Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
-$\begin{array}{c|cccccccc}
\mathrm{x} & 10 & 11 & 16 & 9 & 7 & 15 & 16 & 10 \
\hline \mathrm{y} & 96 & 51 & 62 & 58 & 89 & 81 & 46 & 51
\end{array}$

A) $r = - 0.335$; no linear relation exists
B) $\mathrm { r } = 0.462$; linear relation exists
C) $\mathrm { r } = - 0.284$; no linear relation exists

Question

Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
-$\begin{array}{c|cccccccc}
\mathrm{x} & 10 & 11 & 16 & 9 & 7 & 15 & 16 & 10 \
\hline \mathrm{y} & 96 & 51 & 62 & 58 & 89 & 81 & 46 & 51
\end{array}$

A) $r = - 0.335$; no linear relation exists
B) $\mathrm { r } = 0.462$; linear relation exists
C) $\mathrm { r } = - 0.284$; no linear relation exists

Quizplus · Accepted Answer

The linear correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. The formula for r involves the covariance of the variables divided by the product of their standard deviations, or it can be calculated using a simplified formula that involves sums of squares of the variables and their products. The calculated value of $r = - 0.335$ suggests a weak negative linear relationship between x and y. Since the correlation coefficient is relatively close to 0, it indicates that there is no strong linear relation between the variables.

Compute the Linear Correlation Coefficient Between the Two Variables and Determine