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Addis Ababa University

School of Commerce

Department of Economics

Introduction to Econometrics (Assignment)

Review Questions

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:

; where are regression parameters and 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 , obtain the OLS estimators of

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

Estimate the standard errors of

Test the hypothesis that price influences supply

Obtain a 95% confidence interval for

The following table gives data on quantity supplied and prices of a certain commodities for ten years.

Price 2 3 6 9 10 12 16 19 22 24

Quantity Supplied 10 14 16 19 24 30 32 38 43 50

Plot the data in scatter diagram

Assume that quantity supplied is linearly related to the price of commodity as

Q^s=β_0+β_1 P+U_i. Estimate the model.

Interpret the estimated value of the regression coefficients obtained in (b).

Compute the correlation coefficient (r) and coefficient of determination (r^2)

Interpret the result obtained in d.

Consider the classical regression model Y_i=β_0+β_1 X_i+U_i.The higher the value of σ^2, the larger is the variance of OLS estimates of β ̂_1 and β ̂_2.True or False. Explain briefly?

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).

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.

Consider the OLS regression

C ̂_i=4.4+0.7Y_i

(3.2) (0.39) n=10.

Where C ̂_i is the predicted consumption and Y_i is income.

Construct a 95% confidence interval for the intercept

Construct a 95% confidence interval for the slope.

Test the hypothesis that the true value of the slope is 1.5

Test the hypothesis that the true value of the slope is 1.0

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.

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