Question

C. Calculation Problems (40 marks) 1. Using the data in GPA2.RAW on 4,137 college students, the following equation was esti- mated by OLS: colgpa = 1.392 - 0135 hsperc+.00148 sat n =4,137, R2 = 273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc =5 means the top 5% of the class), and sat is the combined math and verbal scores on the student achievement test. (i) Why does it make sense for the coefficient (ii) What is the predicted college GPA when hsperc = 20 and sat = 1,050? (iii) Suppose that two high school graduates, A and B, graduated in the same percentile from high school, but Student A's SAT score was 140 points higher (about one stan- dard deviation in the sample). What is the predicted difference in college GPA for hsperc to be negative? on (iv) Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa dif- ference of 50, or one-half of a grade point? Comment on your answer these two students? Is the difference large?

Answer 1

quen cola 1392-o.0135 heperc+ o dO148 st M4,13 0 13 The variable hs pere student standin student high sehool. Everyhrag slandling Lower he he else equal he worse as her expeeted callege qpA lower he ohen haperc vedicted hes and Sat 20 he eallege GPA 392 0.0135 (20) 4 O 00148 ( l050) D.G16 theicfee, he roredreted College GpA Ps 66 fhe ditenence betweon 140 tiomer hcoebtiefent stucdent Sat, becaue hsperc s he Sye both predrcted to haue So, A fs 00148 (40) 0 20 hher. oth hsperc frod 6.0014& Ast Now, we wordd have to n Asct Such hat copa o 5 66814- ASat Aset 238 zd100. o

pet haps not urpsol e almost o ond celets haribzu dibt het atandlard deofetions orealicted dibheene college Scoll SAT one sneided t obtio halby berint GpA