Question

determine whether the scatter diagram indicates that a linear relation may exist between the two variables. if the relation is linear, determine whether it indicates a positive or negative association between the variables. use this information to answer the following
do the two variables have a linear relationship?
a. the data points do not have a linear relationship because they do not lie mainly in a straight line.
b. the data points do not have a linear relationship because they lie mainly in a straight line
c. the data points have a linear relationship because they lie mainly in a straight line.
d. the data points have a linear relationship because they do not lie mainly in a straight line
if the relationship is linear do the variables have a positive or negative association?
a. the variables have a positive association
b. the variables have a negative association
c. the relationship is not linear

Explanation:

Step1: Check linear relationship

In a linear relationship, data points should lie mainly in a straight line. Observing the scatter - diagram, the data points do not lie mainly in a straight line.

Step2: Determine association (if linear)

Since the relationship is not linear (from Step1), we don't need to calculate positive or negative association. But if we assume for the sake of the second part (even though the first part shows non - linear), positive association means as one variable increases, the other increases; negative means as one increases, the other decreases. Here, since non - linear, we refer back to the non - linear conclusion.

Answer:

For the first question: A. The data points do not have a linear relationship because they do not lie mainly in a straight line.
For the second question: C. The relationship is not linear.