Q$\mathrm{.}5$ Consider a use case where PCA is applied to a dataset containing various features related to student performance in an educational setting. The dataset includes variables such as exam scores, homework completion rates, attendance, and participation in extracurricular activities. Following are the loading vectors generated for PC$1$ and PC$2$ respectively. $(7$ marks$)$

$$

V$1$

V$2$

Exam scores

$0\mathrm{.}6$

$0\mathrm{.}3$

Homework completion rates

$0\mathrm{.}4$

$-0\mathrm{.}7$

Attendance

$0\mathrm{.}7$

$0\mathrm{.}2$

Participation in extracurricular activities

$0\mathrm{.}5$

$0\mathrm{.}6$

$$

$$

Interpret the loading vectors with respect to PC$1$ and PC$2.$ Comment on what does a datapoint with high PC$1$ and a datapoint with high PC$2$ indicate regarding the student segment it belongs to$.$ Comment about the similarity or contrast about different traits of the students indicated by the features.