Assignment 4, this is statistics.

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)?

Additional Information

These are steps to follow.

For number 1 a,b and C, you are squaring the values, you will take correlation coefficient and square it to find the coefficient of determination , the R square. Then write down the values .

For number 2, you do it backward, take square root of the number to the correlation coefficient of determination .

Number 4 has 2 answers, solve for A first, use Regression equation , Do Algebra, then when you get A, you plug it in back into the Regression equation , create a new regression equation , then Use That to Solve NUMBER 4 Question.

For Number 5, do some Algebra, plug in the numbers. 3 Answers needed.

For 6, use this formulae F=R square of 2 divided by K OVER (1-R Squared 2)divided by N-K-1.

For number 7, the graph is scatter plot . 

I know you know all this already.