Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
-$\begin{array}{r|rrrrrrrr}
x & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline y & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$

A) $\mathrm { r } = 0.708$; linear relation exists
B) $r = 0.235$; no linear relation exists
C) $\mathrm { r } = - 0.708$; linear relation exists
D) $r = 0.708$; no linear relation exists

Question

Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
-$\begin{array}{r|rrrrrrrr}
x & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline y & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$

A) $\mathrm { r } = 0.708$; linear relation exists
B) $r = 0.235$; no linear relation exists
C) $\mathrm { r } = - 0.708$; linear relation exists
D) $r = 0.708$; no linear relation exists

Quizplus · Accepted Answer

The linear correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. A value of r = 0.708 indicates a strong positive linear relationship, suggesting that as x increases, y also tends to increase. This value is significantly different from 0, which supports the existence of a linear relation between the variables.

Compute the Linear Correlation Coefficient Between the Two Variables and Determine