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Consider an equation to explain salaries of CEOs in terms of annual firm
sales, return on equity (roe, in % form), return in firm stocks ( ros, in %
firm):
假設有個式子可以解釋CEO的年度銷售薪水, 回報在股票 (roe, 用%的方式表示)以及公司
配股 firm stock (ros, 用%表示):

log (salary): β0 +β1log(sales) +β2roe +β3ros+u

(1) In terms of model parameters, state the null hypothesis that, after
controlling for sales and roe, ros has no effect on CEO salary. State the
alternative that better stock market performance increases a CEO’s salary.
在變數模式中, 設定虛無假設.在控制銷售以及roe和ros之後,並不會影響CEO的薪水. 請
找出相對的好的股市表現以增加CEO的薪水
(2) using the data in CEOSAL1.RAW, the following equation was obtained by OLS
根據CEOSAL1.RAW,下列公式根據OLS成立:
log(salary)= 4.32 + 2.80 log(sales) + 0.174 roe + 0.00024 ros
( 0.32) (0.035) (0.0041) (0.00054)
n=209, R^2 =0.283
, by what percentage is salary predicted to increase if ros increases by 50
points? Does ros have a practically large effect on salary?
當ros增加50個unit,薪水的漲幅預計會是多少? 根據得出的結果,ros對薪水的影響相對比
較大嗎?
(3) Test the null hypothesis that ros has no effect on salary against the
alternative that ros has a positive effect. Carry out the test at the 10%
significance level.
試驗兩個假設: 一,若ros對CEO薪水沒有影響, 相對於此,另試驗ros對CEO 薪水有正面影
響. 試驗數據: 以10%為準
(4) Would you include ros in a final model explaining CEO compensation in
terms of firm performance? Explain.
在用最後根據公司表現解釋CEO薪水時,你會不會將ros 包括在最後模型裡?請解釋

4.4 are rent rates influenced by the student population in college town? Let
rent be the average monthly rent paid on rental units in a college town in
the US. Let pop denote the total city population, avginc the average city
income, and pstscu the student population as a % of the total population. 1
model to test for a relationship is
在大學城裏,房租是不是受到學生人數的影響呢? 假設 rent 是美國的大學城中每月平均
房租, 假設pop 代表全部的大學城人數, avginc表示大學城的平均收入, pstcu 則是學生
人數(是為百分比,指學生佔全部人數的百分比). 為試驗其關係,其中之一的模型是:
log(rent)= β0 +β1 log(pop) +β2 log (avginc) +β3 pststu +u

(1) State the null hypothesis 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.
假設,學生數佔總人數的百分比對房租不會造成影響,請討論如果有所影響的狀況,如果有,
因素會是甚麼呢?
(2) What signs do you expect for β1 and β2?
預估的β1和β2是?
(3) The equation estimated using 1990 data from rental.RAW for 64 college
towns is
根據1990年的rental.RAW, 全美64個大學城的房租方程式是
^ ^ ^
log (rent)= 0.43 + 0.66log(pop) + 0.507 log(avginc) +0.0056pctstu
n=64, R^2=0,458

what is wrong with the statement: A 10% increase in population is associated
with about a 6.6% increase in rent?
依照這個方程式，以下這句話哪裡是錯的? 當大學城里的人口增加了10%, 房租也增加
6.6%?

(4) Test the hypothesis stated in part (1) at 1% level
假設第一題的數據是1%, 檢視第一題假設




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