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 4.10Nine known planets in

our solar system. Data for the distance from the sun and period of revolution of those planets.

Planet Dist. From Sun

Period of revolution (earth yrs)

Mercury 0.387 0.241

Venus 0.723 0.615

Earth 1.000 1.000

Mars 1.524 1.881

Jupiter 5.203 11.862

Saturn 9.539 29.456

Uranus 19.191 84.070

Neptune 30.061 164.810

Pluto 39.529 248.530

Ex. 4.10Power Model

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

94 74 147 58 86

94 63 86 69 72

128 85 82 86 88

72 74 61 90 89

68 76

130 51 640 28 80

110 33 90 36 38

366 84 80 83 70

61 54 44 106 84

39 42

Alligator Problem1) 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