Answers must be explained below each question, solved in StatCrunch and saved into this Word document.

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

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)?