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Use the data in LAWSCH85 for this exercise. (i) Using the same model as in Problem 4 in Chapter 3, state and test the null hypothesis that the rank of law schools has no ceteris paribus effect on median starting salary. (ii) Are features of the incoming class of students—namely, LSAT and GPA—individually or jointly significant for explaining salary? (Be sure to account for missing data on LSAT and GPA.)

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mirianmoses

Answer:

Step-by-step explanation:

In the model

Log (salary) = B0 + B1LSAT +B2GPA +B3log(libvol) +B4log(cost)+B5 rank+u

The hypothesis that rank has no effect on log (salary) is H0:B5 = 0. The estimated equation (now with standard errors) is

               Log (salary) =    8.34 +    .0047 LSAT +   .248 GPA +   .095 log(libvol)

                                        (0.53)     (.0040)              (.090)            (.033)

                                         +     .038 log(cost)    – .0033 rank

                                              (.032)                    (.0003)

                   n = 136,    R2 = .842.

The t statistic on rank is –11(i.e. 0.0033/0.0003), which is very significant. If rank decreases by 10 (which is a move up for a law school), median starting salary is predicted to increase by about 3.3%.

(ii) LSAT is not statistically significant (t statistic ≈1.18) but GPA is very significance (t statistic  ≈2.76). The test for joint significance is moot given that GPA is so significant, but for completeness the F statistic is about 9.95 (with 2 and 130 df) and p-value ≈.0001.

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