PLEASE ANSWER USING PYTHON ONLY

$9\mathrm{.}3$ Predicting Prices of Used Cars $($Regression Trees$).$ The file ToyotaCorolla.csv contains the data on used cars $($Toyota Corolla$)$ on sale during late summer of $2004$ in the Netherlands. It has $1436$ records containing details on $38$ attributes, including Price, Age, Kilometers, HP$,$ and other specifications. The goal is to predict the price of a used Toyota Corolla based on its specifications. $($The example in Section $9\mathrm{.}7$ is a subset of this dataset.$)$

Data Preprocessing. Split the data into training $(60\%),$ and validation $(40\%)$ datasets.

a$.$ Run a full$-$grown regression tree $($RT$)$ with outcome variable Price and pre$-$ dictors Age$\_08\_04,$ KM$,$ Fuel$\_$Type $($first convert to dummies$),$ HP$,$ Auto$-$ matic, Doors, Quarterly$\_$Tax, Mfr$\_$Guarantee, Guarantee$\_$Period, Airco, Auto$-$ matic$\_$airco, CD$\_$Player, Powered$\_$Windows, Sport$\_$Model, and Tow$\_$Bar. Set random$\_$state$=1.$

i$.$ Which appear to be the three or four most important car specifications for predicting the car$$s price?

ii$.$ Comparethepredictionerrorsofthetrainingandvalidationsetsbyexamining their RMS error and by plotting the two boxplots. How does the predictive performance of the validation set compare to the training set? Why does this occur?

iii. Howmightweachievebettervalidationpredictiveperformanceattheexpense of training performance?

iv$.$ CreateasmallertreebyusingGridSearchCV$()$withcv$=5$tofindafine$-$tuned tree. Compared to the full$-$grown tree, what is the predictive performance on the validation set?

PROBLEMS $249$

$2509$ CLASSIFICATION AND REGRESSION TREES

b$.$ Let us see the effect of turning the price variable into a categorical variable. First, create a new variable that categorizes price into $20$ bins. Now repartition the data keeping Binned$\_$Price instead of Price. Run a classification tree with the same set of input variables as in the RT$,$ and with Binned$\_$Price as the output variable. As in the less deep regression tree, create a smaller tree by using GridSearchCV$()$ with cv $=5$ to find a fine$-$tuned tree.

i$.$ ComparethesmallertreegeneratedbytheCTwiththesmallertreegenerated by RT$.$ Are they different? $($Look at structure, the top predictors, size of tree, etc.$)$ Why?

ii$.$ Predicttheprice,usingthesmallerRTandCT,ofausedToyotaCorollawith the specifications listed in Table $9\mathrm{.}10.$

TABLE $9\mathrm{.}10$

SPECIFICATIONS FOR A PARTICULAR

TOYOTA COROLLA

iii. Compare the predictions in terms of the predictors that were used, the mag$-$ nitude of the difference between the two predictions, and the advantages and disadvantages of the two methods.