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

 

 

 

1. r = 0.25

2. r = 0.33

3. r = 0.90

4. r = 0.14

 

 

 

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

 

 

 

1. r² = 0.54

2. r² = 0.13

3. r² = 0.29

4. r² = 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:

 

 

 

1. X = 42

2. X = 68

3. X = 23

4. 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 R², 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:

 

 

 

1. R² = 0.13, k = 5, N = 120

2. R² = 0.53, k = 5, N = 30

3. R² = 0.28, k = 4, N = 64

4. R² = 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

 

 

 

1. Plot the data and include a regression line in StatCrunch. Copy and paste your graph into your Word document for full credit.

2. What is the correlation coefficient r and what does it mean in this case?

3. What is the coefficient of determination and what does it mean in this case?

4. Is there a statistically significant correlation between dose and cholesterol level in this case?

5. 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)?