compute the correlation coefficient.\n| x | -6 | 6 | -5 | 25 | 26 | 40 | 33 |\n| y | 32 | 6 | 33 | 29 | -5 |…

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$, where $n$ is the number of data - points. Here $n = 7$.

Step2: Calculate $\sum x$, $\sum y$, $\sum xy$, $\sum x^{2}$, $\sum y^{2}$

• $\sum x=-6 + 6-5 + 25+26 + 40+33=119$
• $\sum y=32 + 6+33 + 29-5 + 7-10=92$
• $\sum xy=(-6)\times32+6\times6+(-5)\times33+25\times29+26\times(-5)+40\times7+33\times(-10)$ $=-192 + 36-165 + 725-130 + 280-330=224$
• $\sum x^{2}=(-6)^{2}+6^{2}+(-5)^{2}+25^{2}+26^{2}+40^{2}+33^{2}$ $=36 + 36+25+625+676+1600+1089=4087$
• $\sum y^{2}=32^{2}+6^{2}+33^{2}+29^{2}+(-5)^{2}+7^{2}+(-10)^{2}$ $=1024+36+1089+841+25+49+100=3164$

Step3: Substitute values into the formula

$n = 7$ $n\sum xy=7\times224 = 1568$ $(\sum x)(\sum y)=119\times92=10948$ $n\sum x^{2}=7\times4087 = 28609$ $(\sum x)^{2}=119^{2}=14161$ $n\sum y^{2}=7\times3164 = 22148$ $(\sum y)^{2}=92^{2}=8464$

$r=\frac{1568 - 10948}{\sqrt{(28609 - 14161)(22148 - 8464)}}$ $=\frac{-9380}{\sqrt{14448\times13684}}$ $=\frac{-9380}{\sqrt{197627432}}$ $=\frac{-9380}{14058.001}$ $\approx - 0.667$

Answer:

$-0.667$