$7\mathrm{.}7$ LAB: PCA using $.$cov and eig$()$

The forestfires.csv data base contains meteorological information and the area burned for $517$ forest fires that occurred in Montesinho Natural Park in Portugal. The columns of interest are FFMC$,$ DMC$,$ DC$,$ ISI, temp, RH$,$ wind, and rain.

Read in the file forestfires.csv$.$

Create a new data frame X from the columns FFMC$,$ DMC$,$ DC$,$ ISI, temp, RH$,$ wind, and rain, in that order.

Calculate the covariance matrix for the data in X$.$

Calculate the eigenvalues and eigenvectors for the covariance matrix.

Calculate the amount of variance contained in the first component.

Ex: If only the columns FFMC$,$ DMC$,$ DC$,$ and ISI are used, the output is:

$[6\mathrm{.}35187225$e$+042\mathrm{.}12678877$e$+031\mathrm{.}13496502$e$+013\mathrm{.}31868702$e$+01][[0\mathrm{.}00739596-0\mathrm{.}02478582-0\mathrm{.}585033370\mathrm{.}81059664]$

$[0\mathrm{.}17946956-0\mathrm{.}98322216-0\mathrm{.}0012556-0\mathrm{.}03260793]$

$[0\mathrm{.}983726460\mathrm{.}179649160\mathrm{.}00110826-0\mathrm{.}00268257]$

$[0\mathrm{.}00426876-0\mathrm{.}019647360\mathrm{.}811007490\mathrm{.}58469018]]$

$0\mathrm{.}9669459017392729$

Template:

# import the necessary modules

fires $=$ # read in forestfires.csv

X $=$ # create a new dataframe with the columns FFMC$,$ DMC$,$ DC$,$ ISI, temp, RH$,$ wind, and rain, in that order

X$\_$cov $=$ # calculate the covariance matrix

w$,$v $=$ # calculate the eigenvalues and eigenvectors of matrix X$\_$cov

var $=$ # calculate the percentage of the variance contained in the first principle component

print$($w$,$ v$)$

print$($var$)$