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. 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 0 if the student did not attend the orientation program *2 1 if the student attended the orientation program. (a) Write the logistic regression equation relating x] and x2 to y. O E(Y) = 1 + evo + $1*1 + $2*2 O E(Y) = Bo + 81*1 + $2*2 O E(y) = - efo + #1*1 + $2*2 1 + efo + 81*1 + $2*2 O E(y) = efo + 81*1 + $2*2 (b) What is the interpretation of E(y) when x, = 0? For a given GPA, it is an estimate of the probability that a student who did not attend the orientation program will return to Lakeland for the sophomore year. For a given GPA, it is an estimate of the probability that a student who attended the orientation program will return to Lakeland for the sophomore year. It is an estimate of the GPA for a student who did not attend the orientation program and returned to Lakeland for the sophomore year. It is an estimate of the GPA for a student who attended the orientation program and returned to Lakeland for the sophomore year. (c) Use both independent variables and statistical software to compute the estimated logit. (Round your numerical values to two decimal places.) (x1,*2) = (d) Conduct a test for overall significance using a = 0.05. State the null and alternative hypotheses. Ho: Po = 0 Ha : Po * 0 D HO: B1 = $2 = 0 Ha : All the parameters are not equal to zero. O HO: B1 = B2 = 0 H. : One or more of the paramet ers is not equal to zero. Ho: One or more of the parameters is not equal to zero. Ha: 81 = P2 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? O Reject Ho. There is insufficient evidence to conclude that there is a significant rel O Reject Ho. There is sufficient evidence to conclude that there is a significant relat Do not reject Ho. There is sufficient evidence to conclude that there is a significa Do not reject Ho. There is insufficient evidence to conclude that there is a signifi e) Use a = 0.05 to determine whether each of the independent variables is significant. State the null and alternative hypotheses for GPA. O HO: B, 20 Ha: B 1

0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Reject Ho. There is sufficient evidence to conclude that GPA is a significant factor. Do not reject Ho. There is sufficient evidence to conclude that GPA is a significant factor. Reject Ho. There is insufficient evidence to conclude that GPA is a significant factor. Do not reject Ho. There is insufficient evidence to conclude that GPA is a significant factor State the null and alternative hypotheses for program. O HO: B2 20 Ha: B2 0 O HO : B2 = 0 Ha : $2 > 0 O HO: B2 = 0 Ha : $2 # 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Do not reject H . There is insufficient evidence to conclude that program is a significant factor. Do not reject H . There is sufficient evidence to conclude that program is a significant factor Reject H . There is sufficient evidence to conclude that program is a significant factor. Reject H . There is insufficient evidence to conclude that program is a significant factor. (f) Use the estimated logit computed in part (c) to estimate the probability that students with a 3.0 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. (Round your answer to four decimal places.) What is the estimated probability that students with a 3.0 grade point average who attended the orientation program will return to Lakeland for their sophomore year? (Round your answer to four decimal places.) (g) What is the estimated odds ratio for the orientation program? (Round your answer to four decimal places.)