10776

Comparing Regression Models with and without Data Transformation

This Demonstration shows the difference between regression models with and without data transformation. The transformed case estimates by minimizing the sum of squared differences between and . The untransformed case estimates by minimizing the sum of squared differences between and .

DETAILS

In this Demonstration, we plot the regression model to given data . To find the regression without transforming the data, we need to minimize the sum of the squares of the residuals
.
To find , we minimize with respect to . The value of is hence given by solving the nonlinear equation
. (1)
To avoid having to solve a nonlinear equation, we can transform the data and then use linear regression formulas to calculate . In this case
,
.
Then is given by minimizing
(2)
In this Demonstration, we show the regression model curves corresponding to values of from equation (1) (untransformed) and equation (2) (transformed).
For more information, see A. Kaw, D. Nguyen, and E. Kalu, Numerical Methods with Applications, 2010.

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.