Suppose 50 married couples are asked to provide their ages. For all couples, the husband is exactly 2 years older than his wife. For example, a 50- year-old husband has a wife who is 48 years old. What is the best estimate of the correlation coefﬁcient between the ages of husbands and their wives?
A)No conclusions can be drawn without seeing a scatterplot of the data.
B)The correlation coefﬁcient between the ages of husbands and wives is equal to 1.
C)The correlation coefﬁcient between the ages of husbands and wives is equal to 0.
D)The correlation coefﬁcient between the ages of husbands and wives is equal to −1.

Question

Quizplus · Accepted Answer

The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. In this case, since the age of the husband is perfectly predictable from the age of the wife (and vice versa) with a constant difference of 2 years, the relationship is perfectly linear and positive, leading to a correlation coefficient of 1.

Suppose 50 Married Couples Are Asked to Provide Their Ages