Question

Suppose that two​ variables, X and​ Y, are negatively associated. Does this mean that​ above-average values of X will always be associated with​ below-average values of​ Y? Explain.

Choose the correct answer below.
A. ​No, because there will always be at least one point that does not fit the trend.
B. ​No, because association does not mean that every point fits the trend. The negative association only means that​ above-average values of X are generally associated with​ below-average values of Y.
C. ​No, because when two​ variables, X and​ Y, are negatively​ associated, above-average values of X are associated with​ above-average values of Y.
D. ​Yes, because if one or more​ above-average values of X are associated with​ above-average values of​ Y, the variables cannot be negatively associated.

Answer 1

B

Explanation:

I had this same homework problem. Two variables that are linearly related are negatively associated when​ above-average values of one variable are associated with​ below-average values of the other variable. That​ is, two variables are negatively associated​ if, whenever the value of one variable​ increases, the value of the other variable decreases.​ However, this association does not require every point to fit the trend. A negative association means that​ above-average values of X are generally associated with​ below-average values of Y.

Answer 2

B. ​No, because association does not mean that every point fits the trend. The negative association only means that​ above-average values of X are generally associated with​ below-average values of Y.

Explanation:

If two​ variables, X and​ Y, are negatively associated, then the curve that fits its correlation has a negative slope (assuming that the relation was linear). Therefore, when values of X increase, values of Y decrease and vice versa. But this doesn't guarantee that all above-average values of X will always be associated with​ below-average values of​ Y because not every point fits the trend.