The developer of a new plant fertilizer gathered data about the quantity of fertilizer applied to a lemon tree and the number of lemons it produced. He used a graphing tool to organize the data in a scatter plot and find the line of best fit.

Question

He found that the relationship between grams of fertilizer, x, and the number of lemons, y, is modeled by the equation y = 0.316x + 12.214, and the correlation coefficient for the data is 0.948.

Could this line of best fit be used to make reliable predictions?

A.
No, because the slope of the line is closer to 0 than to 1, which indicates a weak association between the variables.
B.
No, because the correlation coefficient is closer to 1 than to 0, which indicates a weak association between the variables.
C.
Yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association between the variables.
D.
Yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.

Answer 1

The correct answer is:

D. Yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.

The correlation coefficient (r) of 0.948 indicates a strong positive linear relationship between the quantity of fertilizer applied and the number of lemons produced. Since the value is close to 1, it suggests that reliable predictions could be made using the line of best fit. The slope of the line, while it provides information about the direction of the relationship, does not itself determine the strength of the association.