4 Residual diagnostics (14 pts) The data for this question includes results for

Question

4 Residual diagnostics (14 pts) The data for this question includes results for the 2008 mation for each state/district in the lower continental US. We will be relating VDem. Obama's share of the presidential vote in each state, to INC, the median income (in $1000) for each state. presidential election as well as income infor- Consider the following plots for the model E[VDem INC] oBINO residuals vs income Histogram of Normal Q-Q plot forr 40 45 50 5 60 66 70 Theoretical Quantes What problem do you see? How would you fix it? Justify your changes to the regression. (ii) Do you think that your fix will lead to big change in the least-squares regression coefficients? In other words, would you trust the model we've already fit? Why or why not?

Explanation / Answer

1.From the first graph i.e. income(more specifically the median of the income) against the residual plot, we can see most of the residuals are around 0.But for DC the residual is quite high.i.e. income of DC doesn't explain the VDEM well.Moreover the residual of DC looks like an outlier.

So we can exclude that data and again run the regression.In that case, we can get a better regression model with a low sum of the square of residuals and the histogram plot of residual will approach more like the normal distribution.

2.As from the Q-Q plot, we can see there exists an outlier.Most probably that outlier is for DC.So if exclude that entry Q-Q will almost be a straight line i.e. more precision for the regression line.That is the average of the residuals will be zero and we can get a better estimate.

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