Financial Risk Manager Part 1

Cook's distance is given by the formula:

$D_j = \frac{\sum_{i=1}^{n} (\hat{Y}_i^{(-j)} - \hat{Y}_i)^2}{ks^2}$

Where:

• $\hat{Y}_i^{(-j)}$ = fitted value of $\hat{Y}_i$ when the observed value $j$ is excluded
• $k$ = number of coefficients in the regression model
• $s^2$ = estimated error variance from the model using all observations

In this case: $\hat{Y}_i = 1.4110 + 0.1512X_1$ $\hat{Y}_i^{(-j)} = 0.3169 + 1.3667X_1$

The correct answer is 3.3923 (Option A), which represents the Cook's distance for the 5th observation. Cook's distance measures the influence of each observation on the regression coefficients, with larger values indicating more influential observations that may be outliers or leverage points.