## What are the key assumptions of linear regression models?

2 Oct, 2013 at 15:58 | Posted in Statistics & Econometrics | 1 Comment In Andrew Gelman’s and Jennifer Hill’s statistics book Data Analysis Using Regression and Multilevel/Hierarchical Models the authors list the assumptions of the linear regression model. The assumptions — in decreasing order of importance — are:

1. Validity. Most importantly, the data you are analyzing should map to the research question you are trying to answer. This sounds obvious but is often overlooked or ignored because it can be inconvenient. . . .

2. Additivity and linearity. The most important mathematical assumption of the regression model is that its deterministic component is a linear function of the separate predictors . . .

3. Independence of errors. . . .

4. Equal variance of errors. . . .

5. Normality of errors. . . .

Further assumptions are necessary if a regression coefficient is to be given a causal interpretation . . .

Normality and equal variance are typically minor concerns, unless you’re using the model to make predictions for individual data points.

Andrew Gelman

Yours truly can’t but concur (having touched upon this before here), especially on the “decreasing order of importance” of the assumptions. But then, of course, one really has to wonder why econometrics textbooks — almost invariably — turn this order of importance upside-down and don’t have more thorough discussions on the overriding importance of Gelman/Hill’s two first points …

## 1 Comment

1. This is a very sad list. First, if errors are independent, the coefficients are causal. Second, additivity and linearity (which is, by the way, saying the same thing twice) is up to you: Transform the data as you please (or use NLS). Third, equal variance? Ever heard of GLS? Normality of errors is not even a prerequisite for OLS. Only for small sample properties of inference.

This is a list of lies.

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