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Curve Fitting

Resources

Anscombe's
Datasets

Curve Fitting
(888K)

Assignment

Pricing Diamond Rings

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

   Nonlinear regression, also known as curve fitting, nicely integrates statistics and the study of functions. And if in the study of polynomials, exponential or log functions or periodic functions students in your classroom are working with real problems containing real data (and I hope they are) then there is no choice about including this topic. It's already there.

Curve Fitting

The paper Curve Fitting, available as a Word 2 document only, discusses the mathematics needed to understand nonlinear regression. It includes some fully worked examples of how to determine which nonlinear function best fits a set of data as well as a sample assignment. Note that the file is quite large (888K) as it contains numerous screen graphics from a graphics calculator and statistics software.

Anscombe's Dataset

F.J. Anscombe was a pioneer in demonstrating the importance of looking at a set of data before choosing which analyses were appropriate. He created a quartet of paired datasets that wonderfully illustrate this. Anscombe's Datasets contain masters of two overhead transparencies - the first has F.J. Anscombe's famous quartet of datasets with some summary statistics and the second has the scatterplots of these datasets.

Pricing Diamond Rings Assignment

This document is an assignment on finding a regression equation relating the price of a diamond ring with the size of the diamond. It looks at both linear and nonlinear models. Students will need to be familar with both linear and nonlinear regression, including using a curve fitting software program such as CurveExpert.

The data and the idea for this assignment came from the article Diamond Ring Pricing Using Linear Regression in the Journal of Statistics Education v.4, n.3 (1996) by Singfat Chu.

Future Developments

There has been an interesting discussion on the ap-stat mailing list about the interpretation of r and r2 when dealing with nonlinear data. I haven't absorbed it all yet, but when I do I will make a document that discusses this issue available from this page .

| Read Me First! | Introduction | Acknowledgements |
| Looking for Patterns |Stemplots | Dotplots | Histograms |
| Measures of Location | Measures of Spread |
| Boxplots | Normal Plots | Scatterplots |

| Assessment | Datasets | Resources |
| VISITOR'S BOOK | SEARCH | HOME |

| Linear Regression | Normal Distribution |
| Probability | Sampling | Confidence Intervals |
| Hypothesis Testing | Non Linear Regression |