Week 4

Due Friday 30th?

Week 4 Assignment

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)?