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ECS3706 EXAM PACK 2021 [FROM JULY] QUESTION PAPERS & ANSWERS CALL;
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EXAM PACK LATEST2018, 2019, 2020 &
2021 JULY
MEMOS: EXAM PAPERS & ANSWERS
FOR MORE CALL 0763 468 675
,QUESTION A1 (15 marks)
(a) Briefly explain two shortcomings or weaknesses of econometrics. (4)
Econometrics depends on economic theory to provide the variables involved, the
direction of causality and the nature of the functional form.
Econometrics cannot resolve theoretical differences between different schools of
thought. Causality depends only on theory.
Econometrics can only determine correlation, which is the strength and nature of a
relationship. It cannot say anything about causality.
(b) Explain the meaning of an estimator (𝛽̂) in a regression equation. How does it differ
from 𝛽? (3)
𝛽 is the true (population) parameter and 𝐵̂ is the estimated (sample) parameter. the true
relationship between the Xs and Y where the εs take care of deviations in Y not explained by
the Xs. Note that the βs are unknown.
(c) Explain the meaning of R2 and adjusted R2. Refer to their respective shortcomings
and advantages. (Hint: Include the formula of the adjusted R2.) (4)
𝑅2 measures the quality of fit of a regression equation, for the cases of one and more than
one independent variables. It can be represented with the following equation:
Adjusted 𝑅 2 denotes by 𝑅̅ 2 is a modified version of R-squared that has been adjusted for
the number of predictors in the model. It is given by the equation below:
(d) Explain the difference between the error term (𝜀𝑖) and the residual term (𝑒𝑖). (4)
,The error term (𝜀𝑖) is the difference between the true line and the observed value of Y. The
residual term (𝑒𝑖) is the difference between the observed value and estimated value from the
regression equation.
QUESTION A2 (15 marks)
a) Besides the variation in the dependent variable (Y) that is caused by the independent
variable (X), there is almost always variation that comes from other sources as well.
This additional variation comes in part from omitted explanatory variables (e.g., X2
and X3). However, even if these extra variables are added to the equation, there still is
going to be some variation in Y that simply cannot be explained by the model. This
variation probably comes from sources such as omitted influences, measurement error,
incorrect functional form, or purely random and totally unpredictable occurrences. By
random we mean something that has its value determined entirely by chance.
This assumption of normality is not required for OLS estimation.
Question A2B
The error term can be thought of as the composite of a number of minor influences or
errors. As the number of these minor influences gets larger, the distribution of the error
term tends to approach the normal distribution. This tendency is called the Central
Limit Theorem. The t-test and F-test are not applicable unless the error term is normal
distributed.This assumption of normality is not required for OLS estimation. Its major
application is in hypothesis testing, which uses the estimated regression coefficient to
investigate hypotheses about economic behavior. One example of such a test is
deciding whether a particular demand curve is elastic or inelastic in a particular range.
b) Its major application is in hypothesis testing, which uses the estimated regression
coefficient to investigate hypotheses about economic behavior. One example of such a
test is deciding whether a particular demand curve is elastic or inelastic in a particular
range.
Even though Assumption VII is optional, it’s usually advisable to add the assumption of
normality to the other six assumptions for two reasons:
1. The error term can be thought of as the sum of a number of minor influences or errors.
As the number of these minor influences gets larger, the distribution of the error term tends
to approach the normal distribution.
2. The t-statistic and the F-statistic are not truly applicable unless the error term is normally
distributed (or the sample is quite large).
, c) It is not possible to take the logs of variables like gender or race as these you will need to
make use of dummy variables
d) Model specification results in the inclusion of an error term as an error term represents the
margin of error within a statistical model.
e) The error term helps in the omission of other variables for example in model underfitting
QUESTION A3 (15 marks)
(a) Explain the meaning of a type I error in hypothesis testing. Also explain the meaning
of the level of significance. (4)
Type I error: consists of rejecting the true hypothesis whilst type II error consist rejecting the
alternative hypothesis.
The level of significance is the measure of strength for given evidence against or for a given
variable in a regression model that suffices the rejection of the null hypothesis. It is denoted by
alpha and the lower the value the more statistically significant. In research 1% and up to 5%
level of significance is generally accepted in selected cases 10% may also be seen to be
statistically significant, however any greater value is not considered.
(b) Is there a relationship between the t-distribution and the F-distribution? Explain your
answer.(4)
There is no relationship that exists between t-dstibution and F-distribution the reason is first
assumption made regarding t-tests concerns the scale of measurement. The assumption for a t-
test is that the scale of measurement applied to the data collected follows a continuous or
ordinal scale, such as the scores for an IQ test and with regard to F-distibution Each group
sample is drawn from a normally distributed population.
(c) Does a higher level of significance increase the possibility of a statistically significant
regression coefficient? Explain your answer. (3)
The higher level of significance does reduce possibility of a statistically significant
regression coefficient, the greater the level of significance makes the variable less
important to affect the dependant variable. If a variable has low level of significance
for example 5% level of significance it means the variable does affect the dependant
variable by a greater magnitude.
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