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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. - PowerPoint PPT Presentation
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Chapter Four Day Two
Power Models
P. 285 11,12,13
Homework
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
Review of Exponential Models
Untransform log(y) = ax + b
Example
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
Power Models y = a* xb
Show that if y = abx then there is a linear relationship between log x and log y.
Example
Untransform log y = alog(x) + b
Example
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
Steps to Making a Power Model
Find a model that predicts a planet’s period of revolution using the distance from the sun as an explanatory variable.
Example - Planets
Planet Distance from Sun (AU)
Period of Revolution (Earth years)
Mercury .387 .241Venus .723 .615Earth 1.000 1.000Mars 1.524 1.881Jupiter 5.203 11.862Saturn 9.539 29.456Uranus 19.191 84.070Neptune 30.061 164.810Pluto 39.529 248.530
Try an exponential model – linear relationship between x and log y
Try a Power Model – Linear Relationship between log(x) and log(y)
ln(period) = .000254 + 1.50 ln(distance)
Untransform linear log-log Model to get final power model
Evaluating a Model Comment on r2
Comment on residual Plot