26. Refer to Example 9 1. Table 91. and Figure 9.4. Though inference may not be relevant for these data, we use them to illustrate how a single observation can be highly influential in detennining whether to assume a nonlinear relationship

a) Using all 51 observations. fit the quadratic model between murder rate and percentage in poverty Interpret the estimates.

b) Refer to (a). Test whether the quadratic term is needed in the inodel Report the P- value, and interpret.

c) Now refil the quadratic model deleting the observation for D.C. Compare the esumates to (a), and interpret.

d) Refer to (c). Test whether the quadratic term is needed in the model. Report the P. valuc, and interpret.

e) Compare results of the tests in

(b) and (d), and note how a single observation can have a large impact on the fit of a quadratic model Show how you would be warned of this by influence diagnostics for the fit in (a).

f) Show the result of the test for the coefficient of X in the model in

(c) Do the results of this test and the one in

(d) imply that poverty does not affect murder rate? Explain.