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# What are the key assumptions of linear regression models?

Summary:
What are the key assumptions of linear regression models? In Andrew Gelman’s and Jennifer Hill’s 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.

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Lars Pålsson Syll considers the following as important:

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

In Andrew Gelman’s and Jennifer Hill’s 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 …

Yours truly can’t but concur — 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 …

Professor at Malmö University. Primary research interest - the philosophy, history and methodology of economics.