In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Calculate the correlation coefficient, r. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Rain fall (in inches), } x & 9.5 & 7.8 & 12.4 & 11.5 & 17.8 & 9.3 & 6 & 14.6 & 15 \
\hline \text { Yield (bushels per acre), y } & 45.5 & 41.2 & 53.8 & 54 & 77.4 & 44.2 & 26.9 & 71 & 73.8
\end{array}$$
A)0.981
B)0.998
C)0.900
D)0.899

Question

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Calculate the correlation coefficient, r. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Rain fall (in inches), } x & 9.5 & 7.8 & 12.4 & 11.5 & 17.8 & 9.3 & 6 & 14.6 & 15 \
\hline \text { Yield (bushels per acre), y } & 45.5 & 41.2 & 53.8 & 54 & 77.4 & 44.2 & 26.9 & 71 & 73.8
\end{array}$$
A)0.981
B)0.998
C)0.900
D)0.899

Quizplus · Accepted Answer

The correlation coefficient, $r$, measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of $r$ ranges from -1 to 1, where 1 means a perfect positive linear relationship, -1 means a perfect negative linear relationship, and 0 means no linear relationship. To calculate $r$, you typically use the formula involving the sum of the products of the standardized scores of the two variables, or an equivalent formula that involves sums and squares of the original data values. Given the data provided, the calculation of $r$ would involve several steps including finding the means of $x$ and $y$, calculating the deviations from the means, squaring those deviations, multiplying the deviations of $x$ and $y$ for each pair, and then substituting these values into the formula for $r$. Without performing these calculations explicitly here, the correct answer is based on the assumption that these calculations have been done accurately, leading to a correlation coefficient of 0.981, indicating a very strong positive linear relationship between rainfall and wheat yield in the given dataset.

In an Area of the Midwest, Records Were Kept on the Relationship