Your Financial Tutorial

Financial Statistics: Linear Regression - part 3
All information are subject to terms of use

ASSUMPTIONS OF THE REGRESSION RESIDUALS

Building a regression line between on independent variable and one or many independent variables means that you assume that the relationship between all these variables is linear. In fact the linear regression is a particular case of the maximum likelihood method and, even if it simplifies your life on a pure mathematical point of view, this assumption must be tested.

Some statisticians have demonstrate that the linear regression can be used provided that u (regression residuals) has some characteristics:

1. the distribution of u follows a normal law (normality)

2. u tends to 0

3. u has a fixed variance (homoscedasticity)

4. all the u are independent (absence of autocorrelation)

5. u is a random variable.

6. u is independent of the other independent variables (serial independence)

For all the above assumptions, the statisticians have developed a huge range of tests.