Question

the table shows the time, in hours, spent by students on electronic devices and their math test scores. what is the correlation coefficient for this data?

time spent on an electronic device (hours)	math test score
1	99
4	81
0	98
3	90
7	65
5	78
2	90

stat, 1:edit, put in data, stat, -> calc, 4: linreg, enter all the way down make sure you have an
\, if not, mode, down to statdiagnostics on
a -0.896
b 0.977
c 0.896
d -0.977

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$. Let $x$ be the time spent on electronic devices and $y$ be the math - test score.

Step2: Calculate sums

First, calculate $\sum x$, $\sum y$, $\sum x^{2}$, $\sum y^{2}$, and $\sum xy$:
Let $x = [3,1,4,0,3,7,5,2]$ and $y=[85,99,81,98,90,65,78,90]$.
$\sum x=3 + 1+4 + 0+3+7+5+2=25$
$\sum y=85 + 99+81+98+90+65+78+90=686$
$\sum x^{2}=3^{2}+1^{2}+4^{2}+0^{2}+3^{2}+7^{2}+5^{2}+2^{2}=9 + 1+16+0+9+49+25+4 = 113$
$\sum y^{2}=85^{2}+99^{2}+81^{2}+98^{2}+90^{2}+65^{2}+78^{2}+90^{2}$
$=7225+9801+6561+9604+8100+4225+6084+8100 = 59690$
$\sum xy=(3\times85)+(1\times99)+(4\times81)+(0\times98)+(3\times90)+(7\times65)+(5\times78)+(2\times90)$
$=255+99+324+0+270+455+390+180 = 1973$
$n = 8$.

Step3: Substitute into formula

$n\sum xy=8\times1973 = 15784$
$(\sum x)(\sum y)=25\times686 = 17150$
$n\sum x^{2}=8\times113 = 904$
$(\sum x)^{2}=25^{2}=625$
$n\sum y^{2}=8\times59690 = 477520$
$(\sum y)^{2}=686^{2}=470596$
$r=\frac{15784 - 17150}{\sqrt{(904 - 625)(477520-470596)}}$
$=\frac{- 1366}{\sqrt{279\times6924}}$
$=\frac{-1366}{\sqrt{1931896}}$
$=\frac{-1366}{1390.07}$
$=- 0.977$

Answer:

D. - 0.977