(a) In Cindy Lou Who's multivariable calculus class, the teacher gave a multiple choice quiz with 20 questions. After the quiz, the teacher listed the number of correct answers for each student (x) and the number of incorrect answers (y). The mean number of correct answers in the class was 14.3, with a standard deviation of 2.5, and the mean number of incorrect answers was 6.7, also with a standard deviation of 2.5. The correlation between x and y was. . . -1, -0.5, -0.25, 0, 0.25, 0.5, 1, "can't tell without the actual data"
Choose one and explain your answer briefly.
(b) In a longitudinal study on growth, 1034 children were followed for 15 years. Among other data that the investigators collected were the heights of the children each year. Which of the following two correlations is bigger? Justify your answer briefly.
• r1 The correlation between a child's heights at age 4 and at age 18.
• r2 = The correlation between a child's heights at age 16 and at age 18.