In February 2015, a Criminologist (a specialist in criminology) gave job placeme
ID: 3172776 • Letter: I
Question
In February 2015, a Criminologist (a specialist in criminology) gave job placement tests to 5 police officers in the county who had transferred from other counties. The Criminologist gave the same test again at the end of the first year. Both tests were scored on a scale of 1 to 10 (10 is the best score). Using the data given below do all the required computations and make conclusions.
1) Show if the placement test scores can be used as a predictor of their end of year performance? Compute b (slope) and a (intercept) and write the regression equation for this problem. Show all intermediate steps and marks answers for each step clearly. Explain what you find.
2) Justin took the above placement test in 2016, if he scored 5 on the Placement test what will his predicted score is on the End of Year Test in 2016.
3) Explain the difference in results you see for the regression analysis and say what advice you will give to the Police Chief about their performance based on the predictions made from the Placement Test. Read the textbook to see how you interpret results from regression analysis.
ID No: Gender Officer Placement Test (X) End of Year Post Test (Y) 1 Female Ellen 4 10 2 Female Beyonce 5 6 3 Male Christian 6 9 4 Female Brittany 7 8 5 Male Franklin 8 7Explanation / Answer
number of observation=n=5
the linear regression y=a+bx is given as y=10.4 - 0.4*x
a=(sum(y)*sum(x2)-sum(x)*sum(xy))/(n*sum(x2)-(sum(x))2 =10.4
b=(n*sum(xy)*-sum(x)*sum(y))/(n*sum(x2)-(sum(x))2 = -0.4
(2) for x=5, y=10.4 - 0.4*5=8.4
(3) the difference of observed and estimated=6-8.4=-2.4, which seems large. but theoretical it should be near to zero. so linear regression y=a+bx is not good for prediction.
s.n. Placement Test (X) End of Year Post Test (Y) x2 y2 xy 1 4 10 16 100 40 2 5 6 25 36 30 3 6 9 36 81 54 4 7 8 49 64 56 5 8 7 64 49 56 sum 30 40 190 330 236