"The essence of all things is numbers." -- (Pythagoras, ca 550 B.C.) The origin of some mathematical words. Calculus: From the Latin word calculus, meaning "small stone." Stones were used in many ancient counting processes. Circumference: From the Latin word circumferre, meaning "to carry around." Hypotenuse: From the Greek words hypo and teinein, meaning "to stretch under." Theorem: From the Greek word theoros, meaning "spectacle, to look at." To the ancient Greeks, theorems were statements to be observed as laws. What did Herkimer call the mafia leader who retired and went into farming? Answer: The Sodfather. Things Herky would like to know: Is it true that people who have the last laugh are also the slowest thinkers? Do atheists have financial problems because they are a non-prophet organization. ASSIGNMENT #25 Reading: Section 4.1, pages 190 - 195. Exercises: 4.1 and 4.2 (page 188). For each data set, produce a scatter plot. Then come up with the following prediction models. Produce a residual plot for each model. linear: y(hat) = a + bx exponential: y(hat) = abx power: y(hat) = axb Log[y(hat)] = a + bx Log[y(hat)] = a + bLog(x) You are in Section 4.1

OK, don't get overwhelmed here. Just keep in mindthat there are various models that one can attempt to fit to datarepresented in a scatter plot. Sometimes logarithmic models are veryuseful.

Suppose that a prediction model has the formLog[y(hat)] = .0456 + 1.65x. What would this model predict for an xvalue of 2? Substituting into the prediction model yields Log[y(hat)]= .0456 + 1.65(2) = 3.3456. Hence y(hat) = 103.3456 = 2216.15.

Note very carefully that there is no indicationwhatsoever that the model above is a good one. That is, there is noindication that the model "fits" the data well. I wouldn't want topredict that 2,216 is a reasonable estimate when x = 2 unless I hadmore information, such as a scatterplot or a residual plot.

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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. NewYork, 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)