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Chapter Four Day Two. Power Models. Homework. P. 285 11,12,13. Review of Exponential Models. Show that if y = a*b x taking then there is a linear relationship between x and log(y). Review of Exponential Models. Make scatterplot and note very strong non-linear form.

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Chapter four day two

Chapter Four Day Two

Power Models


Homework
Homework

  • P. 285 11,12,13


Review of exponential models
Review of Exponential Models

  • Show that if y = a*bx taking then there is a linear relationship between x and log(y).


Review of exponential models1
Review of Exponential Models

  • Make scatterplot and note very strong non-linear form.

  • Take the log of the y-values and put the results in L3.

  • Do a linreg on L1 vs. L3

  • Write log(y) = bx + a

  • Untransform to get final exponential model


Example
Example

  • Untransform log(y) = ax + b


Power models y a x b
Power Models y = a* xb

  • Hierarchy of Powers

  • y = ax linear

  • Y = ax2 quadratic

  • Y = ax3 cubic

  • Y = ax4 quadratic

  • Y = ax5 5th degree

  • For large x axb < abx for any b


Example1
Example

  • Show that if y = abx then there is a linear relationship between log x and log y.


Example2
Example

  • Untransform log y = alog(x) + b


Steps to making a power model
Steps to Making a Power Model

  • Plot data and note nonlinear form

  • Put log of the x-values in L3

  • Put log of y –values in L4

  • Do linreg on log x vs log y

  • Write log(y) = a(log x) +b

  • Untransform to get final power model


Example planets
Example - Planets

  • Find a model that predicts a planet’s period of revolution using the distance from the sun as an explanatory variable.




Untransform linear log log model to get final power model
Untransform linear log-log Model to get final power model log(y)

  • ln(period) = .000254 + 1.50 ln(distance)


Evaluating a model
Evaluating a Model log(y)

  • Comment on r2

  • Comment on residual Plot