Question

Data shows graduate program admission decisions (Yes: 1 and No: 2), GRE score and undergraduate GPA for twenty-five students.

Tasks:

Examine if the given data is suitable for the application of linear discriminant analysis.

Create a linear discriminant function predicting admission decisions.

Comment on the classification accuracy.

Predict the admission decision given GRE score = 690 and GPA = 3.2.

Perform logistic regression analysis for the data.

Compare the classification accuracies of both methods.

Admit	GRE	GPA
2	790	3.8
1	370	3.4
2	480	2.9
1	580	3.3
1	620	3.9
1	740	3.2
2	490	3.1
2	720	3.7
1	740	3.9
2	460	3.4
1	610	3.3
1	260	2.5
2	740	4
1	700	3.6
1	760	3.5
1	410	2.8
1	700	4
1	800	3.4
2	680	2.9
2	520	3.2
1	700	3.5
1	580	3.3
2	470	3.9
1	640	3.8
2	410	3.8

Answer 1

I have solve the problem in R Code:

library(MASS)
data_GRE=read.csv(file.choose())
data_GRE$Admit=as.factor(data_GRE$Admit)
lda_model=lda(Admit~GRE+GPA,data_GRE)

lda_predtest=predict(lda_model,data_GRE)
table(lda_predtest$class,data_GRE$Admit)

Linear Discriminant Function:

Admit = Wo + W1* GRE + W2*GPA

Wo is the Bias weight

a)

Classification accuracy

table(lda_pred$class,data_GRE$Admit)

	1	2	Total
1	14	8	22
2	1	2	3
Total	15	10	25

Diagonally we see that exact prediction = 14 +2 =16

accuracy = 16 /25 = 0.64

64% is our accuracy

b) Predict the admission decision given GRE score = 690 and GPA = 3.2.

R -code > lda_pred=predict(lda_model,data.frame("GRE"=690,"GPA"=3.2))

Ans: Yes: 1

c)

# Logistic regression

log_model=glm(Admit~GRE+GPA,data_GRE,family = binomial)
log_probs=predict(log_model,data_GRE,type="response")
log_pred=rep(2,25)
log_pred[log_probs>0.5]=1
table(log_pred,data_GRE$Admit)

Classification accuracy is

	1	2	Total
1	1	2	3
2	14	8	22
	15	10	25

= 9/25  

=0.34

34 % is logistic regression, which is less than LDA, Hence LDA method in this problem