Examining Relationships in Linear Regression and Prediction Questions

Week 11Examining Relationships (Part 2): Linear Regression and Prediction
Graded Assignment
This week’s graded assignment involves the U.S. Air Force’s physical fitness testing standards,
which the Air Force strengthens and refines periodically. A recent change to these standards took
effect Oct. 21, 2013, and included the following (see http://www.afpc.af.mil/affitnessprogram/):
• body composition, which is evaluated by abdominal circumference measurements;
• an aerobics component, which is evaluated by a 1.5-mile timed run; and
• muscular fitness, which is evaluated by the number of push-up and sit-ups completed
within 1 minute.
According to the new standards, members who fail the abdominal circumference component but
pass the other components will be administered a body mass index (BMI) screen, and members
who do not pass the BMI will be administered a body fat analysis.
The data contained in the corresponding Excel file were acquired from the records of
members of the 114th Range Operations Squadron (114 ROPS) of the Florida Air National
Guard, which makes up one arm of the reserve component to the U.S. Air Force. The data file
consists of 114 ROPS’ physical fitness test (PFT) and BMI scores. For PFT scores, the higher the
score the more physically fit is the person. For BMI scores—which are calculated based on a
person’s height and weight and measure obesity—the higher the BMI score, the more overweight
and obese is the person. Your assignment is to analyze these data to determine the extent to
which the Air Force can predict service members’ PFT scores by their BMI scores. You are to
import this data set into your statistical software program and do the following (see the
corresponding “Guided Example” from the Gallo document for guidance):
A. Pre-Data Analysis
1. What is the research question and corresponding operational definitions?
2. What is the research methodology/design and why is this methodology appropriate?
3. Conduct an a priori power analysis to determine the minimum sample size needed. Is the
given data set sufficient relative to this minimum sample size? In what way do you think
the size of the given sample will impact the results?
B. Data Analysis
Using the data from the Excel file, conduct a hypothesis test as follows:
1. Formulate the null and alternative hypotheses in symbols and words.
2. Determine the test criteria.
3. Test for the four main assumptions of regression.
4. Run the analysis and record the results.
5. Perform an outlier analysis using Jackknife distances (there should be six outliers).
Compare the results of the analysis without outliers to the results with outliers present.
Determine whether you will keep the outliers or deleted them and explain the reasons for
your decision.
6. Make a decision to reject or fail to reject the null hypothesis and write a concluding
statement.
C. Post-Data Analysis
1. Determine and interpret the effect size.
2. Determine and interpret the power of the study.
3. Determine and interpret the 95% confidence interval and comment on the AIPE.
4. Present at least three plausible explanations for the results.
5. Interpret the findings from a practical perspective.