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 \(X\)

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