1. Transforming Data

2.  P. 265 2,4  P. 276 5,7,9

3.  Make a scatterplot of data  Note non-linear form  Think of a “common-sense” relationship

5.  Average length and weight of Atlantic Ocean rockfish Age (years) Length (cm) Weight (g) AgeLengthWeight 15.221128.2318 28.581229.6371 311.5211330.8455 414.3381432.0504 516.8691533.0518 619.21171634.0537 721.31481734.9651 823.31901836.4719 925.02641937.1726 1026.72932037.7810

7.  Now lets graph length 3 vs. weight  L1 = length  L2 = weight  L3 = length 3  Plot L3 vs. L2  Perform linreg on L3 vs. L2

9.  weight = 4.066 + 0.0147(length) 3  Now report r and r 2  Make residual plot

12.  Exponential Models y = b x Use an exponential model if there is a linear relationship between x and log y.  Power Models y = x b  Use a power Model if there is a linear relationship between log x and log y.

13.  Y = log b x if and only if b y = x  Evaluate  Log 10 100 =  Log 2 8 =  Log 3 1/9 =

14.  log x 125 = 3  Log 4 x = 4

15.  Log b (MN) = log b M + log b N  Log b (M/N) = log b M – log b N  Log b M p = p log b M

16.  Show that if y = ab x, then there is a linear relationship between x and log y

17.  Make scatterplot and note very strong non- linear form.  Take the log of the y-values and put the results in L 3.  Do a linreg on L 1 vs. L 3 (x versus log y)  Write log(y) = bx + a  Untransform to get final exponential model

18.  Log y = a + bx

20. Date (years since 1970) Number of Transistors DateNumber of Transistors 12,250191,180,000 22,500233,100,000 45,000277,500,000 829,0002924,000,000 12120,0003042,000,000 15275,000