Transforming Data

 P ,4  P ,7,9

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

 Average length and weight of Atlantic Ocean rockfish Age (years) Length (cm) Weight (g) AgeLengthWeight

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

 weight = (length) 3  Now report r and r 2  Make residual plot

 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.

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

 log x 125 = 3  Log 4 x = 4

 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

 Show that if y = ab x, 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 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

 Log y = a + bx

Date (years since 1970) Number of Transistors DateNumber of Transistors 12,250191,180,000 22,500233,100,000 45,000277,500, , ,000, , ,000, ,000