Questions for Practice/Assignment
SET A
Candidates are expected to answer the questions in their own words as far as
practicable. The figures in the margin indicate full marks.
Group A
Answer any TWO questions. ( 2×20=40 )
1. Derive the normal equations to estimate the parameters in a two-
independent variable linear regression model using ordinary least
squares technique.
2. What is meant by multicollinearity? What are its types, causes,
consequences, detection methods and remedial measures?
3. Following table gives the information on consumption (Y) and disposable
income (X) of 12 persons.
Person 1 2 3 4 5 6 7 8 9 10 11 12
Y 124 130 106 142 128 102 148 122 154 108 110 150
X 140 156 118 160 148 114 164 136 178 126 130 170
Estimate the linear regression equation of Y on X. Also calculate
a) Estimate linear regression equation of Y on X. (12)
b) Find Coefficient of determination (R2). (2)
c) Find the variances of the estimated coefficients. (4)
d) Find t-values for the coefficients. (2)
Group B
Answer any SIX questions. ( 6×10=60 )
4. What are the assumptions of ordinary least squares method?
5. Prove that total sum of squares (TSS) is equal to the sum of explained
sum of squares (ESS) and residual sum of squares (RSS).
6. Discuss the procedure of White’s test for the test of heteroscedasticity.
7. Define dummy variable. When does the problem of dummy variable trap
occur? Explain the uses of dummy variables as explanatory variables.
8. What is meant by normality assumption? Discuss the procedure for
performing Jarque-Bera (JB) test for normality. Also point out the
limitations of this test. (3+5+2)
9. A researcher estimated a linear regression equation of child mortality per
1000 live births (CM) on per capita GDP (PGDP) and female literacy rate
(FLR) measured in percent for 64 countries. Using a statistical software,
she obtained the following results:
CM hat = 263.6419 – 0.0056 PGDP – 2.2316 FLR
se (11.5932) (0.0019) (0.2099)
R = 0.7077
2 Adj R = 0.6981
2
a) Interpret the above results.
b) Find the t-values and interpret them.
c) Find F and interpret it.
10. The following regression equation is estimated as a production function
(as usual notations):
log Q hat = 1.37 + 0.632 log K + 0.452 log L
se (0.257) (0.219)
R = 0.98
2 N = 40
a) Interpret the coefficients and the R2 value.
b) Test for the significance of the coefficients.
c) Transform this equation into the Cobb-Douglas production function.
d) State the nature of the returns to scale as shown by this function.
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Questions for Practice/Assignment
SET B
Candidates are expected to answer the questions in their own words as far as
practicable. The figures in the margin indicate full marks.
Group A
Answer any TWO questions. ( 2 × 20 = 40 )
11. Derive the normal equations to estimate the parameters in a three-
independent variable linear regression model using ordinary least
squares technique.
12. Explain the procedure to estimate the parameters of a linear regression
equation by using the method of maximum likelihood estimation.
13. Following table gives the information on consumption (Y) and disposable
income (X) of 12 persons.
Person 1 2 3 4 5 6 7 8 9 10 11 12
Y 110 110 112 118 122 126 130 132 144 148 152 156
X 114 118 126 130 136 140 148 156 160 164 170 178
e) Estimate linear regression equation of Y on X. (12)
f) Find Coefficient of determination (R2). (2)
g) Find the variances of the estimated coefficients. (4)
h) Find t-values for the coefficients. (2)
Group B
Answer any SIX questions. ( 6 × 10 = 60 )
14. What are the assumptions of ordinary least squares method?
15. Write a note on lagged models with its usage in econometrics.
16. Write a note on dummy variables as regressors.
17. Describe the relationship between hypothesis testing and confidence
interval.
18. Write a note, with its properties, on the Logit model.
19. The demand function for a commodity is given as Y = b 0 + b1 X1 + b2 X2,
where Y = quantity demanded, X1 = price of the commodity (in Rs), and
X2 = income of the consumer. The following intermediate results are given
(the variables are measured as the deviations taken from their respective
means where Y bar = 70, X1 bar = 6, and X2 bar = 1100) from 15
observations.
Σx1y = -505 Σx2y = 107,500 Σx1x2 = -11,900
Σx1 = 60
2 Σx2 = 2,800,000
2 Σy2 = 4,600
d) Fit an OLS regression equation from the above results. (7)
e) Interpret the regression coefficients. (3)
20. A researcher is trying to estimate a linear regression equation of Y on
three independent variables X1, X2, and X3 with 35 observations. Before
estimating the regression equation she tries to test for any
multicollinearity in the model. She then calculated simple correlation
coefficients between the independent variables and found the results as
follows (as usual notations): r12 = 0.5, r13 = 0.4, and r23 = 0.2.
Test whether there exists any multicollinearity by applying the Farrar-
Glauber test. If so, suggest for the remedial measure to remove
multicollinearity and test whether your measure removes the problem of
multicollinearity or not. (5+5)
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Questions for Practice/Assignment
SET C
Candidates are expected to answer the questions in their own words as far as
practicable. The figures in the margin indicate full marks.
Group A
Answer any TWO questions. ( 2 × 20 = 40 )
21. Describe the procedure to estimate the parameters of a linear regression
equation by using the method of maximum likelihood estimation.
22. What is meant by autocorrelation? Explain the method of Durbin-Watson
test for autocorrelation. Also describe about one remedial measure to
remove autocorrelation. (5+12+3)
23. Following table gives the information on the production of corn (in
quintals) and the use of fertilizer (in kgs.) in ten identical plots of land.
Plot 1 2 3 4 5 6 7 8 9 10
Corn 40 44 46 48 52 58 60 68 74 80
Fertilizer 6 10 12 14 16 18 22 24 26 32
a) Estimate the linear regression equation of corn on fertilizer. (12)
b) Find the coefficient of determination (R2). (2)
c) Calculate the variances of the coefficients. (3)
d) Construct the 95% confidence intervals for the coefficients. (3)
Group B
Answer any SIX questions. ( 6×10 = 60 )
24. What is meant by normality assumption? Discuss the procedure for
performing Jarque-Bera (JB) test for normality. Also point out the
limitations of this test. (3+5+2)
25. Discuss the procedure of Goldfeld-Quandt method for the test of
heteroscedsticity.
26. Write a note, with its properties, on linear probability model.
27. Describe the relationship between hypothesis testing and confidence
interval in regression analysis.
28. A researcher is trying to estimate a linear regression equation of Y on
three independent variables X1, X2, and X3 with 35 observations. Before
estimating the regression equation she tries to test for any
multicollinearity in the model. She then calculated simple correlation
coefficients between the independent variables and found the results as
follows (as usual notations): r12 = 0.5, r13 = 0.4, and r23 = 0.2.
Test whether there exists any multicollinearity by applying the Farrar-
Glauber test. If so, suggest for the remedial measure to remove
multicollinearity and test whether your measure removes the problem of
multicollinearity or not. (5+5)
29. A researcher estimated a regression equation of wheat production (Y),
measured in quintals, on fertilizer (X), measured in kgs, with 10
observations. He estimated the regression equation as Ŷ = 27.12 + 1.66 X
with the intermediate results as Mean of X = 18, Σx2 = 576, and Σû2 = 47.31
(as usual notations). Calculate the 95 percent confidence (or forecast)
interval for Y if (a) X = 35 and (b) X = 25.
30. The following linear probability model was estimated from a sample of
15 senior MBA students of Lockdown Management College (LMC).
mstatus = ‒1.6672 + 0.0975 age ‒ 0.5826 gender
se (1.8235) (0.0694) (0.2110)
F = 4.48 R2 = 0.4276 Adj R2 = 0.3322
where mstatus denotes the marital status (=1, if married; 0 otherwise),
age denotes the age (in years), and gender denotes the gender (=1, if
male; 0, if female). Figures in parentheses are respective standard
errors.
a) Interpret the coefficients. (2)
b) Estimate the value of mstatus for a 26-year old female. What will
be the similar value for a 26-year male? Interpret the values. (6)
c) What do the negative sign and the value of the gender coefficient
mean? (2)
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