Question

Elena collects data to investigate the relationship between the number of bananas she buys and the total cost. Which value for the correlation coefficient is most likely to match a linear relationship of the form y = mx + b?

A) -0.9
B) -0.4
C) 0.4
D) 0.9

Answer 1

For Elena's investigation on the relationship between the number of bananas and the total cost, the value most likely to match a linear relationship would be Option D) 0.9, indicating a strong positive linear relationship.

Step-by-step explanation:

The correlation coefficient indicates the strength and direction of a linear relationship between two variables. In Elena's case, she is trying to determine the relationship between the number of bananas she buys (independent variable) and the total cost (dependent variable). The correlation coefficient ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship at all.

For a linear relationship of the form y = mx + b, we expect a positive correlation coefficient if the slope m is positive (as the number of bananas increases, so does the cost), or a negative correlation coefficient if the slope m is negative (as the number of bananas increases, the cost decreases, which is unlikely in this context).

Option D) 0.9 is most likely to match a linear relationship with a positive slope because it is closest to 1, thus indicating a strong positive linear relationship between the number of bananas and the total cost.