A data scientist develops an Ordinary Least Squares (OLS) regression model. Upon reviewing the diagnostic plots, they observe that a scatter plot of the model's residuals versus the fitted values shows a distinct funnel shape, where the variance of the residuals increases as the fitted values increase. This pattern indicates a violation of a key OLS assumption. Which OLS assumption is violated, and what is the primary consequence of this violation?
The assumption of independence of errors is violated; the coefficient estimates become inefficient, and the model is susceptible to autocorrelation.
The assumption of homoscedasticity is violated; the coefficient estimates remain unbiased, but their standard errors are no longer reliable.
The assumption of linearity is violated; the coefficient estimates become biased, and the model will systematically mis-predict the outcome.
The assumption of normality of errors is violated; the coefficient estimates are no longer the Best Linear Unbiased Estimators (BLUE).
The correct answer is that homoscedasticity is violated, a condition known as heteroscedasticity. A key assumption of OLS regression is homoscedasticity, which means the variance of the errors is constant across all levels of the independent variables. A funnel shape in the residuals vs. fitted plot is a classic sign of heteroscedasticity. When this assumption is violated, the OLS coefficient estimates remain unbiased and consistent. However, the standard errors of the coefficients become biased and inconsistent. This invalidates the t-tests, F-tests, and confidence intervals that are used for hypothesis testing and assessing the significance of the coefficients.
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