In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and theyield of wheat (bushels per acre). Calculate the linear correlation coefficient. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Rainfall (in inches), } \mathrm { x } & 9.8 & 8.1 & 12.7 & 11.8 & 18.1 & 9.6 & 6.3 & 14.9 & 15.3 \
\hline \text { Yield (bushels per acre), y } & 48.5 & 44.2 & 56.8 & 57 & 80.4 & 47.2 & 29.9 & 74 & 76.8
\end{array}$$
A) 0.981
B) 0.998
C) 0.900
D) 0.899

Question

In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and theyield of wheat (bushels per acre). Calculate the linear correlation coefficient. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Rainfall (in inches), } \mathrm { x } & 9.8 & 8.1 & 12.7 & 11.8 & 18.1 & 9.6 & 6.3 & 14.9 & 15.3 \
\hline \text { Yield (bushels per acre), y } & 48.5 & 44.2 & 56.8 & 57 & 80.4 & 47.2 & 29.9 & 74 & 76.8
\end{array}$$
A) 0.981
B) 0.998
C) 0.900
D) 0.899

Quizplus · Accepted Answer

The linear correlation coefficient, often denoted as $r$, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 means a perfect positive linear correlation, -1 means a perfect negative linear correlation, and 0 means no linear correlation. Given the data, calculating $r$ involves several steps including finding the means of $x$ and $y$, calculating the sum of the products of the deviations of each variable from its mean, and dividing by the square root of the product of the sums of the squares of the deviations of each variable. The calculation based on the provided data results in a high positive correlation, which is closest to the value given in option A, 0.981. This suggests a strong positive linear relationship between rainfall and wheat yield in the area studied.

In an Area of the Great Plains, Records Were Kept