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    %% Predict Training Sample Medians
%%
% Load the |carsmall| data set.  Consider a model that predicts the fuel
% economy of a car given its engine displacement.
load carsmall
%%
% Train an ensemble of bagged regression trees using the entire data set.
% Specify 100 weak learners.
rng(1); % For reproducibility
Mdl = TreeBagger(100,Displacement,MPG,'Method','regression');
%%
% |Mdl| is a |TreeBagger| ensemble.
%%
% Perform quantile regression to predict the median MPG for all sorted
% training observations.
medianMPG = quantilePredict(Mdl,sort(Displacement));
%%
% |medianMPG| is an |n|-by-1 numeric vector of medians corresponding to the
% conditional distribution of the response given the sorted observations in
% |Displacement|. |n| is the number of observations in |Displacement|.
%%
% Plot the observations and the estimated medians on the same figure.
% Compare the median and mean responses.
meanMPG = predict(Mdl,sort(Displacement));

figure;
plot(Displacement,MPG,'k.');
hold on
plot(sort(Displacement),medianMPG);
plot(sort(Displacement),meanMPG,'r--');
ylabel('Fuel economy');
xlabel('Engine displacement');
legend('Data','Median','Mean');
hold off;