invalid.
- Correct statements from the options:
- A: Correct - Homoskedasticity means constant variance of residuals.
- B: Correct - Heteroskedasticity means non-constant variance of residuals.
- C: Correct - Serial correlation occurs when residuals are correlated with each other (autocorrelation).
Why D is wrong: Heteroskedasticity violates one of the key assumptions of classical linear regression (homoskedasticity), which affects the efficiency of estimators and validity of statistical tests. While the parameter estimates remain unbiased, the inference about their significance becomes unreliable.
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