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Exploring the Goodness of Fit in Linear Models - Some Final Thoughts

Scott A. Sinex

Students can use the scatter.xls spreadsheet to discover the influence of scatter or noise on the goodness of fit through a directed mode of questioning. Many real-world data sets, especially environmental data, can show considerable scatter. You and your students can explore the many data sets of Langkamp and Hull (2003).

We need to expose students to a wider range of data and even experimental situations where noise can be a problem. The use of r2 and residuals are good first steps that take advantage of available technology for students just starting to explore linear models. Ideal models are great as an early component of learning. However, examining real data puts the process of modeling into the real world of scientific study. This is just the rudimentary beginning of mathematical modeling, but it introduces students to science process skills and the thrill of discovery. Further limitations and other measures of the goodness of fit can be introduced to students as other non-linear models are encountered.

Scott A. Sinex, "Exploring the Goodness of Fit in Linear Models - Some Final Thoughts," Convergence (March 2005)