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ecs3706 assessment 2 semester 02 2023
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BMZ ACADEMY 061 262 1185/068 053 8213/0717 513 144
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ECS3706 Assignment 2 Semester 2 2023
QUESTION A1
a. Definition: The stochastic error term, also known as the disturbance term or the
random error term, represents the unexplained variation in the dependent variable
that cannot be accounted for by the independent variables. It is a theoretical concept
that is not directly observable. On the other hand, the residual refers to the actual
difference between the observed value of the dependent variable and the predicted
value based on the independent variables. It is calculated as the observed value
minus the predicted value.
Representation: The stochastic error term is typically denoted by "ε" or "u" in
equations and models, whereas the residual is denoted by "e" or "r". The stochastic
error term is usually represented in mathematical equations and models, while the
residual is calculated and observed in numerical values.
Interpretation: The stochastic error term is assumed to satisfy certain statistical
properties, such as having a mean of zero and being normally distributed. It
represents the overall randomness and unexplained variation in the model. On the
other hand, the residual represents the specific unexplained variation for each
individual data point. It indicates the deviation of a particular data point from the
predicted value based on the model.
b. Ordinary Least Squares (OLS) is a widely used method for estimating the
coefficients of a linear regression model. It aims to minimize the sum of squared
residuals between the observed and predicted values of the dependent variable.
The steps involved in estimatingthe coefficients using OLS are as follows:
Define the linear regression model: Start by defining the linear regression model
with the dependent variable (Y) and independent variable(s) (X). The model can be
represented as Y = β0 + β1X1 + β2X2 + ... + βkXk, where β0 is the intercept term
and β1, β2, ..., βk are the coefficients associated with each independent variable.
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