The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

124 CHAPTER 7 Correlation, Regression, and Logistic Regression

16. Table 7.7 shows the Math Olympiad scores for 33 math students at
    Churchville Elementary School in Churchville, Pennsylvania in 2002. We
    are interested in how well the fi rst score (test 2) predicts the students next
    score (test 3). Plot the scatter diagram for this data. Compute the Pearson
    correlation coeffi cient and the square of the correlation coeffi cient.
    Calculate the mean score for test 2 and the mean score for test 3.


17. Math Olympiad and regression toward the mean. The least squares regres-
    sion equation for exam score 3, y as a function of exam score 2, x , is:

yx=+0 4986...1 0943

The possible scores for exam 2 are 0, 1, 2, 3, 4, and 5. For each pos-

sible score, use the above regression equation to predict the score for exam

3 for a student who got that score on exam 2. Fill in the predicted scores

for Table 7.8.

18. Having computed the average scores on exams 2 and 3, you know that in
    both cases, the average is somewhere between 2 and 3. So scores on exam
    2 of 0, 1, and 2 are below average, and scores of 3, 4, and 5 are above
    average. Compare the scores on exam 2 with their predicted score for
    exam 2 scores of 0, 1, and 2. Are the predicted scores lower or higher than
    the exam 2 score? Now, for scores 3, 4, and 5, are the predicted scores

Table 7.6

Dosage Versus Sleeping Time

Sleeping time Y (hours) Dosage X ( μ M/kg)

4 3

6 3

5 3

9 10

8 10

7 10

13 15

1 1 1 5

9 15

Σ Y = 7 2 Σ X = 84

Σ Y 2 = 642 Σ X 2 = 1002

Σ XY = 780