The R program below generates hypothetical data concerning student characteristics (GPA and Effort) and whether or not the student should be hired (Hirable).

The following results were extracted from the output and should be used to answer parts a, b. There is no need to run a computer program.

n for training data set=100

Prior probabilities for Hirable: Yes=.55 No p=.45

	Frequency Counts
Hirable
No (n=45)		Effort
	GPA		lots	some
		1.poor	8	8
		2.average	8	12
		3.excellent	3	6
Yes (n=55)		Effort
	GPA		lots	some
		1.poor	9	9
		2.average	5	6
		3.excellent	18	8

		Posterior Probabilities
		Hirable
GPA	Effort	No	Yes
1.poor	lots	0.392	0.608
1.poor	some	0.551	0.449
2.average	lots	0.569	0.431
2.average	some	0.715	0.285
3.excellent	lots	0.201	0.799
3.excellent	some	0.324	0.676

Questions:

1. a) Verify the posterior probability computations for a student with a poor GPA who showed lots of Effort.

		Posterior Probabilities
		Hirable
GPA	Effort	No	Yes
1.poor	lots	0.392	0.608

1. 
   
2. b) How would a student with a poor GPA who showed lots of Effort be classified? Hirable Yes? No?

R program

#HW09

library(faraway)

library(caret)

library(e1071)

library(psych)

library(naivebayes)

set.seed(1432)

### Simulate example data

n <- 100

train = data.frame(Hirable = sample(c("Yes", "No"), n, TRUE),

                   GPA = sample(c("1.poor","2.average","3.excellent"), n, TRUE),

                   Effort = sample(c("lots","some"), n, TRUE))

xtabs(~ GPA + Effort + Hirable, data=train)

nb <- naive_bayes(Hirable ~ GPA + Effort, data=train)

summary(nb)

test1 = data.frame(GPA = c("1.poor"), Effort=c("lots"))

test2 = data.frame(GPA = c("1.poor"), Effort=c("some"))

test3 = data.frame(GPA = c("2.average"), Effort=c("lots"))

test4 = data.frame(GPA = c("2.average"), Effort=c("some"))

test5 = data.frame(GPA = c("3.excellent"), Effort=c("lots"))

test6 = data.frame(GPA = c("3.excellent"), Effort=c("some"))

test=rbind(test1,test2,test3,test4,test5,test6)

test

# Classification

predict(nb, test, type = "class")

nb %class% test

# Posterior probabilities

predict(nb, test, type = "prob")

nb %prob% test

program already post here.