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1 By: Chris Hartl A statistics learning project: 0 Slide 2 2 2 A sentence including a long underscore (______) denotes a question-and-answer exercise. Your next click will put an answer into the space. answer How the Presentation Works Slide 3 3 Presentation Enhancement This presentation is enhanced by the statistical features of the TI-83 calculator. The data used in the presentation can be found in TI-program form here. The raw data is located at the end of the presentation. Slide 4 4 Worksheets on This Presentation Some slides are worksheet slides, containing only open-ended questions. It is recommended that the user answer the questions with the data provided before proceeding to the answer slides. The answers to the worksheet are on the slides proceeding the worksheet slide. Slide 5 5 There are two basic types of transformations: single-variable, and multi-variable transformations. This slideshow will concentrate on one- variable and two-variable transformations. 1 Slide 6 6 1 I. Single Variable Transformations Slide 7 7 This is a sample. While this mean is accurate, it does not appear to come from a normal or ~N population, and thus, the assumptions for a mean test or a mean confidence interval are not met (assuming that n 50 Guidelines for Transformations y 0 x Contains (0,0) and appears to be a power curve, or a curve asymptotic to both horizontal and vertical axes. Suggested transformation: (x,y)(ln(x),ln(y)) x i >0; y i >0 Slide 51 51 Guidelines for Transformations y 0 x Contains a nonzero y-intercept and appears exponential (either growth or decay). Suggested transformation: (x,y)(x, ln(y)) y i >0 Slide 52 52 Guidelines for Transformations y 0 x Contains (0,0) and appears logarithmic. Suggested transformation: (x,y)( x, y) x i 0 Slide 53 53 Guidelines for Transformations y 0 x Contains a nonzero y-intercept and appears logarithmic. Suggested transformation: (x,y)(ln(x),y) x i >0 Slide 54 54 Guidelines for Transformations y 0 x Has nonzero horizontal and vertical asymptotes. Suggested transformation: (x,y)(, ) x i 0;y i 0 Slide 55 55 (x,y) (ln(x),ln(y))(x,y) (x,ln(y)) (x,y) (,y) (x,y) (ln(x),y) (x,y) (, )