Using the Concrete Data.csv dataset $($See Data Files Link in Blackboard$)($a$)$ Describe the data in the data set including necessary summary statistics. What are some issues with the data set and how do you handle them? $($Then create a new dataset where you have handled these problems$).($b$)$ The chief analyst wants to decompose the data into something more manageable, i$.$e$.$ reduce the number of dimensions. Using principal component analysis, reduce the dimensions, using the appropriate technique $.($c$)$ How many dimensions did you decide on$,$ please indicate and show all code and results, and explain how you choose the dimensions. In addition describe the dimensions based on the variables $($like our example in class where we called one dimension $$size$)($d$)$ PCA produces a chart with a unit circle. Produce this chart for this example and explain the pieces of the chart. $($e$)$ Write the linear function for each of the components and calculate the answer for each observation, i$.$e$.$ if you have $5$ dimensions you will create $5$ variables in the dataset, and using the linear function you create $($hint the loadings of the PCA dimensions$),$ you will generate values for each of the observations.

$($f$)$ Interpret all your findings and provide a small summary of all the findings.