A group of garden enthusiasts are growing beans. The first number in parenthesis is the ounces of fertilizer used in a community garden plot with an area of $200 \mathrm{sq}$. $\mathrm{ft}$., the second number is the pounds of beans harvested in the plot: $(12,50),(6,36),(20,60),(5,24),(38,70),(3,24),(8,42),(20,65),(10,40),(15$, $60)$. Your best guess of the correlation coefficient between the two variables is
A) positive, may be 1.3
B) negative, may be -1.4
C) positive, but less than 1.0
D) negative, but greater than -1.0
E) cannot tell because of lack of specification as to which variable is correlated with which

Question

Quizplus · Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and values closer to 0 indicate a weaker linear relationship. Given the pairs of values for fertilizer used and beans harvested, as the amount of fertilizer increases, the pounds of beans harvested generally increases as well, suggesting a positive correlation. However, since the correlation coefficient cannot exceed 1 or be less than -1, option A is incorrect, making option C the best choice.

A Group of Garden Enthusiasts Are Growing Beans 200sq200 \mathrm{sq}200sq ft\mathrm{ft}ft

A Group of Garden Enthusiasts Are Growing Beans $200 \mathrm{sq}$ $\mathrm{ft}$