10S Linearizing Power Law Data 4

Transforming Relationships:
Power Law Models
(4.1 Partial)

Home Learning 14
Read Pages 193 thru 203 & 214 thru 225
Explore the Technology Tool Box: Pg 219
Complete Problems:

4.1, 4.2, 4.3, 4.4, 4.12, 4.14, 4.16

Learning Objectives
•

Understand Monotonic behavior in
Data as the Dependent “Increasing
Only” for Increases in the
Independent or “Decreasing Only” for
Increases in the Independent

•

Understand that Monotonically
Increasing behavior insures an
“Inverse Transform” is possible and preserves the Order of the Data in the original Relationship (Monotonically

•

Understand that a Power Law
Relationship requires that the
Logarithm be taken for “Both” sides of the Equation and results in the
Logarithm being taken for both
Variables

•

Be able to convert Bivariate Data that fits a Power Law Relationship into a set of Linear Bivariate Data

•

Be able to create a Linear Form
Predictor Equation for Bivariate Data that is Power Law and be able to predict new data values for the original Power Law Data

Decreasing has an Inverse but reverses data order) •

Understand that a “Skewness
Assessment” of the Variables of the
Bivariate Data can lead to the selection of a Power Law Transform for data suspected of having a Power
Law Relationship

Detecting Growth by Powers
• Not all variables grow linearly or even exponentially over time. Some relationships are best described by x raised to a power.
Area of a Circle =

x

2

x
0
1
2
3
4

y
0
1
4
9
16
y= sq(x)

Detecting Growth by Powers
• Not all variables grow linearly over time. How can you tell?
1. Begin by investigating a scatterplot of the data. Is it clear what form best describes the growth trend?
2. Sometimes growth by powers looks like linear growth or even exponential growth. Find the LSRL, r-squared, and the residual plot to evaluate what is the best form.

Power Law Models
• To find a power law model that fits our data, we begin by taking the common log (or natural log) of both variables. This allows us