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AP Statistics

AP Statistics. 4.1 Modeling Nonlinear Data. Learning Objective. Create scatter plots of non linear data Transform nonlinear data to use for prediction. Exponential Function: Power function:. Exponential Growth. To show exponential growth: We look for a common ratio

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AP Statistics

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  1. AP Statistics 4.1 Modeling Nonlinear Data

  2. Learning Objective • Create scatter plots of non linear data • Transform nonlinear data to use for prediction

  3. Exponential Function: • Power function:

  4. Exponential Growth • To show exponential growth: • We look for a common ratio • Notice the common ratio is about 3!

  5. Compare Linear versus Exponential Growth • Exponential- increases by a ratio • Linear- increases by a constant (slope)

  6. 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

  7. Prediction in Exponential Models Remember, we can’t find correlation or a regression line unless 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!

  8. How do we make predictions in the exponential growth model? 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

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

  10. Recap!! • 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!

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