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Chapter Four Day Two

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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  1. Chapter Four Day Two Power Models

  2. Homework • P. 285 11,12,13

  3. Review of Exponential Models • Show that if y = a*bx taking then there is a linear relationship between x and log(y).

  4. 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

  5. Example • Untransform log(y) = ax + b

  6. 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

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

  8. Example • Untransform log y = alog(x) + b

  9. 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

  10. Example - Planets • Find a model that predicts a planet’s period of revolution using the distance from the sun as an explanatory variable.

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

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

  13. Untransform linear log-log Model to get final power model • ln(period) = .000254 + 1.50 ln(distance)

  14. Evaluating a Model • Comment on r2 • Comment on residual Plot

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