Using the actual outcome values for those test set observations shown in column Q of the problem $4$ worksheet, which bandwidth would you choose for your final model? Show your calculations and explain why you chose what you did.

Question $4$: Using the worksheet titled problem $4,$ predict the real$-$valued outcome for $5$ test set observations using a training data set of $25$ observations. There are five input attributes, all of which can be considered nominal. Use k$-$NN classification with the basic $$matching$$ distance metric and exponential kernel regression with bandwidths of $1$ and $5.$ Provide your predictions below.