# 4 REGRESSION ANALYSIS

Regression analysis examines a dependence between two or more variables, e.g. an income may be determined by education, years of experience or gender, etc.

Equation which describes a linear dependence (relationship) between two variables is called a simple regression

\[\begin{equation} Y=\beta_0+\beta_1X+u \tag{2.5} \end{equation}\]

Variable \(Y\) on the right side is dependent variable (sometimes called endogenous

Variable \(X\) on the left side is independent variable (sometimes called exogenous)

Variable \(u\) on the left side is unobserved random variable (sometimes called error term)

Regression equation (2.5) suggests that \(X\) causes \(Y\)

Linear dependence can be measured by correlation coefficient, but correlation does not imply causality direction)

Parameters \(\beta_0\) and \(\beta_1\) are the constant and the slope, respectively. These population parameters are not known and should be estimated from the sample data

The slope coefficient provides information about change in \(Y\) with respect to one unit change in \(X\)

\[\begin{equation} \beta_1=\frac{\Delta Y}{\Delta X} \tag{4.1} \end{equation}\]