The table shows the data for 5 perch caught in a lake In Finland. For all calculations --- show...

The table shows the data for 5 perch caught in a lake In Finland. For all calculations --- show the formulas with values used.

What is the {eq}r^2 {/eq} for Weight and Length?

We have:

The calculation for the correlation coefficient:

{eq}\begin{align*} r & =\dfrac{(n\sum xy)-(\sum x\sum y)}{\sqrt{\left [(n\sum x^{2})-(\sum x)^{2} \right ]\left [(n\sum y^{2})-(\sum y)^{2} \right ]}} \\[2ex] & =\dfrac{(5)(14512.5)-(625)(114.7)}{\sqrt{\left [(5)(80025)-(625)^{2} \right ]\left [(5)(2653.39)-(114.7)^{2} \right ]}} \\[2ex] & \approx 0.8526 \end{align*} {/eq}

The coefficient of determination:

{eq}\begin{align*} r^2 & = r \\[2ex] & = (0.8526)^2 \\[2ex] & \approx \bf{0.7270} \end{align*} {/eq}