use the mlba::Wine data set available on Canvas, for this exercise. The data consist of chemical data about some wines from $3$ different wineries in the same region. The target variable is Type. Remember to omit the target variable from the dimension$-$reduction analysis.

$$

$($a$)$ Perform some initial exploratory analysis on your dataset.$$ What variables are present in the data set?$$ Give a brief overview of the dataset.$$

$($b$)$ Should the data be normalized before performing principal component analysis?$$ Explain why or why not.$$ If you think it should be normalized, normalize the data.

$($c$)$ Provide a matrix showing the correlation coefficients of each predictor with each other predictor. Use some type of visualization technique to display the correlations so that the reader can easily see at a glance, which are the strongest correlations. Discuss which sets of predictors seem to $$vary together$.$

$($d$)$ Run PCA on the variables.

$($e$)$ Determine the optimal number of components to extract.$$ Explain the criteria you used to select the number of principal components.

$($f$)*$Bonus$*($optional$)$ Explore the results of your PCA for however many principal components you think should be used.$$ Which of the original attributes are contributing the most to these principal components?