4.1 Exponential Growth and Power Law Models Introduction (Yates)

4.1 Exponential Growth and Power Law Models Introduction (Yates)

I. Previously, we have performed certain transformations on data that was nonlinear in order to make it linear. In AP Statistics, there are two particular kinds of nonlinear data you must be able to perform regression analysis on: these are the exponential and power models.

A. On page 271 (Yates), we see the data and scatterplot of years since 1970 and number of transistors for intel microprocessors. Describe what you see:

B. On page 260 (Yates), we see the data and scatterplot of body weight of mammals (kg) and brain weight (grams). Describe what you see:

C. In the next week, we will further explore this data (and more like it). For now, we need to brush up on some properties of logarithms (Algebra 2) so you will be successful!

II. Properties of Logarithms

1.

2.

3.

III. Derivation of Formulas:

A. If a variable grows exponentially in the form of , then its logarithm grows linearly

in the form . Apply the properties of logarithms in order to use this model to make predictions (solve for y):

B. If a variable grows in the form of a power model, then the logarithm transformation is applied to both variables so we use in order achieve linearity. Apply the properties of logarithms in order to use this model to make predictions (solve for y):

IV. As you can see, this is tedious work. Therefore, I suggest you MEMORIZE the following:

A. Properties of Logarithms

B. Least-Squares Regression Lines

1. If it is linear, use to make predictions

2. If it is exponential, use to make predictions

3. If it is a power model, use to make predictions

V. Homework: Quick Quiz on Math Facts for Achieving Linearity and Making Predictions on TUESDAY!!!!!!!

A. Properties of Logarithms

B. Least-Squares Regression Lines

4. If it is linear, use ______to make predictions

5. If it is exponential, use ______to make predictions

6. If it is a power model, use ______to make predictions