# Chapter Four Day Two - PowerPoint PPT Presentation

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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

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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 = ax2 quadratic

• Y = ax3 cubic

• Y = ax4 quadratic

• 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.

Try an exponential model – linear relationship between x and log y

Try a Power Model – Linear Relationship between log(x) and log(y)

### 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