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MATH154TreesLab_Franklin.tex
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\documentclass{article}
\usepackage{Sweave}
\begin{document}
\input{MATH154TreesLab_Franklin-concordance}
\begin{Schunk}
\begin{Sinput}
> # In addition to using the kaggle data, load the data set mtcars into R via the
> # command data(mtcars). Try to predict the fuel efficiency (mpg) via a regression tree, and try to predict the transmission type (automatic or manual) via a classification
> # tree.
> #You may want to compare the regression tree to a linear model.
> # plot(mtcars) will give you all the pairwise scatter plots. Notice that most of the
> # relationships with MPG are non-linear.
>
> # Additionally, R has a package called randomForest. The most useful function,
> # which implements the algorithm discussed in class, is of the same name. Compare
> # the classification rates for a random forest to that of a simple tree.
>
> install.packages("tree", repos = 'http://cran.stat.ucla.edu/' )
\end{Sinput}
\begin{Soutput}
The downloaded binary packages are in
/var/folders/7r/l1jbh8ns1wv15whvm188ss900000gn/T//RtmpUvuFWS/downloaded_packages
\end{Soutput}
\begin{Sinput}
> install.packages("randomForest", repos = 'http://cran.stat.ucla.edu/' )
\end{Sinput}
\begin{Soutput}
The downloaded binary packages are in
/var/folders/7r/l1jbh8ns1wv15whvm188ss900000gn/T//RtmpUvuFWS/downloaded_packages
\end{Soutput}
\begin{Sinput}
> library(tree)
> library(randomForest)
> library(datasets)
> data(mtcars)
> mtcars
\end{Sinput}
\begin{Soutput}
mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
\end{Soutput}
\begin{Sinput}
> names(mtcars)
\end{Sinput}
\begin{Soutput}
[1] "mpg" "cyl" "disp" "hp" "drat" "wt" "qsec" "vs" "am" "gear"
[11] "carb"
\end{Soutput}
\begin{Sinput}
> dim(mtcars)
\end{Sinput}
\begin{Soutput}
[1] 32 11
\end{Soutput}
\begin{Sinput}
> # Regression Tree
> test.index = sample(c(1:nrow(mtcars)),nrow(mtcars)/2 )
> training.index= c(1:nrow(mtcars))[-test.index]
> test.data = mtcars[test.index,]
> training.data = mtcars[training.index,]
> cars.regression <- tree(mpg ~ cyl+disp+hp+drat+wt+qsec+vs+am+gear+carb, data=training.data)
> plot(cars.regression )
> text(cars.regression , cex=.75)
> my.prediction <- predict(cars.regression, test.data)
> # find RSS
> residuals = (test.data$mpg - my.prediction)^2
> sum(residuals^2)
\end{Sinput}
\begin{Soutput}
[1] 9636.102
\end{Soutput}
\begin{Sinput}
> # plot residuals
> plot(residuals)
> # plot of actual and predictions
> plot(test.data$mpg)
> points(my.prediction, col = 'red')
> # Classification Tree
> # Use a classification tree to predict transmission type of car
> # Transmission (0 = automatic, 1 = manual)
> cars.class<-tree(am ~ mpg+cyl+disp+hp+drat+wt+qsec+vs+gear+carb, data=training.data)
> summary(cars.class)
\end{Sinput}
\begin{Soutput}
Regression tree:
tree(formula = am ~ mpg + cyl + disp + hp + drat + wt + qsec +
vs + gear + carb, data = training.data)
Variables actually used in tree construction:
[1] "wt"
Number of terminal nodes: 2
Residual mean deviance: 0.05952 = 0.8333 / 14
Distribution of residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.8333 0.0000 0.0000 0.0000 0.1667 0.1667
\end{Soutput}
\begin{Sinput}
> plot(cars.class)
> text(cars.class)
> my.prediction.class <- predict(cars.class, test.data)
> plot(test.data$am)
> points(my.prediction.class,col = 'purple', pch = ".")
> # how many incorrect predictions
> incorrect.predict = sum(abs(my.prediction.class - test.data$am) > .5)
> incorrect.predict
\end{Sinput}
\begin{Soutput}
[1] 4
\end{Soutput}
\begin{Sinput}
> # proportion of correct predictions
> (nrow(test.data) - incorrect.predict )/ nrow(test.data)
\end{Sinput}
\begin{Soutput}
[1] 0.75
\end{Soutput}
\begin{Sinput}
> #####
> # Comparing to a Linear model
> plot(mtcars)
> cars.lm <- lm ( mpg ~ cyl+disp+hp+drat+wt+qsec+vs+am+gear+carb, data= training.data)
> prediction.lm <- predict(cars.lm, test.data)
> # find RSS
> residuals.lm = (test.data$mpg - prediction.lm)^2
> sum(residuals.lm^2)
\end{Sinput}
\begin{Soutput}
[1] 5953355
\end{Soutput}
\begin{Sinput}
> # plot residuals
> plot(residuals.lm, main = "Residuals from Linear Model")
> # plot of actual and predictions
> plot(test.data$mpg, main= "Plot of Actual vs. Prediction from Linear Model")
> points(prediction.lm, col = 'red')
>
> # to do:
> # reduce the number f variables? stepwise regression?
> # consider nonlinear relationships
>
\end{Sinput}
\end{Schunk}
\end{document}