Answer
$r=-0.99974$
neither the best nor the worst
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|c|c}
\hline & x & y & xy & xx & yy \\
\hline & 0 & 0 & 0 & 0 & 0 \\
& 5 & -5 & -25 & 25 & 25 \\
& 2 & -2.1 & -4.2 & 4 & 4.41 \\\hline
\Sigma & {\bf 7} & -{\bf 7.1} & -{\bf 29.2} & {\bf 29} & {\bf 29.41} \\\hline
& & & & & \\
points & 3 & & -87.6 & 87 & 88.23 \\
& & & & & \\
m= & -0.99737 & & & & \\
b= & -0.03947 & & & & \\
& & & r= & -0.99974 & \\
\end{array}
m,b, and r are calculated according to the above formulas.
Correlation Coefficient: $r=-0.99974$
indicates a very good fit, but after calculating the other two cases, we find that it
is neither the best nor the worst of the three
