Useful Data Transformations

11 Pages Posted: 21 Oct 2008

See all articles by Phillip E. Pfeifer

Phillip E. Pfeifer

University of Virginia - Darden School of Business

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This note addresses what can be done in those situations where it is not reasonable to assume that the relationship between the dependent second-independent variables is linear.




One of the important assumptions behind the linear model is that the mean of Y is linearly related to X:

mean of Y½X = a + bX

An implication of this assumption is that the change in the mean of Y for a unit increase in X is equal to b, a constant, regardless of the magnitude of X. For example, the point forecast of Y is b units higher at X = 11 than at X = 10, and it is also b units higher at X = 91 than at X = 90, even though on a percentage basis the change from 90 to 91 is much smaller than the change from 10 to 11. Although this linearity assumption is often reasonable, especially over a limited range of X and Y values, situations will arise where it is not tenable.

Figure 1.

. . .

Keywords: quantitative analysis, general, regression analysis, statistics

Suggested Citation

Pfeifer, Phillip E., Useful Data Transformations. Darden Case No. UVA-QA-0329, Available at SSRN:

Phillip E. Pfeifer (Contact Author)

University of Virginia - Darden School of Business ( email )

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