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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 Create residual plots. Exponential Function: Power function:. Exponential Growth. To show exponential growth:

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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 • Create residual plots

  3. Exponential Function: • Power function:

  4. Exponential Growth • To show exponential growth: • We look for a common ratio

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

  6. Algebraic Properties of Logarithms • ** • The rules for logarithms are • #1) log (AB)= log A + log B • #2) log(A/B)= log A - log B • #3) log x^p = p log x

  7. How do we make predictions in the exponential growth model? • Linearize our data (take log y) • If a variable grows exponentially, its logarithm grows linearally. • How do we transform our data back to make predictions?

  8. Power Law Models • When does a power law become linear? How? • Take the log x and log y • How do we make prediction in power law models?

  9. Linear • Plot graph: L₁, L₂ • Plot residuals: L₁, L₃ • stat/calc/8/L₁,L₂,Y₁ ỳ=a+bx

  10. Exponential • Plot graph: L₁, L₃ • stat/calc/8/L₁,L₃,Y₁ • Plot residuals: L₁, L₄

  11. To predict: type in calc (10^(Y₁(x)) • To write out your new equation:

  12. Power • Plot graph: L₃, L₄ • Stat/calc/8: L₃, L₄, Y₁ • Plot Residuals: L₃, L₅

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