Q4 Homework Bivariate Regression

Problem 1: Does officer height actually help law enforcement administrators predict the weight of male cadet recruits? This question was researched by a statistician who was interested in finding if she could predict a male applicant’s weight based on his height. She theorized that as height increases, weight will increase. Eight male applicants were measured for height in inches (Mean = 73, s = 3.295) and weighed (Mean = 175 lbs., s = 22.991 lbs.). Facts: The correlation between height and weight is Pearson r = .717, a = -190, b = 5, syest = 16.036, N = 8.

 1. Compute the Magnitude of Effect (MOE) of height on officer “weight?”

 2.   How many pounds is an officer who is (theoretically) zero inches tall predicted to weigh?

 3.   How many pounds is an officer who is 68 inches tall predicted to weigh?

 4.   What is the increase in pounds for every additional inch tall an officer measures?

 5.   Based on a 95% confidence level, what is the highest weight in pounds an officer who measures to 68 inches will weight?

 1.   51.4%

2. -190.0

3.  150.0

4.    5.0

5.  181.430

Problem 2: It is believed USDA officers who generally score high on the USDA entrance exam also are more effective at identifying fraud offenders. Therefore, it follows that by using a person’s USDA entrance exam score, an administrator will be able to predict the number of fraud offenders that investigator could identify. The entrance exam mean is 42.444, with a standard deviation of 12.197. The mean number of fraud offenders identified for this group of 9 investigators is 1022.222, s = 142.217. The correlation between USDA entrance exam scores and “fraud identifications” is r = .685, b = 7.991, a = 683.047 syest = 103.563.

 6. Compute the Magnitude of Effect (MOE) of USDA entrance exam scores on “fraud identifications?”

 7.   How many fraud identifications will an officer who scores (theoretically) zero on the USDA entrance exam be predicted to achieve?

 8.   How many fraud identifications can an officer who scores 35 on the USDA exam predicted to net?

 9.   What is the increase in fraud identifications for every additional point in the entrance exam?

 10.   Based on a 95% confidence level, what is the highest number of fraud identifications an officer who scores 35 on the USDA entrance exam expected to get?

 6.    47.0%

7.   683.047

8.   962.733

9.     7.991

10. 1165.716

Problem 3: The bureau of ATF rate their officers ranging from 1 to 8, with the higher number being the better rating. Each officer also takes the Myers-Briggs personality test. The mean personality rating was 23.833 with a standard deviation of 9.368.  The mean ATF rating score was 3.850 with a standard deviation of 2.218. Facts: The correlation between Meyers-Briggs scores and ATF ratings scores could be characterized as fairly strong and positive (r = .829), a = -.828, b = .196, Syest = 1.241,    N = 6. 

 11.   What is the Magnitude of Effect (MOE) of personality scores on ATF rating?

 12. What ATF score is an officer who attains a (theoretical) value of zero on the personality test predicted to attain?

 13. What ATF score is an officer who attains a value of 37 on the personality test predicted to attain?

 14. What ATF score is an officer who attains a value of 22 on the personality test predicted to attain?

 15. What ATF score is an officer who attains a value of 8 on the personality test predicted to attain?

 16. What is the change in ATF scores for each incremental increase in Myers-Briggs scores?

 17. Based on a 95% confidence level, what is the lowest ATF score a person who scores 37 on Myers-Briggs predicted to attain?

 11.  68.7%

12.   -.828

13.   6.424

14.   3.484

15.    .742

16.    .196

17.   3.922

Problem 4: The mean of auto theft is 67.200, with a standard deviation of 8.871. The mean of armed robbery is 61.200, with a standard deviations of 7.463. Facts: The correlation between the number of auto thefts and armed robberies is r = 0.898,  a = 10.464,  b = .755,  Syest = 3.287,    N = 5. 

 18. Compute the Magnitude of Effect (MOE) of auto thefts on armed robberies?

 19. How many robberies is a neighborhood that has (theoretically) zero auto thefts predicted to attain?

 20. How many robberies is a neighborhood that has 78 auto thefts predicted to have?

 21. How many robberies is a neighborhood that has 68 auto thefts predicted to have?

 22. How many robberies is a neighborhood that has 50 auto thefts predicted to have?

 23.  What is the change in robberies for each additional auto theft that occurs in that neighborhood?

 24. Based on a 95% confidence level, what is the fewest number of armed robberies a neighborhood that has 78 auto thefts will have?

 18.  80.6%

19.  10.464

20.  69.354

21.  61.804

22.  48.214

23.    .755

24.  62.911