1. For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables:

a. *r* = 0.25

b. *r* = 0.33

c. *r* = 0.90

d. *r*= 0.14

2. For each coefficient of determination below, calculate the value of the correlation coefficient:

a. *r*^{2} = 0.54

b. *r*^{2} = 0.13

c. *r*^{2} = 0.29

d. *r*^{2} = 0.07

3. Suppose a researcher regressed surgical patients’ length of stay (dependent variable) in the hospital on a scale of functional ability measured 24 hours after surgery. Given the following, solve for the value of the intercept constant and write out the full regression equation:

Mean length of stay = 6.5days; mean score on scale = 33; slope = -0.10

4. Using the regression equation calculated in Exercise 3, compute the predicted value of Y (length of hospital stay) for patients with the following functional ability scores:

a. X = 42

b. X = 68

c. X = 23

d. X = 10

5. Use the regression equation below for predicting graduate GPA for the three presented cases.

Y? = -1.636 + 0.793(undergrad GPA) + 0.004(GREverbal) – 0.0009(GREquant)

+0.009(Motivation)

Subject undergrad GPA GREverbal GREquant Motivation

1 2.9 560 540 55

2 3.2 550 590 65

3 3.4 600 550 70

6. Using the following information for *R*^{2}, *k*, and *N*, calculate the value of the *F* statistic for testing the overall regression equation and determine whether *F* is statistically significant at the 0.05 level:

a. *R*^{2} = 0.13, *k* = 5, *N* = 120

b. *R*^{2} = 0.53, *k* = 5, *N* = 30

c. *R*^{2} = 0.28, *k* = 4, *N* = 64

d. *R*^{2} = 0.14, *k* = 4, *N* = 64

7. According to the University of Chicago, as men age, their cholesterol level goes up. A new drug (XAB) is being tested to determine if it can lower cholesterol in aging males and at what dose. The data for the first test subject is below:

Dose (mg) 2 3 5 6 8 10

Cholesterol level (mg/dL) 310 124 201 110 52 20

- Plot the data and include a regression line in
**StatCrunch.** Copy and paste your graph into your Word document for full credit. - What is the correlation coefficient
*r*and what does it mean in this case? - What is the coefficient of determination and what does it mean in this case?
- Is there a statistically significant correlation between dose and cholesterol level in this case?
- What is the predicted cholesterol level for a person taking a dose of 4 mg? What about if they are not taking the drug at all (0 mg)?