The graph on the right shows $10$ observations located in two input dimensions. The red lines show how the input dimensions are being stratified. The number in the middle of each observation shows the y$-$value associated with each observation. Use this information

$1.$ Draw the decision tree associated with the stratification shown above.

$2.$ Calculate the Sum of Squared Residuals for the decision tree above.

$3.$ Suppose that the observation with the y$-$value of $15$ was in the same rectangle with the observations with y$-$value $17$ and y$-$value $18.$ What would this new tree look like?

$4.$ Calculate the Sum of Squared Residuals for this new decision tree.

$5.$ Suppose that you were trying to decide which decision tree to use by using cost complexity pruning. What would $$ have to be for you to keep the original decision tree?

$6.$ Let$$s pretend that the two decision trees you made above came from a bagging process. Calculate the predicted y$-$value for an observation at the point $(2\mathrm{.}5,1).$

$7.$ What is the main difference between bagging and random forest?