Predicting Housing Median Prices. The file BostonHousing.xls contains information on over 500 census tracts in Boston, where for each tract 14 variables are recorded. The last column (CAT.MEDV) was derived from MEDV, such that it obtains the value 1 if MEDV>30 and 0 otherwise. Consider the goal of predicting the median value (MEDV) of a tract, given the information in the first 13 columns. Partition the data into training (60%) and validation (40%) sets.

a. Perform a k-NN prediction with all 13 predictors (ignore the CAT.MEDV column), trying values of k from 1 to 5. Make sure to normalize the data (click normalize input data). What is the best k chosen? What does it mean?

b. Predict the MEDV for a tract with the following information, using the best k: