Basic of Multiple Regression and Underlying Assumptions

Use of Multiple Linear Regression

• Identify relationship
• Test theories (CAPM)
• Forecast

Multiple Linear Regression

$$Y_i=b_0+b_1{x}_1+b_2{x}_2+\cdots +b_i{x}_i+ϵ$$

Assumptions

• Linearity
• Homoskedasity: Variance of error term is same for all observations
• Normality in error term
• Indendence:
  • Error term uncorrelated
  • No exact linear relation between independent variables (Multicolinearity)

Testing assumptions:

• Direct plot (Linearity)
• Variance Inflation Factor(VIF) and Tolerance (1/VIF) $\to$ Multicolinearity
• Correlation Matrix $\to$ Multicolinearity
• QQ-plot $\to$ Normality
• Scatter plot of residual versus variables $\to$ Homoskedascity