What does it mean to say that two variables are positively associated? Negatively associated? What does it mean to say that two variables are positively associated?

A. There is a relationship between the variables that is not linear.

B. There is a linear relationship between the variables.

C. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases.

D. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.

The correct option is D. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.

Step-by-step explanation:

Two variables are associated when a variation in one of them produces a variation on the other one, it means that there is a dependence relationship.

When this association is positive, it implies that both variables have the same behaviour (when one increases the otherone increases or if one decreases the otherone too). On the contrary, two variables are negatively associated when one of them increases or decreases and the otherone has the opposite trend. For example, the following equations describes positive (1) and negative (2) associations:

(1) y = 2x + 3

(2) y = 1/x

As you can see, in case (1) when "x" is bigger⇒ "y" is bigger / "x" is lower ⇒"y" is lower too. On the contrary, in equation (2), when "x" is bigger, "y" (1/x) is lower.