# I Central limit theorem, panel study

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1. Mar 25, 2017

I am doing a panel study with multiple linear regression.
When I want to make sure that the residuals are normally distributed, as is a requirement for the regression model, can I assume so due the Central limit theorem (given the size is sufficient)? Or does it not apply when there is a time dimension?
The study is based on 73 companies with variable values once a year for 6 or 7 years.

Mons

2. Mar 25, 2017

### Number Nine

The central limit theorem will not guarantee this; nor will anything, really. Given an appropriately chosen regression model, the errors may or may not be normally distributed. If they're not, then you'll have to either transform the data in some way, or fit a regression model with a different error distribution (which takes a fair bit of expertise).

A bigger problem is the fact that your errors will almost certainly be correlated, since companies are being measured repeatedly. This is really a time series problem, not a straightforward regression problem.