Review Questions 1 Econometrics deals with the measurement of economic relationships which are stochastic or random. The simplest form of economic relationships between two variables X and Y can be represented by:
Yi =β0 +β1Xi +Ui ;where β0 and β1 =are regression parameters and
Ui = the stochastic disturbance term
What are the reasons for the insertion of U-term in the model?

2 The following data refers to the demand for money (M) and the rate of interest (R) in for eight different economics:
M (In billions) 56 50 46 30 20 R% 6.3 4.6 5.1 7.3 8.9
35 37 61 5.3 6.7 3.5
OLS estimators of
a. Assuming a relationship
α and β
M = α + βR + U i , obtain
the
b. Calculate the coefficient of determination for the data and interpret its value
c. If in a 9th economy the rate of interest is R=8.1, predict the demand for money(M) in
this economy.

3. The following data refers to the price of a good ‘P’ and the quantity of the good supplied, ‘S’.
P27514828
S 15 41 32 9 28 43 17 40
a. Estimate the linear regression line Ε(S) = α + βP
ˆ
b. Estimate the standard errors of αˆ and β
c. Test the hypothesis that price influences supply
d. Obtain a 95% confidence interval for α

4. The following results have been obtained from a simple of 11 observations on the values
of sales (Y) of a firm and the corresponding prices (X).
X = 519.18
Y = 217.82
∑X2 =3,134,543 i

i
Estimate the regression line of sale on price and interpret the results
∑XiYi =1,296,836 ∑Y 2 = 539,512
What is the part of the variation in sales which is not explained by the regression line?
Estimate the price elasticity of sales.
iii)

5. The following table includes the GNP(X) and the demand for food (Y) for a country over
ten years period.
year 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 Y 6 7 8 10 8 9 10 9 11 10
X 50 52 55 59 57 58 62 65 68 70
a. Estimate the food function
b. Compute the coefficient of determination and find the explained and unexplained
variation in the food expenditure.
c. Compute the standard error of the regression coefficients and conduct test of
significance at the 5% level of significance.

6. A sample of 20 observation corresponding to the regression model Yi = α + βX i + U i
gave the following data.

∑Y =21.9 i
∑X =186.2 i
∑(Xi −X)(Yi −Y)=106.4 a. Estimate α and β
∑(Y −Y)2 =86.9 i
∑(X −X)2 =215.4 i
b. Calculate the variance of our estimates
c. Estimate the conditional mean of Y corresponding to a value of X fixed at X=10.

7. Suppose that a researcher estimates a consumptions function and obtains the following
results:
C= 15 + 0.81Yd n=19
(3.1) (18.7) R2 = 0.99
where C=Consumption, Yd=disposable income, and numbers in the parenthesis are the ‘t-ratios’
a. Test the significant of Yd statistically using t-ratios
b. Determine the estimated standard deviations of the parameter estimates

8. State and prove Guass-Markov theorem

9. Given the model:
Yi =β0 +β1Xi +Ui with usual OLS assumptions.
variance.