Over the past few years the percentage of students who leave Lakeland College at
ID: 3244259 • Letter: O
Question
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 firstyear 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.
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:
x1 = GPA at the end of the first semester
x2 = 0 if the student did not attend the orientation program OR 1 if the student attended the orientation program
Can you please show all the steps including Minitab and the calculations. Thank you
a) Write the logistic regression equation relating x1 and x2 to y.
b) What is the interpretation of E(y) when x2 = 0?
c) Use both independent variables and Minitab to compute the estimated logit.
d) Conduct a test for overall significance using = 0.05.
e) Use = 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?
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 1Explanation / Answer
(a) Y:return (1/0) X1:GPA X2:program
then model is : ln(p/1-p) = b0 + b1*x1 + b2*x2 ; p= prob[Y=1]
(b)E(y) = 0 when x2=0 means that what is the expectation of return if the program varible is ommited or ignored or the student haven't attended the program.
(c)in minitab stat>regression>binary logistic regression
output:
Binary Logistic Regression: Return versus GPA, Program
Link Function: Logit
Response Information
Variable Value Count
Return 1 66 (Event)
0 34
Total 100
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant -6.89256 1.74725 -3.94 0.000
GPA 2.53880 0.672870 3.77 0.000 12.66 3.39 47.35
Program 1.56075 0.563142 2.77 0.006 4.76 1.58 14.36
Log-Likelihood = -40.169
therefore,
logit(p) = ln(p/1-p) = -6.89 +2.53X1 + 1.56X2
(d)overall goodness of fit of the model
Goodness-of-Fit Tests
Method Chi-Square DF P
Pearson 62.2773 88 0.983
Deviance 69.2474 88 0.930
Hosmer-Lemeshow 11.8792 8 0.157
all the p values > .05. so the model fits well!
(e)according to the prev output all the coefficient's p value is <.05
thus they are significant
(f)we know p= exp(M1)/1+exp(M1) ; M1 defines the model above
now X1=2.5 and X2=0 ; then p=.36
sly for X1=2.5 X2=1 p=.73
this can answer your question (h) !! orientation is necessary
(g) from first output est odds ratio of orientation prog is 4.76. i.e returning to college is 4.76 times higher for those who attended the program.
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