WellEd, a large 4-year community college, is concerned about student dropout rat

Question

WellEd, a large 4-year community college, is concerned about student dropout rate at the end of the first year. Last year, WellEd started a voluntary one-week orientation program to help students adjust to campus life. If WellEd is able show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all students. WellEd's administration also suspects that students with a lower GPA have a higher probability of leaving WellEd at the end of the first year. In order to investigate the relation of these two variables to retention, WellEd selected a random sample of 100 students from last year's class and ran a logistic regression. The dependent variable is coded as y = 1 if the student returned to WellEd for the sophomore year and y = 0 if not. The two independent variables are: X_1 = GPA at the end of first semester X_2 = 0 if the student did not attend the orientation program, 1 if the student did attend orientation. The logistic regression is given by: E(y) = e^beta_0 + beta_1x_1 + beta_2x_2/1 + e^beta_0 + beta_1x_1 + beta_2x_2 From the analysis does using a computer package, the coefficients for the logistic regression are estimated as: Based on the information provided, answer the following: a) Estimate the probability that students with a 2.5 GPA who did not attend the orientation program will return to WellEd for their sophomore year. What is estimated probability for students with a 2.5 GPA who attended the orientation program? What are the respective odds? b) What is the estimated Odds ratio for the orientation program? Would you recommend making the orientation program as a required activity? Why or Why not?

Explanation / Answer

Part-a

For student with 2.5 GPA and not attended program,

Log(p/(1-p))=-6.89+2.539*2.5+1.561*0= -0.5425

So, p/(1-p)=exp(-0.5425)=0.581293201

Hence p=0.581293201/(1+0.581293201)= 0.36760621

For student with 2.5 GPA and attended program,

Log(p/(1-p))=-6.89+2.539*2.5+1.561*1=1.0185

So, p/(1-p)=exp(1.0185)=2.76903809

Hence p=2.76903809/(1+2.76903809)= 0.734680315

Part-b

Odds ratio for orientation program =exp(1.561)= 4.763582447

We wil recommend making the orientaition program as a required activity as odds ratio is much larger than 1

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