Find the value of the linear correlation coefficient r.
-$$\begin{array} { r | r r r r r }
\mathrm { x } & 47.0 & 46.6 & 27.4 & 33.2 & 40.9 \
\hline \mathrm { y } & 8 & 10 & 10 & 5 & 10
\end{array}$$
A) 0.156
B) -0.175
C) 0
D) 0.175

Question

Find the value of the linear correlation coefficient r.
-$$\begin{array} { r | r r r r r } 
\mathrm { x } & 47.0 & 46.6 & 27.4 & 33.2 & 40.9 \
\hline \mathrm { y } & 8 & 10 & 10 & 5 & 10
\end{array}$$
A) 0.156
B) -0.175
C) 0
D) 0.175

Quizplus · Accepted Answer

We can use a calculator or a statistical software to find the linear correlation coefficient r. The formula for r is:

$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{n\sum x^2 - (\sum x)^2}\sqrt{n\sum y^2 - (\sum y)^2}}$

where n is the number of data points, $\sum$ denotes summation, and $\sqrt{}$ denotes square root.

Using the data in the table:

$n = 5$
$\sum x = 195.1$
$\sum y = 43$
$\sum x^2 = 10080.3$
$\sum y^2 = 435$
$\sum xy = 1465.4$

Substituting these values into the formula, we get:

$r = \frac{5(1465.4) - (195.1)(43)}{\sqrt{5(10080.3) - (195.1)^2}\sqrt{5(435) - (43)^2}} \approx 0.175$

Therefore, the value of the linear correlation coefficient r is approximately 0.175, which is answer choice D.

Find the Value of the Linear Correlation Coefficient R x47.046.627.433.240.9y81010510\begin{array} { r | r r r r r } \mathrm { x } & 47.0 & 46.6 & 27.4 & 33.2 & 40.9 \\\hline \mathrm { y } & 8 & 10 & 10 & 5 & 10\end{array}xy​47.08​46.610​27.410​33.25​40.910​​

Find the Value of the Linear Correlation Coefficient R $\begin{array} { r | r r r r r } \mathrm { x } & 47.0 & 46.6 & 27.4 & 33.2 & 40.9 \\\hline \mathrm { y } & 8 & 10 & 10 & 5 & 10\end{array}$