Regression  Assumptions
As with any other method, linear regression is based on assumptions
which have to be fulfilled for correct results:

The expected relationship between X and Y is linear: one should carefully
distinguish linear, curvilinear and nonlinear relationships. While curvilinear
relationships can be transformed into
linear ones, nonlinear relationships cannot.

All measurements are independent of each other; any trend over time, or
any common correlation to a third variable, must be avoided.

For each X, the Y values are distributed normally.

For each X, the Ydistribution has the same variance (homoscedastic
data). This requirement is often not met, especially with data covering
a large range (several orders of magnitude).
These assumptions should be checked by inspecting the data and
the residuals. One should always look at the XY plot, at the histogram of the residuals, and at the residuals plotted against X_{i}. Further, it is a good idea to check whether the residuals are uncorrelated (e.g. using the DurbinWatsonTest) as the confidence intervals of the parameters will be wrong in case of serial correlation among the residuals.
