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BEA621S - BASIC ECONOMETRICS FOR AGRICULTURE - 2ND OPP - NOV 2024 |
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" nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCESAND APPLIED SCIENCES
SCHOOL OF AGRICULTURE AND NATURAL RESOURCES.SCIENCES
DEPARTMENT OF AGRICULTURAL SCIENCESAND AGRIBUSINESS
QUALIFICATION: BACHELOR OF SCIENCE IN AGRICULTURE (AGRIBUSINESS MANAGEMENT)
QUALIFICATION CODE: 07BAGA
LEVEL: 7
COURSE CODE: BEA621S
COURSE NAME: BASICECONOMETRICSFOR
AGRICULTURE
DATE: JANUARY 2025
PAPER 2
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER(S) Prof David Uchezuba
MODERATOR: Mr Mwala Lubinda
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers.
PERMISSIBLE MATERIALS
1. Examination question paper
2. Answering book
THIS QUESTION PAPER CONSISTS OF 12 PAGES (Excluding this front page}
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SECTION 1 MULTIPLE CHOICE (20 MARKS)
Question 1
The relationship between a farmer's consumption expenditure (Y} and income {X} is
expressed as follows, E(y Ix;)= f(x;) .Which of the following statements about the
equation is incorrect?
A} It is known as the conditional expectation function
B} It is known as the population regression function
C} It is known as the population regression
D} It is known as the population distribution function
Question 2
Which of the following is incorrect about the interpretation of the
equation Y; = /31 + /32x 1 + /32x2 + µ; ?
A} The expected mean value of y is conditionally related to x;
B} The values of x are unobservable
C} The expected mean value or average response of Y varies with X
D} The equation is a linear function
Question 3
Y; /J /J If an estimable model is given as, = 1 + 2X; +µ;.Which of the following statements is
incorrect?
A} The equation is a sample regression function
/J B} The 2 is the estimator for /32
/J C} The value of 2 is known as the parameter estimate
/J D} The value of 2 cannot be negative
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Question 4
Y; fi µ; Which of the following parameters in the equation = jJ1 + 2X; + can be calculated
L:XY L~;' , using the formula?
where x; = (X -X) and Y; = (Y -Y).
A) P2
B) P1
C) .r;
D) µ;
Question 5
The function y = f (x) is said to be a linear function of ( x), which of the following
statements is incorrect about this linear function?
A) x must appear with a power or index of 1 only.
B) x must not be multiplied or divided by any other variable
C) The rate of change of y with respect to x must be independent of the value of x
D) x can appear as a square root (
Question 6
Consider the following models
E(y / X;) = /31+ /32X; 2 + µ; .....................................................................(.A.. )
E(y/ x;) =/31+ /J;x; + µ; ......................................................................(.B..)
Which of the following statements about equations (A) and (B) is incorrect?
A) Equation (A) is linear in parameter and (B) is non-linear in parameter
B) Equation (A) is linear in variable and (B) is non-linear in variable
C) Equation (A) is non-linear in variable and (B) is linear in variable
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D) Equation (A) is linear in parameter and (B) linear in variable
Question 7
The farmer's consumption function is fitted as
Y; = /Ji+ /J2X; + µ;
Which of the following is INCORRECTabout why µ; was included in the model?
A) We do not know other variables affecting consumption expenditure ( y)
B) Even if we know, we may not have information (data) about all factors affecting ( y)
C) There may be measurement errors in the way data was collected
D) We include A because it is a non-random and systematic component of the model
Question 8
According to the Gauss-Markov theorem, which of the following statements is NOT CORRECT?
An estimator says the ordinary least square (OLS)estimator jJ2 , is said to be the best linear
unbiased estimator of /32 , if the following conditions hold.
A) jJ2 , must be a linear function of the dependent variable ( y)
B) jJ2 , must be unbiased, i.e, its average or expected value E(P 2 ) must be equal to /32
C) jJ2 , must have minimum variance
D) jJ2 , must have a mean of zero
Question 9
An unbiased estimator such as jJ2 , one with the least (minimum) variance is said to be
A) An inefficient estimator
B) An efficient estimator
C) A random noise
D) An asymptote
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Question 10
Consider the following regression model estimated using the OLSmethod.
y =463.5136-0.390lx 1 +0.17925x 2
(91.2835) (0.1213) (0.0477)
(Standard errors are in parenthesis)
Using equation (12.1), calculate the t-statistic for the x1 and x2 variables
A) 3.2159 and 3.710
B) 3.2801 and 3.7578
C) 3.2159 and 3.7578
D) 3.2009 and 3.7011
Question 11
Which one of the following incorrectly defines the coefficient of correlation between variables?
A. Its value is between -1 and +l.
B. It can be positive or negative
C. It is a measure of association
D. It is the same as R2
Question 12
The statistical significance of a parameter in a regression model refers to:
a) The conclusion of testing the null hypothesis that the parameter is equal to zero,
against the alternative that it is non-zero.
b) The probability that the OLSestimate of this parameter is equal to zero.
c) The interpretation of the sign (positive or negative) of this parameter.
d) All of the above
Question 13
All of the following are possible effects of multicollinearity EXCEPT:
a) the variances of regression coefficient estimators may be larger than expected
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b) the signs of the regression coefficients may be opposite of what is expected
c) a significant F ratio may result even though the t ratios are not significant
d) removal of one data point may cause large changes in the coefficient estimates
Question 14
Suppose that you estimate the model Y =SO+B1X+ u. You calculate residuals and find that
the explained sum of squares is 400 and the total sum of squares is 1200. The R-squared is
a) 0.25
b) 0.33
c) 0.5
d) 0.67
Question 15
In linear regression, the assumption of homoscedasticity is needed for
I. unbiasedness
II simple calculation of variance and standard errors of coefficient estimates.
Ill. The claim that the OLSestimator is BLUE.
a) I only.
b) II only.
c) Ill only.
d) II and Ill only.
Question 16
Which of the following is/are consequences of over-specifying a model (including
irrelevant variables on the right-hand side)?
I. The variance of the estimators may increase.
II. The variance of the estimators may stay the same.
Ill. Bias of the estimators may increase.
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a) I only.
b) II only.
c) Ill only.
d) I and II only.
Question 17
Heteroscedasticity means that
a) Homogeneity cannot be assumed automatically for the model.
b) the observed units have different preferences.
c) the variance of the error term is not constant.
d) agents are not all rational.
Question 18
By including another variable in the regression, you will
a) look at the t-statistic of the coefficient of that variable and include the variable
only if the coefficient is statistically significant at the 1% level.
b) eliminate the possibility of omitted variable bias from excluding that variable.
c) decrease the regression R2 if that variable is important.
d) decrease the variance of the estimator of the coefficients of interest.
Question 19
Which of the following statements is TRUEconcerning OLSestimation?
a) OLSminimises the sum of the vertical distances from the points to the line
b) OLSminimises the sum of the squares of the vertical distances from the points to
the line
c) OLSminimises the sum of the horizontal distances from the points to the line
(d) OLSminimises the sum of the squares of the horizontal distances from the points
to the line.
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Question 20
The residual from a standard regression model is defined as
a) The difference between the actual value, y, and the mean, y-bar
b) The difference between the fitted value, y-hat, and the mean, y-bar
c) The difference between the actual value, y, and the fitted value, y-hat
d) The square of the difference between the fitted value, y-hat, and the mean, y-bar
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SECTION2 TRUE OR FALSEQUESTIONS{20 Marks}
Assume a regression model of consumption y = f} 1+/Ji·+ 11_
I}.
The t-test of significance requires that the sampling distributions of estimators jJI and
ft2 follow the normal distribution. True or False
II}. Even though the disturbance term in the CLRM is not normally distributed,
the OLSestimators are still unbiased. True or False
Ill}. If there is no intercept in the regression model, the estimated 11.(= u.)will not sum to
I
I
zero. True or False
IV}. The p-value and the size of a test statistic mean the same thing. True or False
V}. In a regression model that contains the intercept, the sum of the residuals
is always zero. True or False.
VI}. If a null hypothesis is not rejected, it is true. True or False.
fi VII}. The higher the value of a~, the larger the variance of 2• True or False.
VIII}. The conditional and unconditional means of a random variable are the
same things. True or False
IX} In the two-variable PRF,if the slope coefficient f} 2 is zero, the intercept /J1
y. is estimated by the sample mean True or False
X}. The conditional variance, var( y /r;) =rr2, and the unconditional variance
of Y, vary = q'2 .y , will be the same if X did not influence Y. True or False
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SECTION 3 ESSAY-TYPEQUESTIONS (60 Marks)
Question 1 (20 Marks)
1.1. The average salary of thirteen workers and their level of education was analyzed to
determine whether education can explain the variation in salary earned using an
ordinary least square method represented by the following model, y = /J1+ f}2.r + ".
Where y = salary earned (million$) x = years of education and u = error term. The sum
of the squares of the analysis is given as follows.
LY _Lx II
=112.771
II
=156
i=I
i=I
II
_L(y - y) 2 = I05. L2
i=I
II
LiJ•}'I.x.I = I31. 7856
i=I
II
_Lx2 = 182
i=I
rII
rr2 =9.6928
i=I
Calculate the value of the following
1.1.1 The slope parameter
1.1.2. The intercept parameter
1.1.3. The variance of the regression
1.1.4. The variance of slope parameter
1.1.5. The explained sum of squares
1.1.6. The total sum of squares
1.1.7. The coefficient of determination
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
1.2 . Fit the equation of the regression line
1.3. Predict the mean inventory value y for x = 10.90
1.4. Interpret the value of the slope parameter
(2 Marks)
(2 Marks)
(2 Mrks)
Question 2 (20 Marks)
1.1. Use the output of the regression in question 1.1. to set up an Analysis of Variance
(ANOVA) table using the format in Table 1.
(10 Marks)
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Table 1
ANOVATABLE
Source of variation df
SS
MSS
F-stat
Prob
ESS
()
RSS
()
TSS
()
Note: ESS= Explained sum of squares, RSS= Residual Sum of Squares, TSS= Total sum of
squares.
1.2. Determine the 95 % confidence interval for the true value of the salary of workers
given their education level.
(5 Marks)
1.3. A post-regression diagnostic shows the following distribution of the data, skewness=
-0.3937, Kurtosis= 2.0462. Calculate the Jarque-Bera statistics
(2 Marks)
1.4. What is the optimal value of the distributions of this test?
1.4.1 Skewness
(1 Mark)
1.4.2. Kurtosis
(1 Mark)
1.5. What is the null hypothesis of this test?
(1 Mark)
Question 3 (20 Marks}
3.1. What are the consequences of the following violation of a classical linear regression
model?
3.1.1 Non-linearity in regression parameter
(2 Marks)
3.1.2 Stochastic regressors in a regression model
(2 marks)
3.1.3. Non-zero mean of the disturbance term
(2 marks)
3.1.4. Heteroscedasticity in the model
(2 marks)
3.1.5. Auto-correlated disturbances
(2 marks)
3.1.6. Sample observation is less than the number of regressors
(2 marks)
3.1.7. Insufficient variability in regressors
(2 marks)
3.1.8. Multicollinearity
(2 marks)
3.1.9. Specification bias
(2 marks)
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3.1.10. Non-normality of disturbances
Formulas and statistical tables
N
LX;Y;
/J2=-i=-~--
Z:xi2
i=I
= R2 1- N i=I
, or
Z:CY-;Y) 2
i=I
N
(LX;YY
= ( R2
Ni=I N
)
LX;2LY;2
i=I
i=I
JB=n
[
-S+2---
6
(K
-3)
24
2
]
(2 marks)
f = /32-/32
se(/32 )
~,""" ESS = /J;~x-:-")
-. I
I
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T-distribution table
Cl
,
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1a
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
OC'
0.25
0.50
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.6S5
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.681
0.679
0.677
0.674
0.10
0.20
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.303
1.296
1.289
1.282
0.05
0.10
6.314
2.920
2.353
2.132
2.015
i.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.671
1.658
1.645
0.025
0.05
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.000
1.980
1.960
0.01
0.02
31.821
6.965
4.54
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.390
2.358
2.326
0.005
0.010
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.70.,.
2.660
2.617
2.576
0.001
0.002
318.31
22.327
10.214
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.610
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.307
3.232
3.160
3.090
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