# Linear regression conditions

• Jun 8th 2009, 04:11 AM
kipperstein
Linear regression conditions
In order to run a simple linear regression and then analyze the results statistically when using the least squares approach, certain conditions must be satisfied. Which one of the following statements is NOT one of the conditions that must be satisfied?
a) The distribution of the Yi values must be normally distributed.
b) The distribution of the εi values must be normally distributed.
c) The distribution of the Xi values must be normally distributed
d) The variance σ2 must be constant
e) The εi error terms must be independent or at least uncorrelated among themselves.
• Jun 8th 2009, 07:22 AM
matheagle
The weakest of these is
c) The distribution of the Xi values must be normally distributed
since usually the x's are fixed.
We usually make the errors i.i.d. $N(0,\sigma^2)$ rvs which then makes the Y's $N(0,\sigma^2)$ rvs.
BUT there are all kinds of programs to analyze the data if the underlying distribution isn't normal or if the variances aren't constant...
BUT in the basic situation the x's aren't even random, they are fixed.
HOWEVER there is the random effect model, where the x's are not constant.

Some of this is lame, under normality independence is equivalent to uncorrelated.
And there is weighted least squares, which means that the epsilon's do not have constant variance.
BUT under the most basic situation, we need not have the x's as random.