Answer
$r=0$
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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(b)
Using Excel, we set up a table
\begin{array}{|c|c|c|c|c|c|c}
\hline & x & y & xy & xx & yy \\
\hline & 0 & 1 & 0 & 0 & 1 \\
& 1 & 0 & 0 & 1 & 0 \\
& 2 & 1 & 2 & 4 & 1 \\\hline
\Sigma & {\bf 3} & {\bf 2} & {\bf 2} & {\bf 5} & {\bf 2} \\\hline
& & & & & \\
points & 3 & & 6 & 15 & 6 \\
& & & & & \\
m= & 0 & & & & \\
b= & 0.666667 & & & & \\
& & & r= & 0 & \\
\end{array}
m,b, and r are calculated according to the above formulas.
Correlation Coefficient: $r=0$
indicates that $y$ does not depend linearly on $x$
and, after calculating the other two cases, we find that it
is the worst of the three
