Question

Choose any research problem of your own in which there is one dependent variable and two or more independent variables. From your choice, present a conceptual framework showing the relationship among variables . Argue for the theoretical rationale of the relationships among variables on the conceptual framework presented above . Write a regression model representing the above relationships

Answer 1

Regression models involve the following parameters and variables:

The independent variables, X and W

The dependent variable, Y

The error term, ε

The general regression function would be-

Y= f (X, W)

Where, f (X, W) is the statistical function involving independent variables X and W to arrive at the value of dependent variable Y.

Lets take a demographics example-

Suppose that a country contains Population- P_t persons at time t. The current population depends on population P_(t-1), Natural increase during period t- (t-1) and net migration during period t- (t-1).

Population t= Population _(t-1) +Natural Increase _{t- (t-1)} + Net Migration _{t- (t-1)}

Where-

Natural increase = Births _{t- (t-1)} – Deaths _{t- (t-1)}

Net Migration = Immigration _{t- (t-1)} – Emigration _{t- (t-1)}

Hence, change in population during period t will be-

Population t – Population _(t-1) = Natural Increase _{t- (t-1)} + Net Migration _{t- (t-1)}

Change (Population _t) = Natural Increase _{t- (t-1)} + Net Migration _{t- (t-1)}

Change (Population _t) = Births _{t- (t-1)} – Deaths _{t- (t-1)} + = Immigration _{t- (t-1)} – Emigration _{t- (t-1)}

This relationship might appear straightforward. As the logic might dictate, increase or decrease in population during time t will depend on the net change in number of living persons through births and deaths and also on net change of population in and out of the country through immigration and emigration. The relationship of dependent variable (population) with each of the independent variables (births, deaths, immigration and emigration) is linear.