Exam (elaborations)
ECS3706 Assignment 2 Semester 2 2023 – DUE 29 SEPT 2023
- Course
- Econometrics (ECS3706)
- Institution
- University Of South Africa
QUESTIONS WITH ANSWERS
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ECS3706 Assignment 2Semester 2 2023 – DUE 29
SEPT 2023
lenovo
[COMPANY NAME] [Company address]
, ECS3706 Assignment 2 Semester 2 2023
QUESTION A1 (15 marks)
(a) One of the most challenging concepts to master in this module is
distinguishing between the stochastic error term and the residual. List
three differences between the stochastic error term and the residual (3)
Nature: The stochastic error term (ε) represents unobservable, inherent
randomness in a statistical model, while the residual (e) is the difference
between the observed values and the predicted values.
Assumptions: The stochastic error term is assumed to follow certain statistical
properties, often including a mean of zero and constant variance, whereas the
residual is the actual deviation from the model's predictions and may not always
meet these assumptions.
Purpose: The stochastic error term is a theoretical concept used to formulate
statistical models, while the residual is a specific data point's deviation from the
model, often used for model evaluation and diagnostics.
(b) Explain in detail how Ordinary Least Squares (OLS) works in
estimating the coefficients of a linear regression model. (3)
Ordinary Least Squares (OLS) is a method for estimating the coefficients of a
linear regression model by minimizing the sum of squared residuals. Here's a
detailed explanation:
Model Specification: Start with a linear regression model of the form: Y = β0 +
β1X1 + β2X2 + ... + βn*Xn + ε, where Y is the dependent variable, X1, X2, ...,
Xn are the independent variables, β0, β1, β2, ..., βn are the coefficients to be
estimated, and ε is the error term.
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