Chapter Four Day Two

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# Chapter Four Day Two - PowerPoint PPT Presentation

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

Power Models

Homework
• P. 285 11,12,13
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 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
• Untransform log(y) = ax + b
Power Models y = a* xb
• Hierarchy of Powers
• y = ax linear
• Y = ax3 cubic
• Y = ax5 5th degree
• For large x axb < abx for any b
Example
• Show that if y = abx then there is a linear relationship between log x and log y.
Example
• Untransform log y = alog(x) + b
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
• 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
• ln(period) = .000254 + 1.50 ln(distance)
Evaluating a Model
• Comment on r2
• Comment on residual Plot