To clarify the clarification posted by dogboy, the assumptions of simple and multiple linear regression are as follows (these are called the Gauss-Markov conditions):
- Linear relationship between the independant variables and the dependant variable; if this is not the case, then one of the following steps is necessary:
- A polynomial term needs to be applied;
- The variable should be transformed (logarithm, square root, arcsine square root etc.);
- The suitability of a regression approach should be reconsidered.
- Homoscedasticity of the residuals
- Independance of the observations
- The independant variables must either be controlled or measured with great precision compared to the dependant variable; if this is not the case, then major axis regression should be applied
If these conditions are not met, not only will the beta coefficients be biased, but the model's predictive capacity will likely be misrepresented.