Central limit theorem, panel study

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SUMMARY

The discussion centers on the application of the Central Limit Theorem (CLT) in the context of a panel study involving multiple linear regression with data from 73 companies over 6 to 7 years. It is established that the CLT does not guarantee the normal distribution of residuals, especially when a time dimension is involved. The presence of correlated errors due to repeated measurements necessitates consideration of time series analysis rather than standard regression techniques. Transforming data or selecting a regression model with a different error distribution may be required to address non-normality.

PREREQUISITES
  • Understanding of multiple linear regression
  • Familiarity with the Central Limit Theorem
  • Knowledge of time series analysis
  • Experience with error distribution in regression models
NEXT STEPS
  • Explore techniques for transforming data to achieve normality in residuals
  • Learn about time series regression models and their applications
  • Investigate methods for diagnosing and correcting correlated errors in regression
  • Study alternative error distributions for regression analysis
USEFUL FOR

Researchers conducting panel studies, statisticians working with regression models, and data analysts focusing on time series data will benefit from this discussion.

monsmatglad
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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
 
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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.
 

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