$3.$ This question should be answered using the Ionosphere data set, which is part of the mlbench package. This radar data was collected by a system in Goose Bay, Labrador. The data frame consists of $351$ observations on $35$ independent variables. The last column in the dataframe is a categorical variable, $$Class$,$ defining the free electrons in the ionosphere: $$good$$ radar returns are those showing evidence of some type of structure in the ionosphere. $$bad$$ returns are those that do not.

$($a$)$ Produce some numerical and graphical summaries of the Ionosphere data. Do there appear to be any patterns?

$($b$)$ Notice that the second the column contains only one single value, so remove that column and work on the rest of the questions using the new dataset. Perform a K$-$Nearest Neighbors $($KNN$)$ algorithm with K $=1,$ where Class is the response, and the rest columns in the dataset as predictors.

$($c$)$ Compute the confusion matrix and overall fraction of correct predictions. Explain what the confusion matrix is telling you about the types of mistakes made by KNN algorithm.

$($d$)$ Split the data randomly into a training set $(70\%)$ and a test set $(30\%).$ Make sure to use set.seed$(4323),$ for reproducible results. Fit the KNN model $($K $=3)$

$($e$)$ Repeat $($d$)$ using K $=5.$

$($f$)$ Repeat $($d$)$ using K $=7.$

$($g$)$ Which of these methods appears to provide the best results on this data? Please answer and mark a$,$b$,$c$,$d$,$e$,$f$,$g for clarity