A researcher is interested in how a number of variables effe

A researcher is interested in how a number of variables effect admission into graduate school. The predictors are GRE scores, GPA, and prestige of the undergraduate institution (Rank), where GRE and GPA are quantitative but Rank is categorical with 4 levels (1 = highest prestige. 4 = lowest prestige). Rank could be treated as ordinal, but for this example well assume it is nominal. Below is the partial output for fitting a logistic model for Y = 1 if admitted and 0 if not. What is the fitted value pi as a function of X? Interpret the coefficient for GPA in context of this problem. Interpret the coefficient for Rank 4 in context of this problem, where Rank 4 = 1 if the students undergraduate institution has the lowest prestige rank and 0 otherwise. What is the odds ratio for Rank = 3 vs. Rank = 4? Based on the model, find the odds that a student from a highest-ranked institution, with a GPA of 3.8 and GRE score of 760, is admitted into graduate school. Find the probability of being admitted into graduate school for the same scenario. Find the Z test statistic for testing if the coefficient for GRE is 0. Test if the coefficient is zero for alpha = 0.05.

Solution

1) the fitted value is -3.99

2) the coefficient of GPA score is 0.804 hence there is 80.4% effect of GPA on admission into graduate school

3) Rank4 means there is lowest prestige in undergraduate institution., here the coefficient is -1.551 so it has negative eddect on admission into graduate school, so. if rank4=1 then it will tend to get lower admission into graduate school