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. *r ^{2}* = 0.54

b. *r ^{2}* = 0.13

c. *r ^{2}* = 0.29

d. *r ^{2}* = 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 *R ^{2}*,

a. *R ^{2}* = 0.13,

b. *R ^{2}* = 0.53,

c. *R ^{2}* = 0.28,

d. *R ^{2}* = 0.14,

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

- Plot the data and include a regression line in
**StatCrunch.**Copy and paste your graph into your Word document for full credit. - What is the correlation coefficient
*r*and what does it mean in this case? - What is the coefficient of determination and what does it mean in this case?
- Is there a statistically significant correlation between dose and cholesterol level in this case?
- 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)?

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