We have to calculate the correlation coefficiente from the data in the table.
We can write the formula as:
[tex]\rho=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{\sqrt[]{\lbrack n\sum^{}_{}x^2-(\sum^{}_{}x)^2\rbrack\lbrack n\sum^{}_{}y^2-(\sum^{}_{}y)^2\rbrack}}[/tex]
We can use the sums already calculated and replace withe the values as:
[tex]\begin{gathered} \rho=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{\sqrt[]{\lbrack n\sum^{}_{}x^2-(\sum^{}_{}x)^2\rbrack\lbrack n\sum^{}_{}y^2-(\sum^{}_{}y)^2\rbrack}} \\ \rho=\frac{6\cdot3405-32\cdot1105}{\sqrt[]{(6\cdot220-32^2)(6\cdot364525-1105^2)}} \\ \rho=\frac{20430-35360}{\sqrt[]{(1320-1024)(2187150-1221025)}} \\ \rho=\frac{-14930}{\sqrt[]{296\cdot966125}} \\ \rho=\frac{-14930}{\sqrt[]{285973000}} \\ \rho\approx\frac{-14930}{16910.74} \\ \rho\approx-0.883 \end{gathered}[/tex]
Answer: the correlation coefficient is r = -0.883.
