A study was donc looking at the relationship between students getting admitted (

Question

A study was donc looking at the relationship between students getting admitted (yes/no) into graduate school based on their gre, gpa, and institutional rank. The variables were: Dependent variable admit - admittance (coded as yes or no) Independent variables gre gre scores (continuous variable) gpa - gpa scores (continuous variable) rank rank of 1-4 (1-highest prestige; 4-lowest prestige) rank(1) compares those with rank 1 to those with rank 4 rank(2) compares those with rank 2 to those with rank 4 rank(3) compares those with rank 3 to those with rank 4 The output table for the multiple logistic regression model for admittance is below: Predictor OR 1.002 002 804 038 015 re rank rank(1) rank(2) rank(3 1.551 876 211 4.718 2.401 1.235 004 017 591 Constant The difference between which two ranks predicted the most change in admittance? a. rank 1 vs. rank 4 b. rank 2 vs. rank 4 c. rank 3 vs. rank 4 What is the odds ratio for gpa?

Explanation / Answer

a.) Given Probability for Ranks:

rank1: 0.000

rank2: 0.017

rank3: 0.591

rank4: 1 - (sum of all above) = 1 - 0.608 = 0.392

As per above proababilities, it is clear that difference in probabailites for rank1 and rank4 is highest.

So option a is correct.

b.) Odds ratio is given as:

OR = p / 1-p

for gpa, p = 0.015

So, OR = 0.015 / 0.985

OR = 0.0152

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