Answer
$r=0.3273$
the worst of the three
Work Step by Step
Regression line: $y=mx+b,$
$m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n}$
$n=$ number of data points.
Correlation Coefficient: $r=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{n(\sum x^{2})-(\sum x)^{2}}\cdot\sqrt{n(\sum y^{2})-(\sum y)^{2}}}$
{\bf Interpretation}
If $r$ is positive, the regression line has positive slope;
if $r$ is negative, the regression line has negative slope.
If $r=1$ or $- 1$, then all the data points lie exactly on the regression line;
if it is close to $\pm 1$, then all the data points are close to the regression line.
If $r$ is close to $0$, then $y$ does not depend linearly on $x.$
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(c)
Using Excel, we set up a table
\begin{array}{|c|c|c|c|c|cc}
\hline & x & y & xy & xx & yy & \\
\hline & 4 & -3 & -12 & 16 & 9 \\
& 5 & 5 & 25 & 25 & 25 \\
& 0 & 0 & 0 & 0 & 0 \\\hline
\Sigma & {\bf 9} & {\bf 2} & {\bf 13} & {\bf 41} & {\bf 34} \\\hline
& & & & & \\
x points & 3 & & 39 & 123 & 102 \\
& & & & & \\
m= & 0.5 & & & & \\
b= & -0.83333 & & & & \\
& & & r= & 0.327327 & \\
\end{array}
m,b, and r are calculated according to the above formulas.
Regression line:$\qquad y=0.5x-0.8333,$
Correlation Coefficient: $r=0.3273$
which after calculating (a) and ($b$), turns out to be the worst of the three
