Question

What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.

Answer 1

The answer is

`0.596`

To solve this problem, we must find the numbers of the linear regression (y = ao + a1*x). They can be found resolving the following equation system:

`\begin{gathered} n\cdot a_0+\Sigma x_i\cdot a_1=\Sigma y_i \\ \Sigma x_(i)a_(0)+\Sigma(x_(i))^(2)a_(1)=\Sigma x_(i)y_(i) \end{gathered}`
`\begin{gathered} 15a_o+512,9a_1=129,6 \\ 512,9a_o+22281,63a_1=5110,04 \end{gathered}`

When you have solved this system, you will get that ao = 3.7488 and a1 = 0.143

Afterward, we must find the error:

`Error\text{ = }\Sigma(y_i-a_o-a_1\cdot x_1)^2\text{ = 175.58}`

Then, we find the value of St:

`St=\Sigma(y-M)^2=272,656`

Finally, the correlation coefficient is equal to:

`r\text{ =}\sqrt{(St-Error)/(St)}=√(0.356)=0.596`

Therefore, the correlation coefficient is 0.596.