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)

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)?