# Author: david@openintro.org (David Diez)
# License: Creative Commons Attribution-ShareAlike 4.0
#    https://creativecommons.org/licenses/by-sa/4.0/
#
# Simulation and Analysis Context
#
# When a course has an especially high fail rate, faculty
# sometimes investigate ways to improve the rate. One strategy
# is to gate the class using a preparedness test.
#
# Suppose we examine a particular course with a high fail rate
# where about 25% of students fail the course, and the faculty
# last semester had each student take a pre-course test.
# The faculty notice that students who performed poorly on
# the test seemed to fail at higher rates than students who
# scored very well, and they decided that the test will be
# worth implementing as a preparedness test for the next
# semester. However, they still have a problem: what score
# must students get before they are allowed to enter the course?
#
# The faculty decide that students must have at least
# an 80% chance of passing based on the preparedness test.
# In other words, the faculty want to determine the score S
# such that, if a student gets score S, the student has
# an 80% chance of passing. They would also expect that
# students who score much higher than S would pass at an
# even higher rate.


# _____ Load & Plot Class Data _____ #
d <- read.csv("pretest_pass-class_data.csv")
head(d)
dim(d)

hist(d$score)
table(d$pass)
boxplot(d$score ~ d$pass)
color <- ifelse(d$pass == 1, "black", "red")
plot(d$score, jitter(d$pass), col = color)


# _____ Build Model _____ #
model <- glm(pass ~ score, data = d, family = binomial)
summary(model)


# _____ Plot the Model _____ #
plot(d$score, d$pass, col = color)
d.new <- data.frame(score = seq(0, 100))
fitted <- predict(model, d.new, type = "response", se.fit = TRUE)
lower <- fitted$fit - 1.96 * fitted$se.fit
upper <- fitted$fit + 1.96 * fitted$se.fit
lines(d.new$score, fitted$fit)
lines(d.new$score, lower, lty = 3)
lines(d.new$score, upper, lty = 3)
abline(h = 0.8, lty = 2)
cbind(d.new, fitted$fit, lower, upper)