Question

Find the value of the correlation coefficient. You may either compute it yourself from the formula, using the information below to help you, or use something like Excel or a graphing calculator to compute it for you.

Answer 1

We have to calculate the correlation coefficiente from the data in the table.

We can write the formula as:

`\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}}`

We can use the sums already calculated and replace withe the values as:

`\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(-14930)/(16910.74) \\ \rho\approx-0.883 \end{gathered}`

Answer: the correlation coefficient is r = -0.883.