$1$ Question $1$

Using the Domotic$1.$txt 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 dimen$-$

sions, 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.

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