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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. - PowerPoint PPT Presentation
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Chapter FourDay One
Transforming Data
P. 265 2,4 P. 276 5,7,9
Homework
Make a scatterplot of data
Note non-linear form
Think of a “common-sense” relationship
First Steps to Achieving Linearity
Average length and weight of Atlantic Ocean rockfish
Example
Age(years)
Length(cm)
Weight(g)
Age Length
Weight
1 5.2 2 11 28.2 3182 8.5 8 12 29.6 3713 11.5 21 13 30.8 4554 14.3 38 14 32.0 5045 16.8 69 15 33.0 5186 19.2 117 16 34.0 5377 21.3 148 17 34.9 6518 23.3 190 18 36.4 7199 25.0 264 19 37.1 72610 26.7 293 20 37.7 810
Achieving Linearity Now lets graph length3 vs. weight
L1 = length L2 = weight L3 = length3
Plot L3 vs. L2 Perform linreg on L3 vs. L2
weight = 4.066 + 0.0147(length)3
Now report r and r2
Make residual plot
Model
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.
Y = logb x if and only if by = x
Evaluate
Log10100 =
Log 2 8 =
Log 3 1/9 =
Review of Logartithms
logx 125 = 3
Log 4 x = 4
Solve each equation
Logb (MN) = logb M + logb N
Logb (M/N) = logb M – logb N
Logb Mp = p logb M
Laws of Logarthims
Exponential Models Show that if y = abx, 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 (x versus log y) Write log(y) = bx + a Untransform to get final exponential model
Review of Exponential Models
Log y = a + bx
Untransform
Date(years since 1970)
Number of Transistors
Date Number of Transistors
1 2,250 19 1,180,0002 2,500 23 3,100,0004 5,000 27 7,500,0008 29,000 29 24,000,00012 120,000 30 42,000,00015 275,000
Building an Exponential Model