Compute the Linear Correlation Coefficient Between the Two Variables and Determine

Multiple Choice

Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
-To investigate the relationship between yield of soybeans and the amount of fertilizer used, a researcher divides a field into eight plots of equal size and applies a different amount of fertilizer to each plot. The table shows the yield of soybeans and the amount of fertilizer used for each plot.
$\begin{array}{c|cccccccc}\text { Amount of fertilizer (pounds) , } & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 & 4.5 \\\hline \text { Yield of soybeans (pounds) , y } & 25 & 21 & 27 & 28 & 36 & 35 & 32 & 34\end{array}$

A) $r = 0.819$ ; linear relation exists
B) $\mathrm { r } = 0.729$ ; no linear relation exists
C) $r = 0.683$ ; linear relation exists
D) $\mathrm { r } = 0.683$ ; no linear relation exists