Question: ( 15x3 = 45 points ) Use the "Poverty" dataset. This dataset of size n = 51 is for the 50 states and the District of Columbia in the United States. We wish to develop an equation for estimating Y = an index of violent crime from X = poverty rate, which is the percent of the state’s population living in households with incomes below the federally defined poverty level.

1. Fit a simple linear regression model with Y = ViolCrime and X = PovPct . Click the "Storage" button in the Minitab Regression Dialog and select each of the items in the left-hand list (i.e., Fits, Residuals, Standardized residuals, Deleted residuals, Leverages, Cook’s distance, DFITS). Write down the estimated regression equation and the MSE for this model.
2. Which state has the highest leverage and what is that leverage? [Leverages are in the column labeled "HI"]
3. Is the leverage in the previous part higher than the threshold 3( p / n )?
4. Use the estimated regression equation from part (a) to calculate the fitted value for observation #9, the District of Columbia. [You can check your answer with the one Minitab provides in the column labeled "FITS" but there will be some rounding error.]
5. Use your answer from the previous part together with the actual ViolCrime of the District of Columbia to calculate the residual. [You can check your answer with the one Minitab provides in the column labeled "RESI".]
6. What is the leverage for the District of Columbia?
7. Use the residual from part (e), the MSE from part (a), and the leverage from part (f) to calculate the internally studentized residual for the District of Columbia. [You can check your answer with the one Minitab provides in the column labeled "SRES" – remember Minitab calls these "Standardized residuals."]
8. Delete the District of Columbia from the dataset as follows: select Data > Subset Worksheet, click "Use rows that match a condition" for "How do you want to create a subset," select "Exclude rows that match the condition" for "Do you want to include or exclude rows," select "Location" for "Column," and check "District_of_Columbia" in the box labeled "Values." Then refit the simple linear regression model with Y = ViolCrime and X = PovPct (de-select each of the items in the left-hand list of the Storage tab to avoid having a whole new set of columns added to your worksheet). Write down the estimated regression equation and the MSE for this model.
9. Use the residual from part (e), the MSE from part (h), and the leverage from part (f) to calculate the studentized deleted residual for the District of Columbia. [You can check your answer with the one Minitab provides in the column labeled "TRES" in the original worksheet – remember Minitab calls these simply "Deleted residuals."]
10. Use the estimated regression equation from part (h) to calculate the predicted value for the District of Columbia (i.e., based on the model fit to the subset worksheet excluding the District of Columbia). [Note: the answer won’t make a whole lot of sense, but don’t worry about this since we’re simply going to use this predicted value for part (k).]
11. Use the fitted value from part (d), the predicted value from part (j), the MSE from part (h), and the leverage from part (f) to calculate the DFFITS for the District of Columbia. [You can check your answer with the one Minitab provides in the column labeled "DFIT" in the original worksheet.]
12. Is the absolute value of DFFITS in the previous part higher than the threshold given in the online notes, ?
13. Use the residual from part (e), the MSE from part (a), and the leverage from part (f) to calculate the Cook’s distance for the District of Columbia. [You can check your answer with the one Minitab provides in the column labeled "COOK" in the original worksheet.]
14. Is the Cook’s distance from the previous part higher than the upper threshold given in the notes, 1?
15. Briefly summarize your findings with respect to the District of Columbia. You might want to consider graphical evidence too!

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