1. 4.1 Modeling Nonlinear Data

2.  Create scatter plots of non linear data  Transform nonlinear data to use for prediction  Create residual plots

3.  Exponential Function:  Power function:

4.  To show exponential growth: ◦ We look for a common ratio xyratio 13 28.72.9 326.93.09 482.63.07 52402.91

5.  Linear- increases by a constant (slope)  Exponential- increases by a ratio

6.  **  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.  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.  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.  Plot graph: L₁, L₂  Plot residuals: L₁, L₃  stat/calc/8/L₁,L₂,Y₁ ỳ=a+bx L₁L₂L₃ XYL₂-Y₁(L₁)

10.  Plot graph: L₁, L₃  stat/calc/8/L₁,L₃,Y₁  Plot residuals: L₁, L₄ L₁L₂L₃L₄ (residuals) XYlog y (log(L₂) L₃-Y₁(L₁)

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

12.  Plot graph: L₃, L₄  Stat/calc/8: L₃, L₄, Y₁  Plot Residuals: L₃, L₅ L₁L₂L₃L₄L₅ XYLog (x)Log (y)L₄-Y₁(L₃)