Simple Regression Model

In economic analysis, there are two statistical techniques that are used to find the relations between two or several variables. There are two techniques: correlation and regression. Correlation shows how strong is the link between the analysed variables regression explains and allows to predict the value of one factor in relation to the others.

Simple regression aims to highlight the relationship between a dependent variable explained (endogenous) and an independent variable (explanatory, exogenous). The simple regression model (unifactorial regression model) is defined through a mathematical relation built up in the context of economic theory, which implies that the economic phenomenon is the result of two factors: the essential factor and the non-essential factors, invariable upon the economic phenomenon as effect (collected in the resultative variable).

The simple regression model is as follows:

Y = f(x) +

In a simple regression econometric model, the relation is as follows:

yi = b + a . Xi i+ i

Where:

Yi resultative characteristic (explained)

Xi factorial characteristic (explanatory)

Ei residual variable.

In order to form a hypothesis underlying the regression model we need to keep in mind the following:

I2: the data series is not affected by measurement errors

I2: the residual variable has zero mean

I3: the dispersion of the residual variable is invariable in time, namely it has the property of homoscedasticity

I4: the residues are not self-correlated
I5: the factorial (explicative) variable is not correlated with the residual variable
I6: the errors of the model are usually distributed according to a distribution of zero mean and 2

dispersion.