Mathematics homework help

Week 4 Assignment

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INDICATE IF YOU HAVE YOUR OWN ACCESS AND USE TO STATCRUNCH. ALL ANSWERS MUST SHOW ALL STEPS WITH A SHORT EXPLAINATION OF EACH STEP, SHOW GRAPHS AND COPY TO  BOTH EXCEL SPREASHEET AND WORD DOC.

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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)?