Stats Questions

Week 4 Assignment

1.        (1pt) For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables:

1. r = 0.25
2. r = 0.33
3. r = 0.80
4. r = 0.14

2.        (1pt) For each coefficient of determination below, calculate the value of the correlation coefficient:

1. r² = 0.54
2. r² = 0.13
3. r² = 0.39
4. r² = 0.07

3.        (1pt) 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 = 6.5 days; mean score on scale = 33; slope = -0.10

4.        (1pt) 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:

1. X = 42
2. X = 68

5.        (4 pts) Reexamine the Fellows Research Groupdata we used in week 2’s assignment (the excel file is named “Fellows Mental Health Data” and is also in this week’s assignment area). Using this data set again, perform a correlation analysis using the General Practitioner Assessment of Cognition score (“GPCOG”) as a predictor of the Mental Health Survey Score (“MentalHlth”) of all subjects.

1. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch.  Copy and paste your graph and regression output into your Word document for full credit.
2. What is the correlation coefficient r and what is the coefficient of determination here? What does the coefficient of determination mean in this case?
3. Is there a statistically significant correlation between cognition and mental health in this sample?
4. What hypotheses did you test?

6.        (5 pts) 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           190           110           52           20

1. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch.  Copy and paste your graph and regression output into your Word document for full credit.
2. What is the correlation coefficient r and what is the coefficient of determination here? What does the coefficient of determination mean in this case?
3. Is there a statistically significant correlation between the dose and cholesterol in this sample?
4. What hypotheses did you test?
5. Using StatCrunch, what is the predicted cholesterol level for a person taking a dose of 7 mg? Copy and paste your regression output from StatCrunch into your Word document for full credit.

7.        (5 pts) A study by the University of Montreal examined a new test to deepen the evaluation of mental states through the creation and validation of a practical measure, the Mental States Task (MST). The researchers examined many factors including age and the valid and reliable PANAS test. The data is in an excel file named “Montreal_Study_on_Mental_States” and is also in this week’s assignment area. Using this data set, perform a correlation analysis using the subject’s age (“AGE”) as a predictor of their PANAS score (“PANAS”) of all the subjects.

1. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch.  Copy and paste your graph and regression output into your Word document for full credit.
2. What is the correlation coefficient r and what is the coefficient of determination here? What does the coefficient of determination mean in this case?
3. Is there a statistically significant correlation between age and the PANAS score in this sample?
4. What hypotheses did you test?
5. Using StatCrunch, what is the predicted PANAS score for a subject that is 23 years old? Copy and paste your regression output from StatCrunch into your Word document for full credit.

8.        (1pt) Use the multiple regression equation below for predicting graduate GPA for the two subjects below:

           Y′ = -1.636 + 0.793(undergrad GPA) + 0.004(GREverbal) – 0.0009(GREquant) +0.009(Motivation)

9.        (1pt) Using the following information for R², k, and N, calculate the value of the F statistic for testing the overall multiple regression equation and determine whether F is statistically significant at the 0.05 level: 

1. R² = 0.13, k = 5, N = 120
2. R² = 0.18, k = 3, N = 64