The Crime2 data file at the text website illustrates how a single observation can be highly influential in determining whether the model should allow nonlinearity.

(a) With all 51 observations, fit the quadratic model between y = murder rate and x = percentage in poverty.

Test whether the quadratic term is needed. Report the Pvalue, and interpret.

(b) Refit the model, deleting the observation forD.C. Report the P-value for testing the quadratic term, and interpret.

(c) Compare

(a) and (b), and use the scatterplot to explain how a single observation can have a large impact on whether the quadratic term seems needed. Show how you would be warned of this by influence diagnostics for the fit in (a).