AP Statistics4.1 Modeling Nonlinear Data

Create scatter plots of non linear data

Transform nonlinear data to use for prediction

Learning Objective

Exponential Function:

Power function:

To show exponential growth:◦ We look for a common ratio

◦ Notice the common ratio is about 3!

Exponential Growth

x y ratio

1 3

2 8.7 8.7/3=2.9

3 26.9 26.9/8.7=3.09

4 82.6 82.6/26.9=3.07

5 240 2.91

Linear- increases by a constant (slope)

Exponential- increases by a ratio

Compare Linear versus Exponential Growth

The following table shows the heights of a Pasfor tree after 5 months.

Graph age vs. height. (L1 vs. L2)

Notice the graph shows an exponential growth model

x y

1 3

2 8.7

3 26.9

4 82.6

5 240

Remember, we can’t find correlation or a regression lineunless the data is linear. So how do we do this?

Take the logarithm of y.In L3= log (L2)Now graph (x,log y)= (L1, L3)What do you notice? The data is linear!!! So now we can use it to

predict!

Prediction in Exponential Models

(L1) x

(L2) y

(L3) log y

1 3

2 8.7

3 26.9

4 82.6

5 240

If a variable grows exponentially, its logarithm grows linearally.

** this question will be a multiple choice on your test. For example:

The oil production per year shows an exponential increase in productivity. How would you predict data using this model?

A) Graph the year versus oil production B) Graph the logarithm of year versus oil production C) Graph the year versus the logarithm of oil production D) Graph the logarithm of year versus the logarithm of oil

production E)We can’t predict data of exponential growth.

Answer: C) Graph the year versus the logarithm of oil production

How do we make predictions in the exponential growth model?

 The following data is a power function. When does a power law become linear? Take the log x and log y in L3 and L4Then graph L3, L4 :(log x, log y) What do you notice? It’s linear!!

Power Law Models

length weight

1 2

2 17

3 53.1

4 129.2

5 248.7

L1 L2 L3 (Log L1)

L4 (log L2)

1 2

2 17

3 53.1

4 129.2

5 248.7

What do we need to actually know from section 4.1?

If data grows exponentially- graph (x, log y)

If data grows to a power function- graph ( log x, log y)

That is it!!!! So don’t stress too much about this section-if you know these 2 facts, you are good!

Recap!!