"One cannot escape the feeling that mathematical formula have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even then their discoverers, and that we get more out of them than was originally put into them." -- (Heinrich Hertz) Some 1500 years ago, an American Indian people called the Anasizi lived in what is now the southwestern United States. They, along with the Navajo and Pueblo tribes, produced coiled baskets, rugs, quilts, and clothing that displayed complex geometric patterns. How did Herkimer discover that it was raining cats and dogs? Answer: When he went outside, he stepped into a poodle. Herky 's friends: LUKE WARM...this guy doesn't like things too hot. ISSIAH LOTT...nobody can get this fellow to shut up. ASSIGNMENT #22 Reading: Study page 11A in the STAT PACK. Review Chapter 3 material, as necessary. Make sure you can interpret r2, the coefficient of determination. (Page 149). Exercises: 3.51 and 3.52, beginning on page 166. Problem 3.52 is an excellent "matching problem." Do this carefully. Think! For the data in 3.51, do the following. Plot the year (x) vs. record in seconds (y). Identify outliers and influential points. Find the LSRL and fit to the scatter plot. Interpret slope, y-intercept, r, and r2. Plot the residuals, with year as x-axis. Show that the sum of the residuals is zero. Look over the questions asked in in the text relating to this problem. Jot down a brief response. to them.

You are working with ideas from Chapter 3.

Basically, the coefficient of determination, r2, is the percentage of the variation in the values of y that is explained by the least-squares regression line of y on x. Note that r2 is never negative. If r2 is close to 1, you have a reasonably good linear fit. Note, however, if you know only that r2 = .9876 (for instance), then r = .9938 or r = -.9938. Unless you have more information, you can't determine if you have a strong positive association or a strong negative association.

Experiment a bit with the spreadsheet program SCATTERPLOT/REGRESSION LINE. This interactive scatterplot allows you to input five points within a restricted domain. A scatterplot of the five points in displayed. The least squares regression line equation is also displayed. The program than produces two "extreme" points to the left and right of the original domain. These points are on the LSRL. They determine the line. You can clink on the line displayed and move it around so that it goes through these two points. You than have a scatterplot of five points along with the LSRL.

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York, W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. New York, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W. Norton & Company, 1982 (ISBN 0-393-09426-X)