$2\mathrm{.}1$ Suppose we have a GPA table of some students as follow:

$\backslash$table$[[$Students$,$High School GPA,College GPA$],[$Alice$,3\mathrm{.}8,2\mathrm{.}8],[$Bob$,3\mathrm{.}1,2\mathrm{.}2],[$Carl$,4\mathrm{.}0,3\mathrm{.}5],[$David$,3\mathrm{.}3,2\mathrm{.}5]]$

Please calculate the Correlation coefficient and decide if High school and college GPA is correlated. If so$,$ are they positively or negatively correlated

$2\mathrm{.}2$ Suppose we have a table contains the experiment results of a drug trail:

$\backslash$table$[[,\backslash$table$[[$Heart rate$],[$increase$]],$No Heart rate increase,Total$],[$Treated$,36,14,50],[$Not Treated,$30,25,55],[$Total$,66,39,105]]$

Please do the Chi$-$square calculation with the above table.