Regression Model with Transformations

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This Demonstration shows the simple linear regression model for various datasets. You can transform the response variable (i.e. the dependent variable), and display the least-squares fit, the coefficient of determination , and estimates of the marginal variance of , as well as the conditional variance assumed to be common across all values of . Box–Cox and Tukey power transformations are available; you can vary the power parameter and display a plot of the effect of various values of on . When the transformation used is either Box–Cox or Tukey's transformation, a plot of versus the parameter is shown.

Contributed by: Karl Heiner (SUNY at New Paltz) and Stan Wagon (Macalester College) (December 2015)
Open content licensed under CC BY-NC-SA



Snapshot 1: a linear fit to curvilinear data

Snapshot 2: a linear fit to curvilinear data with a log transformation on the response variable

Snapshot 3: a linear fit to curvilinear data with plot of versus power parameter for the Box–Cox transformation on the response variable

Data sources: lead [1], lichen [2], birth weight and AIDS [3], kittiwakes [4], Mazda prices [5], CPK enzyme [6]. For more information on linear statistical models including transformations and the coefficient of determination, see [7].


[1] J. L. Devore, Probability and Statistics for Engineering and the Sciences, Pacific Grove, CA: Brooks/Cole, 1991.

[2] J. L. Devore and K. N. Berk, Modern Mathematical Statistics with Applications, Belmont, CA: Thomson Brooks/Cole, 2007.

[3] A. J. Dobson, An Introduction to Generalized Linear Models, 2nd ed., Boca Raton: Chapman & Hall/CRC, 2002.

[5] G. K. Smyth. "Kittiwake Colonies." Australasian Data and Story Library (OzDASL). 2011.

[6] G. K. Smyth. "Age and Price of Mazda Cars." Australasian Data and Story Library (OzDASL). 2011.

[7] G. K. Smyth. "Bood CPK in Cross-Country Skiers." Australasian Data and Story Library (OzDASL). 2011.

[4] M. Kutner, C. Nachtsheim, J. Neter, and W. Li, Applied Linear Statistical Models, 5th ed., Boston: McGraw-Hill, 2005.

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