4.1. Using the data in GPA2.RAW on

4.1. Using the data in GPA2.RAW on 4,137 college students, the following equation
was estimated by OLS:

colgpaˆ = 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 five percent 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 on hsperc to be negative?
(ii) What is the predicted college GPA when hsperc = 20 and sat = 1050?
(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 standard deviation in the sample). What is the predicted difference in college GPA for these two students? Is the difference large?
ที่มา: Wooldridge (2002: 103)
4.2. The variable rdintens is expenditures on research and development (R&D) as a percentage of sales. Sales are measured in millions of dollars. The variable profmarg is profits as a percentage of sales.
Using the data in RDCHEM.RAW for 32 firms in the chemical industry, the following
equation is estimated:

rdintensˆ =(.472) + (.321) log(sales) + (.050) profmarg
rdinˆtens _ (1.369) _ (.216) log(sales) _ (.046) profmarg
n = 32, R2 = .099

(i) Interpret the coefficient on log(sales). In particular, if sales increases by 10%, what is the estimated percentage point change in rdintens? Is this an economically large effect?
(ii) Test the hypothesis that R&D intensity does not change with sales, against the alternative that it does increase with sales. Do the test at the 5% and 10% levels.
(iii) Does profmarg have a statistically significant effect on rdintens?
ที่มา: Wooldridge (2002: 155)


4.3. Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States.
Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percent of the total population. One model to test for a relationship is

log(rent) = β0 + β1log( pop) + β2log(avginc) +β3pctstu + u.

(i) State the null hypothesis (H0) that size of the student body relative to the
population has no ceteris paribus effect on monthly rents. State the alternative that there is an effect.
(ii) What signs do you expect for β1 and β2?
(iii) The equation estimated using 1990 data from RENTAL.RAW for 64 college towns is

log(ˆrent) =(.043) + (.066) log(pop) +(.507) log(avginc) + (.0056) pctstu
log(ˆrent) _ (.844) _ (.039) log(pop) _ (.081) log(avginc) _ (.0017) pctstu
n = 64, R2 = .458.
What is wrong with the statement: “A 10% increase in population is associated with about a 6.6% increase in rent”?
(iv) Test the hypothesis stated in part (i) at the 1% level.

ผลลัพธ์ (บอสเนีย) 1:

4.1. Koristeći podatke u GPA2.RAW na 4.137 studenata, sljedeće jednadžbe
je procijenjena od strane OLS: colgpa = 1,392-0,0135 hsperc + 0,00148 sat n = 4.137, R2 = 0,273, gdje se colgpa mjereno na skali od četiri tačke , hsperc je postotak u maturanata razred srednje škole (definirane tako da se, na primjer, hsperc _ 5 znači prvih pet posto klase), a sat je u kombinaciji matematike i verbalni rezultate na test postignuća učenika. (i) Zašto to smisla za koeficijent na hsperc biti negativan? (ii) koja je predvidio College GPA kada hsperc = 20 i sat = 1050? (iii) Pretpostavimo da dva maturantima, A i B, diplomirala u istom percentila iz srednje škole, ali rezultat Student A satelit je 140 poena više (oko jedne standardne devijacije u uzorku). Ono što je predvidio razlika u koledžu GPA za ova dva studenta? Da li je razlika velika? ที่ มา: Wooldridge (2002: 103) 4.2. Varijabilni rdintens je potrošnja na istraživanje i razvoj (R & D), kao postotak od prodaje. Prodaja se mjeri u milijunima dolara. . Varijabla profmarg je profit kao postotak od prodaje Korištenje podataka u RDCHEM.RAW za 32 firmi u kemijskoj industriji, sljedeće jednadžbe se procjenjuje: rdintens = (472.) + (.321) Log (prodaja) + (. 050) profmarg rdintens _ (1.369) _ (.216) log (prodaja) _ (.046) profmarg n = 32, R2 = 0,099 (i) Tumačenje koeficijent na log (prodaja). Konkretno, ako je rast prodaje od 10%, što je procijenjeni postotak promjene trenutku rdintens? Da li je to ekonomski veliki uticaj? (Ii) Testirajte hipotezu da intenzitet R & D ne mijenja sa prodajom, protiv alternativne to je to povećanje sa prodajom. Da li test na 5% i 10% nivoa. (Iii) Da li profmarg imaju statistički značajan učinak na rdintens? ที่ มา: Wooldridge (2002: 155) 4.3. Da li se najam stope uticajem studentske populacije u koledžu gradu? Neka najam biti prosječne mjesečne zakupnine za iznajmljivanje jedinice u koledž grad u SAD-u. Neka pop označava ukupnom broju stanovnika, avginc prosjeka grada prihoda, a pctstu studentske populacije kao posto od ukupnog stanovništva. Jedan model za testiranje veze dnevnik (najam) = β0 + β1log (pop) + β2log (avginc) + β3pctstu + u. (I) država nulta hipoteza (H0) da veličina studentskog tijela u odnosu na stanovništvo ima ne ceteris paribus efekta na mjesečnoj rente. Država je alternativa da postoji efekt. (Ii) Šta znaci očekujete za β1 i β2? (Iii) Jednadžba procjenjuje se na 1990 podataka iz RENTAL.RAW za 64 koledž gradova je log (najam) = (. 043) + (0,066) log (pop) + (. 507) log (avginc) + (0,0056) pctstu log (najam) _ (0,844) _ (0,039) log (pop) _ (0,081) log (avginc) _ (0,0017) pctstu n = 64, R2 = .458. Što nije u redu sa izjavom: "A povećanje od 10% u populaciji je povezana sa oko povećanje od 6,6% u najam" (iv) Testiranje hipoteza navedeno u dijelu (i) na nivou 1%.