ASSIGNMENT 2 2026 ANSWERS
, QUESTION A1
(a) Briefly explain
i. Stochastic error term
This is a random variable included in a regression model to capture the influence of all
factors affecting the dependent variable that are not explicitly included in the model. It
accounts for randomness, measurement errors, omitted variables, and the inherent
unpredictability of human behaviour. It is called "stochastic" because it is random and not
perfectly predictable. Therefore, the stochastic error term (εi) is the true but unobserved
error term as in Yi = β0 + β1Xi + εi
ii. A regression analysis
It is a statistical technique that attempts to “explain” movements in one variable, the dependent
variable, as a function of movements in a set of other variables, called the independent (or
explanatory) variables, through the quantification of one or more equations. It allows
researchers to estimate how changes in the independent variable(s) are associated with
changes in the dependent variable, and to make predictions based on that relationship.
iii. The total sum of the squares
TSS measures the total variation in the observed values of the dependent variable around
its mean. It is calculated as the sum of the squared differences between each actual
observed value (Yᵢ) and the mean of Y (Ȳ). TSS is decomposed into the Explained Sum of
Squares (ESS) and the Residual Sum of Squares (RSS): TSS = ESS + RSS.
, QUESTION A1
(a) Briefly explain
i. Stochastic error term
This is a random variable included in a regression model to capture the influence of all
factors affecting the dependent variable that are not explicitly included in the model. It
accounts for randomness, measurement errors, omitted variables, and the inherent
unpredictability of human behaviour. It is called "stochastic" because it is random and not
perfectly predictable. Therefore, the stochastic error term (εi) is the true but unobserved
error term as in Yi = β0 + β1Xi + εi
ii. A regression analysis
It is a statistical technique that attempts to “explain” movements in one variable, the dependent
variable, as a function of movements in a set of other variables, called the independent (or
explanatory) variables, through the quantification of one or more equations. It allows
researchers to estimate how changes in the independent variable(s) are associated with
changes in the dependent variable, and to make predictions based on that relationship.
iii. The total sum of the squares
TSS measures the total variation in the observed values of the dependent variable around
its mean. It is calculated as the sum of the squared differences between each actual
observed value (Yᵢ) and the mean of Y (Ȳ). TSS is decomposed into the Explained Sum of
Squares (ESS) and the Residual Sum of Squares (RSS): TSS = ESS + RSS.
