Two quantitative predictor variables,1X1and2X2, and a categorical response variable,Y, are recorded for twenty-five observations. The information is illustrated in the predictor space below, where the response variable for each observation is categorized as eitherRedorBlue.

(a)Sketch the tree corresponding to the partition of the predictor space illustrated below.

(b)What is the error rate associated with this tree (or this partition of the predictor space)?

(c)Suppose we are given a new observation with1=8X1=8and2=3X2=3. What response would be predicted for this observation, based upon the tree (or the partition)?

(d)Suppose we are given a new observation with1=8X1=8and2=3X2=3. What response would be predicted for this observation, based uponk-nearest neighbours with=3k=3?

Use the Manhattan distance between a pair of points

(, )=|11|+|22|(,)=|11|+|22|

instead of Euclidean distance