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Answer: A Cook's distance value greater than 1 indicates that an observation has a large impact on the regression parameters.
## Explanation **C is correct.** Cook's distance, denoted as D, is a measure used in regression analysis to identify influential data points. When D > 1, it indicates that an observation has a substantial impact on the estimated regression parameters, making it an outlier that disproportionately affects the model. **A is incorrect** because residual plots typically display residual values (errors) on the y-axis and fitted values or explanatory variables on the x-axis, not the reverse. **B is incorrect** because residual plots can detect various issues beyond just outliers within 4 standard deviations, including model specification problems like omitted nonlinear relationships. **D is incorrect** because Cook's distance measures the sensitivity of fitted values when dropping a single observation, not two largest observations.
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A junior trader on a derivatives trading desk is using historical data to run a linear regression model that regresses the price of an option against the underlying stock price. The trader conducts an analysis of the regression results to identify potential outliers and assess their impact on the estimated coefficients. Which of the following statements correctly describes the given approach for identifying outliers?
A
A residual plot compares the error values on the x-axis against the realization of the explanatory variables on the y-axis.
B
Residual plots can only detect outliers that are typically within 4 standard deviations of the model mean.
C
A Cook's distance value greater than 1 indicates that an observation has a large impact on the regression parameters.
D
Cook's distance measures the sensitivity of the fitted values in a regression when the two largest observations are dropped.
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