I have always been fascinated with the criteria used by institutions to decide whether a student qualifies for a graduate program or not. In this situation, logistic regression can be applied to find the probability of being admitted or not using three critical predictors. The response/outcome variable will be “Admit” which is categorical with yes and no as responses. Dependent variable two continuous variables, Graduate Record Exam Scores (GRE) and Grade Point Average (GPA). A third predictor will be categorical, the prestige of the undergraduate school (rank) which will take 1 through 4 as the responses with one the highest rank. From these variables, I will be trying to predict two groups of the outcome variables but in four different sets as the dependent variable “Rank” has four outcomes. Therefore, there will be four different probabilities depending on the rank level. However, the continuous variables will remain constant in all the four logistic equations that are expected to have different probabilities. Usually, logistic regression analysis predicts one dimension of the binary outcome variable, and this can be used to tell the other option in the same variable (Tamayo & Cañizares, 2014). In this case, the model will evaluate the probability of being admitted, therefore when subtracted from 1, the likelihood of not being admitted is found. If one predictor variable will be statistically significant say GPA, it means that a change in its value will affect the outcome variable proportionally. For instance, when the GPA increases, the probability of being admitted to a graduate program will also increase across all outcomes for rank 1 through 4 and vice versa. In essence, when a predictor variable has a positive and significant relationship with the outcome variable, its odds ratio is usually greater than 1 and p<0.05 if the confidence level used is 95% (Das, Maiti & Pradhan, 2010). Therefore, it will mean that regardless of the prestige level of the undergraduate school of the student, the higher the GPA, the higher the probability of being enrolled in a graduate program.

References

Das, U., Maiti, T., & Pradhan, V. (2010). Bias correction in logistic regression with missing categorical covariates. Journal Of Statistical Planning And Inference, 140(9), 2478-2485. http://dx.doi.org/10.1016/j.jspi.2010.02.018

Tamayo, A., & Cañizares, R. (2014). Predictors of Engineering Licensure Examination Using Logistic Regression. British Journal Of Education, Society & Behavioural Science, 4(12), 1621-1629. http://dx.doi.org/10.9734/bjesbs/2014/11343

This form of analysis has many flexible uses in research and so has become a popular tool for applied researchers in particular. In order to conduct this type of analysis we need to "dummy code" categorical variables by providing them with numerical values. Using 0 and 1 instead of 1 and 2 also creates an advantage as our slope estimate is easier to interpret. What specific statistics do we look to interpret when we conduct a logistic regression? Using this example, what would be some example statistics you would want to interpret?

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