More on Two-Variable Data Chapter 4

Transforming Relationships Section 4.1

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

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.

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

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

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

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

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

If a variable grows exponentially, its logarithm grows linearly.

Practice Problems pg. 212 #4.6-4.11

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

Practice Problems pg. 222 #4.17-4.25