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Chapter Four Day Two

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Chapter Four Day Two

Power Models

- P. 285 11,12,13

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

- 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

- Untransform log(y) = ax + b

- 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

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

- Untransform log y = alog(x) + b

- 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

- 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)

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

- Comment on r2
- Comment on residual Plot