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The above Boosted Model is a Gradient Boosted Model which generates 10000 trees and the shrinkage parameter \(lambda= \) which is also a sort of learning rate . Next parameter is the interaction depth \(d\) which is the total splits we want to here each tree is a small tree with only 4 splits.

The summary of the Model gives a feature importance plot .In the above list is on the top is the most important variable and at last is the least important variable.

And the 2 most important features which explain the maximum variance in the Data set is lstat lower status of the population (percent) and rm which is average number of rooms per dwelling.

Generic gradient boosting at the * m* -th step would fit a decision tree
h
m
(
x
)
{\displaystyle h_{m}(x)}
to pseudo-residuals. Let
J
m
{\displaystyle J_{m}}
be the number of its leaves. The tree partitions the input space into
J
m
{\displaystyle J_{m}}
disjoint regions
R
1
m
,
…
,
R
J
m
m
{\displaystyle R_{1m},\ldots ,R_{J_{m}m}}
and predicts a constant value in each region. Using the indicator notation , the output of
h
m
(
x
)
{\displaystyle h_{m}(x)}
for input * x* can be written as the sum: