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 0 1 X i U i

; were

0 and

1 are regression parameters and

U i the stochastic disturbance term

What are the reasons for the insertion of U-term in the model?

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

35

37

61

R%

6.3 4.6

5.1

7.3

8.9

5.3

6.7

3.5

Assuming a relationship M R U i , obtain the OLS estimators o and

Calculate the coefficient of determination for the data and interpret its value

If in a 9th economy the rate of interest is R=8.1, predict the demand for money(M) in this economy.

The following data refers to the price of a good ‘P’ and the quantity of the good supplied, ‘S’.

P

2

7

5

1

4

8

2

8

S

15

41

32

9

28

43

17

40

Estimate the linear regression line (S ) P

Estimate the standard errors of ˆ and ˆ

Test the hypothesis that price influences supply

Obtain a 95% confidence interval for

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).

= 519.18

217.82

X 2 3,134,543

X iYi

1,296,836

Y 2 539,512

Estimate the regression line of sale on price and interpret the results

What is the part of the variation in sales which is not explained by the regression line?

Estimate the price elasticity of sales.

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

Estimate the food function

Compute the coefficient of determination and find the explained and unexplained variation in the food expenditure.

Compute the standard error of the regression coefficients and conduct test of significance at the 5% level of significance.

A sample of 20 observation corresponding to the regression model Yi X i U i

gave the following data.

Estimate and

Calculate the variance of our estimates

Estimate the conditional mean of Y corresponding to a value of X fixed at X=10.

Suppose that a researcher estimates a consumptions function and obtains the following results:

C 15

0.81Yd

n 19

(3.1)

(18.7)

R 2 0.99

where C=Consumption, Yd=disposable income, and numbers in the parenthesis are the ‘t-ratios’

Test the significant of Yd statistically using t-ratios

Determine the estimated standard deviations of the parameter estimates

State and prove Guass-Markov theorem (BLUE,) B- hat is Best, Linear, unbiased estimator of the true beta B