Two-Variable Relationships

 Practice Problem Solutions

1. See the Activity Based book for solutions.

2. So you've just graded your class's second midterm and went through the trouble to discover that the correlation between midterm1 and midterm2 is 0.68. Oh no! You just realized that you graded a problem wrong, and that score on midterm2 should go up by 5 points. How does this affect the correlation? Explain.

Correct Answer:
It does not affect the correlation. The correlation measures the strength of the linear relationship. Imagine the affect on the scatterplot (midterm2 vs. midterm1) of adding the 5 points; the "cloud" of points would merely be shifted up by 5; the nature of the linear relatinship would not change.

3. The correlation between midterms 1 and 2 is positive. Is it possible that, on average, the class did worse on midterm 2 than on midterm 1? Explain.

Correct Answer:
Yes, it's possible. The positive correlation means that students who did above average on midterm 1 tended to score above average on midterm 2. However, the average on midterm 2 might have been lower. (Perhaps it was a more difficult exam.) Moral: correlation measures the relationship between x and y relative to standard units.
 

4. One of your students, Rapunzel, scored half a standard deviation above average on the first midterm. The average on the second midterm was 75. Can you predict Rapunzel's score? If no, explain what additional information is required. If yes, then predict!

Correct Answer:
No. You need to know the standard deviation of the second midterm. So, smarty-pants, lets say the standard deviation was 5. Now can you predict?