ECON 505
Econometrics Midterm Fall 2014
Q-1) (30 pts) Using table 5.5 answer the following questions.
To find out if there is any relationship between teacher’s pay(salary) and per
student expenditure in public schools, the following model was suggested:
Payi=Beta1+Beta2*Spendi+ui
a) find β1(hat) and β2(hat). How do you interpret your estimate of β2(hat).
b) draw sample regression function for this regression model.
c) What is R2 ? What is your interpretation about R2.
d) establish a 90 percent confidence interval for β2. Would you reject the
hypothesis that the true slope coefficient is 3.(H0: β2 =3)
e) Is your estimate of β2(hat) significant at 1% level? How about 5%.
Q-2)(20 pts) Suppose you are given the following regression equation. :
Yi= β1 + β2Xi+u
If we add a constant value to each X value, does β2 and β1 change? Does it
change error terms? Show your work.
i
Q-3)(5 pts) if Var(u1)=Var(u2)=Var(u3)=....Var(un)=σ2 +1
Say if the variance of error term is heteroscedastic or homoscedastic.
Q-4)(15 pts) Suppose you are given the following equation. Yi= β1+u
Use OLS to estimate β1.
i
Q-5)(15 pts) if you are given the following regression equation : Yi= β1 +
β2Xi+u
i
a) write down the equation for the population regression function(PRF)
b) write down the equation for the sample regression function(SRF)
c) what is Yi-Yihat equal to?
d) what is Yi -E(Y/Xi) equal to?
Q-6)(15 pts) Consider the following regression output where the dependent
variable is yearly salary in dollars and independent variable is number of
school year finished.
Yihat=2033+4560Xi
se=(976) (1961)
a) how do you inerpret β2(hat)?
b)if n(sample size)=22 what is the p value of this regression.
c) for a person who went to school for 15 years, what is the expected salary.