A researcher conducted a study to evaluate a strength-injury hypothesis. He collects data on a group of 100 elderly men. Specifically, the study was designed with four predictor variables, age (age), medical index (medical), strength index (strength), and cardiovascular index (cardio).The researcher sets out to determine how accurately a physical injury index (injury, which is the number and severity of accidents)can be predicted from a linear combination of four different measures for elderly men?
Using an alpha level of .05, the above scenario, and the information provided in the SPSS output answer the following questions.
Be sure to provide specifics (symbols and values) to receive full points.
1.(2 points) First – check for multicollinearity. Conduct the appropriate diagnostic analysis and indicate your findings, based on the Variance Inflation Factor.
2.Regress injury index (INJURY) on age (age), medical index (medical), strength index (strength), and cardiovascular index (cardio).
a.(2 points) What proportion of the variance in injury index is explained by AGE, MEDICAL, STRENGTH, and CARDIO?
b.(2 points) Does the set of variables significantly predict injury index? Indicate how you came to this conclusion.
c.(2 points) Indicate whether these four variables have a significant influence on injury index (account for all 4 variables)? Indicate how you came to this conclusion.
d.(2 points) Which of these four variables have the greatest influence (relative importance) on injury index? Indicate how you came to this conclusion.
e.(2 points) Choose any one of the four predictor (independent) variables and explain its beta value as it relates to the criterion (dependent) variable.
3.(3 points) Complete Table 1 and Table 2 based on the SPSS outputfor this study (use 3 decimal placesand applicable asterisksfor full points).
Table 1
Means, Standard Deviations, and Correlations for Regression of Overall Injury Index (N = 100)
1 / 2 / 3 / 4 / 51. Overall Injury Index / 1.000
2. Age / 1.000
3. Medical Index / 1.000
4. Strength Index / 1.000
5. Cardio Index / 1.000
Means
Standard Deviations
Table 2
Results of Regression of Overall Injury Index
Independent Variables / B / / tAge
Medical Index
Strength Index
Cardio Index
Note. R2 = .______(p < .______).
*p < .05, **p < .01, ***p < .001
CDAA No. 4 – Part 1 – MLR
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You are interested in better understanding who does well and who does poorly in statistics courses. You have been provided with a set of data containing 100 randomly selected students who have taken a college statistics course. The data contain the students’ average performance on statistics exams, students’ scores on math and English aptitude tests that students took in their senior year of high school and the students’ high school grade point average in math, English, and all other courses. The specific research questions for this study are: “How well do students’ high school test scores and grade point averages (GPA) predict a students’ test performance in statistics courses?” and “Do students’ high school grade point averages contribute significantly over and above their aptitude test scores in predicting exams scores in statistics?”The dataset contains a total of 6 variables for a sample of 100 students. For this assignment, you will use an a priori alpha level of .05 ( = .05) for all analyses. Your dependent measure will be the students’ average percentage correct on exams in a college statistics course (StatExam) and the independent variables are as follows:
MathTestScore on a math aptitude test taken senior year of high school
EngTestScore on an English aptitude test taken senior year of high school
MathGPAHigh school GPA in math courses
EngGPAHigh school GPA in English courses
OtherGPAHigh school GPA in courses other than English and math
Using the above scenario and the information provided from the SPSS output, complete/answer each of the following questions. Be brief – but be thorough(i.e., provide specific symbol and value information) in order to receive the maximum possible points for each question. Be sure to answer all parts and sub-parts of each question.
1.(3 points) Check for multicollinearity. Conduct the appropriate diagnostic analyses and indicate your findings below based on the Variance Inflation Factor (VIF). Be sure to include what you found, the criteria for which it was judged against, and indicate whether there is a concern or not for each independent variable.
2.Using the full dataset – run the regression analysis to answer the following questions:
“How well do students’ high school test scores and grade point averages (GPA) predict a students’ test performance in statistics courses?” and “Do students’ high school grade point averages contribute significantly over and above their aptitude test scores in predicting exams scores in statistics?”
2a.(3 points) In answering the first research question, indicate what proportion of the total variance in the statistics courses performance is explained by the entire set of independent variables?Is this proportion of explained variance significant? Indicate how you made that decision (be sure to show applicable values).
2b.(3 points) What proportion of the total variance in the statistics courses performance is explained by the set of control (aptitude) variables? Is this proportion of explained variance significant? Indicate how you made that decision (be sure to show applicable values).
2c.(3 points) In answering the second research questionas to whether the set of GPA variables explained a significant proportion of additional total variance in the dependent measure, indicate what proportion of the total variance in the statistics courses performance is explained by the set of grade-point average variables? In other words, what is the contribution of high school grade point averages over and above high school test scores?Is this proportion of explained variance significant? Indicate how you made that decision (be sure to show applicable values).
3.(4 points) Of the five independent variables, which ones (if any) have a significant influence on the dependent measure? Indicate how you made your determination (be sure to show applicable values).
4.(3 points) List the independent variables based on their relative importance from greatest to least influence. Indicate how you made your determination (be sure to show applicable values). Careful on the selection.
5.(2 points) Choose any two of the five predicator (independent) variables and briefly explain its beta value as it relates to the criterion (dependent) variable.
6.(4 points) Complete Table 1 and Table 2 based on the SPSS output for this study (using 3 decimal places and applicable asterisks for full points).
(BONUS – up to 5 points) Write a results section for this analysis. Your result section should be similar to the in-class example, including a complete narrative. You do not need to submit/send the tables, as they will have already been submitted for grade with CDAA No. 4. Be sure to use the example as a guide so as to not loose points. Double-check your writing and numbers before turning in this assignment.
This bonus option will be accepted via e-mail for grading as long as it is received by Monday, April 24, 2006. Be sure that you cc: a copy to yourself and confirm with me that I have received the attachment by the deadline.
CDAA No. 4 - MLR
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Table 1
Means, Standard Deviations, and Correlations for Regression of Statistics Course Performance (N = 100)
1 / 2 / 3 / 4 / 5 / 61. Statistics Exam / 1.000
2. Math Aptitude Test / 1.000
3. English Aptitude Test / 1.000
4. Math GPA / 1.000
5. English GPA / 1.000
6. Other Courses GPA / 1.000
Means
Standard Deviations
CDAA No. 4 - MLR
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Table 2
Results of Regression of Statistics Course Performance on Test Scores and GPA
Independent Variables / B / / tModel 1
Math Aptitude Test
English Aptitude Test
Model 2
Math Aptitude Test
English Aptitude Test
Math GPA
English GPA
Other Courses GPA
Note. R2 = ______for Model 1, (p ______);
R2 = ______for Model 2, (p ______;
Total R2 = ______, (p ______).
***p < .001
CDAA No. 4 - MLR
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