Chapter Four Day Two
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Transcript of Chapter Four Day Two
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Chapter Four Day Two
Power Models
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P. 285 11,12,13
Homework
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Show that if y = a*bx taking then there is a linear relationship between x and log(y).
Review of Exponential Models
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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
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Untransform log(y) = ax + b
Example
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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
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Show that if y = abx then there is a linear relationship between log x and log y.
Example
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Untransform log y = alog(x) + b
Example
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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
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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
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Try an exponential model – linear relationship between x and log y
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Try a Power Model – Linear Relationship between log(x) and log(y)
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ln(period) = .000254 + 1.50 ln(distance)
Untransform linear log-log Model to get final power model
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Evaluating a Model Comment on r2
Comment on residual Plot