ECS4863Assignment 1 2025
Unique Number:
Due date: 16 May 2025
QUESTION 1
1.1
Omitted variable bias occurs in a regression model when a relevant explanatory variable that
influences the dependent variable is left out of the model. This omitted variable must also be
correlated with at least one of the included explanatory variables. Its exclusion causes the
estimated coefficients to be biased and inconsistent, meaning they do not reflect the true
relationship.
A positive bias means the estimated coefficient is overstated — it is larger than its
true value.
A negative bias means the estimated coefficient is understated — it is smaller than its
true value, or possibly has the wrong sign.
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replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
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responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
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Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
1.1
Omitted variable bias occurs in a regression model when a relevant explanatory
variable that influences the dependent variable is left out of the model. This omitted
variable must also be correlated with at least one of the included explanatory
variables. Its exclusion causes the estimated coefficients to be biased and
inconsistent, meaning they do not reflect the true relationship.
A positive bias means the estimated coefficient is overstated — it is larger
than its true value.
A negative bias means the estimated coefficient is understated — it is smaller
than its true value, or possibly has the wrong sign.
1.2
When regressors are strictly exogenous, we can test for serial correlation
(autocorrelation in the error terms) using the Durbin-Watson test or the Breusch-
Godfrey test. In simple terms, serial correlation exists when the error terms are
correlated over time, violating the assumption of independence. Under strict
exogeneity, the tests are valid because the explanatory variables are not correlated
with past, present, or future errors, ensuring unbiased results when detecting serial
correlation.
1.3
Heteroscedasticity refers to the situation in which the variance of the error terms in a
regression model is not constant across all observations. This violates a key
assumption of the classical linear regression model. When heteroscedasticity is
present:
The Ordinary Least Squares (OLS) estimates remain unbiased, but
The standard errors are incorrect, leading to invalid hypothesis tests (e.g.
unreliable t- or F-statistics),
Unique Number:
Due date: 16 May 2025
QUESTION 1
1.1
Omitted variable bias occurs in a regression model when a relevant explanatory variable that
influences the dependent variable is left out of the model. This omitted variable must also be
correlated with at least one of the included explanatory variables. Its exclusion causes the
estimated coefficients to be biased and inconsistent, meaning they do not reflect the true
relationship.
A positive bias means the estimated coefficient is overstated — it is larger than its
true value.
A negative bias means the estimated coefficient is understated — it is smaller than its
true value, or possibly has the wrong sign.
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
1.1
Omitted variable bias occurs in a regression model when a relevant explanatory
variable that influences the dependent variable is left out of the model. This omitted
variable must also be correlated with at least one of the included explanatory
variables. Its exclusion causes the estimated coefficients to be biased and
inconsistent, meaning they do not reflect the true relationship.
A positive bias means the estimated coefficient is overstated — it is larger
than its true value.
A negative bias means the estimated coefficient is understated — it is smaller
than its true value, or possibly has the wrong sign.
1.2
When regressors are strictly exogenous, we can test for serial correlation
(autocorrelation in the error terms) using the Durbin-Watson test or the Breusch-
Godfrey test. In simple terms, serial correlation exists when the error terms are
correlated over time, violating the assumption of independence. Under strict
exogeneity, the tests are valid because the explanatory variables are not correlated
with past, present, or future errors, ensuring unbiased results when detecting serial
correlation.
1.3
Heteroscedasticity refers to the situation in which the variance of the error terms in a
regression model is not constant across all observations. This violates a key
assumption of the classical linear regression model. When heteroscedasticity is
present:
The Ordinary Least Squares (OLS) estimates remain unbiased, but
The standard errors are incorrect, leading to invalid hypothesis tests (e.g.
unreliable t- or F-statistics),
