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# Straightening Google's Growth   #
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# read in google data

data=read.table("google.txt",header=T,sep="\t",skip=2)
attach(data)

# the two variables are period and employees

# plot growth against employees

plot(period, employees)

# fit a line -- we use rline in the LearnEDA package

library(LearnEDA)  # this is LearnEDA_1.01

fit=rline(period, employees)

# print the line of the form a + b (x - xC)

fit$a
fit$b
fit$xC

# add the line to the graph

curve(fit$a+fit$b*(x-fit$xC), add=TRUE)

# to see if this line is a suitable fit, we look at the residuals

plot(period, fit$residual); abline(h=0)

# one way of detecting the curvature is by the half-slope ratio

fit$half.slope.ratio

# want to straighten the graph
# we reexpress data by trying power transformations on the y variable

rline(period,sqrt(employees))$half.slope.ratio

rline(period,log(employees))$half.slope.ratio

rline(period,employees^.25)$half.slope.ratio

rline(period,employees^.16)$half.slope.ratio

# plot the straightened data and summarize

fit=rline(period,employees^.16)

plot(period,employees^.16)
curve(fit$a+fit$b*(x-fit$xC), add=TRUE)

# plot the residuals

plot(period,fit$residual); abline(h=0)