1. More on Two-Variable Data
Chapter 4

2. Transforming Relationships
Section 4.1

3. Monotonic Function
f(t) moves in one direction as its argument t increases.
Two types
1. Increasing
2. Decreasing

4. Transforming Data
If variable to be transformed takes values that are 0 or negative, apply a linear transformation to make all values positive.
Choose a power or logarithmic transformation that approximately straightens the data.

5. Monotonicity of Power Functions
Increasing for positive powers p
They preserve the order of observations
Decreasing for negative powers p
They reverse the order of observations

6. Concavity of Power Functions
Powers greater than 1 are concave up.
Powers less than 1 are concave down.

7. Linear Growth
Increases by a fixed amount in each equal time period.

8. Exponential Growth
Increases by a fixed percentage of the previous total.

9. Logarithmic Transformation
If you have an exponential function, you can transform it using logarithm properties
log(AB) = logA + log B
log(A/B) = logA – logB
logXp = p logX

10. If a variable grows exponentially, its logarithm grows linearly.

11. Practice Problems
pg. 212 #

12. Power Law Model
y = a*xp
Data becomes linear when we apply the logarithm transformation to both variables

13. Practice Problems
pg. 222 #