The correlation between a family's weekly income and the amount they spend on restaurant meals is found to be r = 0.30. Which must be true?
I. Families tend to spend about 30% of their incomes in restaurants.
II. In general, the higher the income, the more the family spends in restaurants.
III. The line of best fit passes through 30% of the (income, restaurant$) data points.
A) II only
B) I only
C) III only
D) II and III only
E) I, II, and III

Question

Quizplus · Accepted Answer

II only. A correlation coefficient (r) of 0.30 indicates a positive but weak relationship between two variables, in this case, weekly income and spending on restaurant meals. This means that, generally, as income increases, spending on restaurant meals also increases, but not necessarily by a fixed percentage or with a high degree of predictability. Options I and III misinterpret the meaning of the correlation coefficient.

The Correlation Between a Family's Weekly Income and the Amount