AP+Statistics+Chap+4+Section+1

# AP+Statistics+Chap+4+Section+1 - AP Statistics Chapter 4...

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AP Statistics Chapter 4 Section 1

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3 types of models Linear: Exponential: Power: b mx y + = x ab y = b ax y =
If…then If the growth is best modeled by an exponential equation, then the log of the response variable graphed against the explanatory variable will be linear. If the growth is best modeled by a power equation, then the log of the response variable graphed against the log of the explanatory variable will be linear.

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Process 1. Draw scatterplot and describe 2. Assess growth – Is it linear, exponential, or power (use r) 3. Draw appropriate scatterplot for type of growth. (linear – same, exponential – log y versus x, power – log of y versus log of x) 4. Find linear model for adjusted scatterplot 5. Look at residuals to assess strength of model 6. Use linear model for prediction 7. Convert back to original data 8. Find model for original data
85 90 91 92 93 94 95 96 12000 10000 8000 6000 4000 2000 YEAR # of transactions in millions versus the year This scatterplot shows a slightly curved pattern in a positive direction.

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Compare the correlation coefficients: R = .9695 R = .9983 Exponential shows the strongest relationship R = .9973
4.0 3.9 3.8 3.7 3.6 3.5 Logs of # of transactions 1 90 91 92 93 94 95 96 Year

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90 91 92 93 94 95 96 Year 4 3.75 3.5 Logs of # of Transactions x y 0467 . 4197 . ˆ
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AP+Statistics+Chap+4+Section+1 - AP Statistics Chapter 4...

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