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. r2 = 0.54
b. r2 = 0.13
c. r2 = 0.29
d. 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:
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 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:
a. R2 = 0.13, k = 5, N = 120
b. R2 = 0.53, k = 5, N = 30
c. R2 = 0.28, k = 4, N = 64
d. 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
a. Plot the data and include a regression line in StatCrunch. Copy and paste your graph into your Word document for full credit.
b. What is the correlation coefficient r and what does it mean in this case?
c. What is the coefficient of determination and what does it mean in this case?
d. Is there a statistically significant correlation between dose and cholesterol level in this case?
e. 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)