ECS4863
Assignment 1 2025
Unique #:
Due Date: 16 May 2025
Detailed solutions, explanations, workings and
references.
+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),
Which ultimately affects confidence intervals and the reliability of inferences.
1.4
Varsity Cube 2025 +27 81 278 3372
Assignment 1 2025
Unique #:
Due Date: 16 May 2025
Detailed solutions, explanations, workings and
references.
+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),
Which ultimately affects confidence intervals and the reliability of inferences.
1.4
Varsity Cube 2025 +27 81 278 3372
