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Chapter Four Day One

Chapter Four Day One. Transforming Data. Homework. P. 265 2,4 P. 276 5,7,9. First Steps to Achieving Linearity. Make a scatterplot of data Note non-linear form Think of a “common-sense” relationship. Example. Average length and weight of Atlantic Ocean rockfish. Achieving Linearity.

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Chapter Four Day One

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  1. Chapter FourDay One Transforming Data

  2. Homework • P. 265 2,4 • P. 276 5,7,9

  3. First Steps to Achieving Linearity • Make a scatterplot of data • Note non-linear form • Think of a “common-sense” relationship

  4. Example • Average length and weight of Atlantic Ocean rockfish

  5. Achieving Linearity • Now lets graph length3 vs. weight • L1 = length • L2 = weight • L3 = length3 • Plot L3 vs. L2 • Perform linreg on L3 vs. L2

  6. Model • weight = 4.066 + 0.0147(length)3 • Now report r and r2 • Make residual plot

  7. Types of Nonlinear Models • Exponential Models y = bx Use an exponential model if there is a linear relationship between x and log y. • Power Models y = xb • Use a power Model if there is a linear relationship between log x and log y.

  8. Review of Logartithms • Y = logb x if and only if by = x • Evaluate • Log10100 = • Log 2 8 = • Log 3 1/9 =

  9. Solve each equation • logx 125 = 3 • Log 4 x = 4

  10. Laws of Logarthims • Logb (MN) = logb M + logb N • Logb (M/N) = logb M – logb N • Logb Mp = p logb M

  11. Exponential Models • Show that if y = abx, then there is a linear relationship between x and log y

  12. 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 (x versus log y) • Write log(y) = bx + a • Untransform to get final exponential model

  13. Untransform • Log y = a + bx

  14. Building an Exponential Model

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