Question

Q) Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland is able to show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all first-year students. Lakeland’s administration also suspects that students with lower GPAs have a higher probability of leaving Lakeland at the end of the first year. In order to investigate the relation of these variables to retention, Lakeland selected a random sample of 100 students from last year’s entering class. The data are contained in the data set named Lakeland; a portion of the data follows.

Student | GPA | Program | Return |

1 | 3.78 | 1 | 1 |

2 | 2.38 | 0 | 1 |

3 | 1.30 | 0 | 0 |

4 | 2.19 | 1 | 0 |

5 | 3.22 | 1 | 1 |

6 | 2.68 | 1 | 1 |

7 | 2.72 | 0 | 0 |

8 | 1.74 | 0 | 0 |

9 | 1.86 | 0 | 0 |

10 | 3.53 | 1 | 1 |

11 | 3.12 | 0 | 1 |

12 | 1.21 | 0 | 0 |

13 | 3.01 | 1 | 1 |

14 | 2.70 | 0 | 0 |

15 | 2.47 | 1 | 1 |

16 | 2.37 | 0 | 1 |

17 | 2.28 | 1 | 0 |

18 | 2.76 | 0 | 0 |

19 | 2.24 | 0 | 0 |

20 | 3.10 | 1 | 1 |

21 | 2.86 | 0 | 1 |

22 | 2.62 | 0 | 1 |

23 | 3.07 | 1 | 1 |

24 | 2.18 | 0 | 1 |

25 | 3.30 | 1 | 1 |

26 | 2.43 | 1 | 0 |

27 | 2.38 | 0 | 0 |

28 | 1.23 | 0 | 0 |

29 | 2.63 | 1 | 1 |

30 | 4.00 | 1 | 1 |

31 | 2.21 | 1 | 0 |

32 | 1.73 | 0 | 0 |

33 | 2.62 | 1 | 0 |

34 | 2.65 | 1 | 1 |

35 | 2.82 | 1 | 1 |

36 | 3.77 | 1 | 1 |

37 | 2.38 | 1 | 1 |

38 | 3.11 | 1 | 1 |

39 | 2.82 | 0 | 1 |

40 | 2.16 | 1 | 0 |

41 | 2.66 | 1 | 0 |

42 | 3.33 | 1 | 1 |

43 | 2.77 | 1 | 0 |

44 | 4.00 | 1 | 1 |

45 | 2.33 | 0 | 0 |

46 | 3.41 | 0 | 0 |

47 | 1.98 | 1 | 0 |

48 | 3.06 | 1 | 1 |

49 | 3.98 | 1 | 1 |

50 | 3.24 | 1 | 1 |

51 | 3.22 | 0 | 0 |

52 | 3.05 | 1 | 1 |

53 | 2.66 | 0 | 0 |

54 | 2.88 | 1 | 1 |

55 | 2.60 | 1 | 1 |

56 | 3.12 | 1 | 1 |

57 | 3.12 | 1 | 1 |

58 | 2.72 | 1 | 1 |

59 | 3.38 | 1 | 1 |

60 | 3.29 | 0 | 1 |

61 | 3.49 | 1 | 1 |

62 | 2.89 | 1 | 1 |

63 | 2.46 | 1 | 1 |

64 | 1.90 | 1 | 1 |

65 | 2.77 | 1 | 1 |

66 | 2.61 | 0 | 0 |

67 | 2.44 | 1 | 0 |

68 | 3.10 | 1 | 1 |

69 | 3.87 | 1 | 1 |

70 | 3.25 | 1 | 1 |

71 | 2.44 | 1 | 1 |

72 | 2.66 | 1 | 1 |

73 | 3.06 | 1 | 1 |

74 | 2.75 | 0 | 1 |

75 | 3.65 | 1 | 1 |

76 | 1.66 | 0 | 0 |

77 | 3.41 | 1 | 1 |

78 | 2.91 | 1 | 1 |

79 | 2.15 | 0 | 1 |

80 | 1.54 | 0 | 0 |

81 | 3.45 | 1 | 1 |

82 | 1.98 | 0 | 0 |

83 | 2.22 | 0 | 0 |

84 | 2.51 | 0 | 0 |

85 | 2.99 | 1 | 1 |

86 | 3.48 | 1 | 1 |

87 | 2.75 | 1 | 1 |

88 | 3.71 | 1 | 1 |

89 | 2.11 | 0 | 0 |

90 | 2.86 | 1 | 1 |

91 | 2.87 | 1 | 1 |

92 | 2.64 | 0 | 1 |

93 | 1.61 | 0 | 0 |

94 | 3.48 | 1 | 1 |

95 | 3.04 | 1 | 1 |

96 | 2.25 | 0 | 1 |

97 | 2.54 | 0 | 0 |

98 | 2.57 | 1 | 1 |

99 | 1.70 | 1 | 1 |

100 | 3.85 | 1 | 1 |

The dependent variable was coded as y = 1 if the student returned to Lakeland for the sophomore year and y=0 if not. The two independent variables are:

**x _{1} =** GPA at the end
of the first semester

**x _{2} =** 0 if the
student did not attend the orientation program

1 if the student attended the orientation program

a) Write the logistic regression equation relating x_{1}
and x_{2} to y.

b) What is the interpretation of E(y) when x_{2} =
0?

c) Use both independent variables and Minitab to compute the
estimated logit. **Insert a minitab output here.**

**d)** Conduct a test for overall significance
using a = 0.05. **Insert a minitab output here.**

**e)** Use a = 0.05 to determine whether each of
the independent variables is significant.

f) Use the estimated logit computed in part (c) to compute an estimate of the probability that students with a 2.5 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. What is the estimated probability for students with a 2.5 grade point average who attended the orientation program?

g) What is the estimated odds ratio for the orientation program? Interpret it.

h) Would you recommend making the orientation program a required activity? Why or why not?

Answer #1

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