Cancer Cell Activity (p. 258). It will not always be obvious which transformation will work best; be willing to experiment. Hierarchy of Powers!

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Presentation transcript:

Cancer Cell Activity (p. 258)

It will not always be obvious which transformation will work best; be willing to experiment. Hierarchy of Powers!

Power transformations at work

Power Models 1)Many characteristics of living things described closely by power laws (pulse, length of life, number of eggs a hen lays, etc.) 2)Apply a logarithmic transformation to both variables.

Example 4.10 Nine known planets in our solar system. Data for the distance from the sun and period of revolution of those planets. PlanetDist. From Sun Period of revolution (earth yrs) Mercury Venus Earth1.000 Mars Jupiter Saturn Uranus Neptune Pluto

Ex Power Model

Lengths (left: in inches) and Weights of Alligators (right: in pounds)

Alligator Problem 1)Graph the original data. Does it appear linear? Does it make sense to find linear regression for this data? 2)Ln both x and y. Does your “new” data look more linear than the original data? 3)Create a linear regression line from the straightened data. What is the slops of this line? How is it related to the proportion of length vs. weight? 4)What is r? How would you classify this value of r? 5)Draw a residual plot to ensure your model is a good fit for the data. 6)Perform an inverse transformation on your data. Make weight estimates, to the nearest pound, for alligators of these lengths: a) 100 inches b) 110 inches c) 120 inches