In a large statistics class students have taken two exams Fo

In a large statistics class, students have taken two exams. For each of the following situations, report what you would expect for the value of the correlation coefficient between exam 1 score and exam 2 score. Give a brief justification for your answer.

1. Every student scores ten points lower on exam 2 than on exam 1.

2. Every student scores twice as many points on exam 2 than on exam 1.

3. Every student scores half as many points on exam 2 than on exam 1.

4. Every student guesses randomly on every question on both exams.

5. Every student scores 100 points for his/her combined score on the two exams.

Solution

1. the coefficient will be exactly one since it measures linear dependence and these are perfectly linearly dependent. 2. the coefficient will be exactly one since it measures linear dependence and these are perfectly linearly dependent. 3. the coefficient will be exactly one. it doesn\'t matter which score is higher. 4. the expected value will be 0 since there won\'t be any correlation between random values. 5. the coefficient will be -1. every high score is matched by a low score on the other test.