Predicting success in calculus

The following data compares students college GPAs and Math SAT scores with whether or not they passed Math 140 at Hampden-Sydney.

calc = read.csv("calculusResults.csv")
head(calc)

##   mathSAT collegeGPA passed
## 1     630      3.261      1
## 2     675      3.932      1
## 3     620      3.597      1
## 4     595      3.540      1
## 5     630      3.289      1
## 6     515      3.187      1

In this case the two explanatory variables (SAT score and GPA) are both quantitative, but the response variable is a binary categorical variable: Pass/Fail. Below is an example of a simple logistic regression model based on only one explanatory variable: collegeGPA.

successModel = glm(passed~collegeGPA,data=calc,family="binomial")
successModel

## 
## Call:  glm(formula = passed ~ collegeGPA, family = "binomial", data = calc)
## 
## Coefficients:
## (Intercept)   collegeGPA  
##      -4.933        2.228  
## 
## Degrees of Freedom: 149 Total (i.e. Null);  148 Residual
## Null Deviance:       160.6 
## Residual Deviance: 135.9     AIC: 139.9

Here is a plot of the data and the logistic regression model.

plot(calc$collegeGPA,calc$passed)
curve(predict(successModel,data.frame(collegeGPA=x),type='response'),add=T)

You can use this logistic regression model to predict the log-odds of a student passing Math 140.

predict(successModel,data.frame(collegeGPA=2.0))

##         1 
## -0.476925