Question

The following table provides a set of training data that contains 10 observations, 2 characteristics and a qualitative response variable that tells us if the patient should be classified as sick and go immediately to emergency.

Observation	X1	X2	Y
1	4	1	Healthy
2	1	0	Healthy
3	2	4	Sick
4	3	2	Healthy
5	1	2	Sick
6	2	5	Sick
7	4	3	Healthy
8	3	4	Sick
9	2	3	Sick
10	6	2	Healthy

.Suppose we want to create an automatic predictor using a linear classifier for this data set. Using your classifier give the prediction for :

a. X 1 = 3 and X 2 = 4

b. X 1 = 4 and X 2 = 5

c. X 1 = 2 and X 2 = 2

d. What problem could be found with this linear classifier?

Answer 1

data stored in Book1.csv file below where yellow onces are the train observations and green are the prediction parts

X1 X2 1 Healthy 4Sick 2Healthy 2 Healthy 4 Predict 12 5 Predict 2 Predict 15

Created the proper dataset above

Now done the analysis below in R

> library(e1071) > datal-read. csv("Book1.csv") > datal$x1-as.factor (datal$x1) > datal$x2-as.factor (datal$x2) > datal$Y-as.factor (datal$Y) > data1 X1 x2 1 4 1 Healthy 2 1 0 Healthy sick 4 3 2 Healthy sick sick 7 4 3 Healthy sick sick 10 6 2 Healthy 11 3 4 Predict 12 4 5 Predict 13 2 2 Predict > train-datal [1:10,] > str(train) "data. frame' 10 obs. of 3 variables: $ x1: Factor w/ 5 1evels "1","2","3","4",..: 4 1 2 3 1 2 432 5 $ X2: Factor w/ 6 levels "o","1","2","3",..: 2 1 5 3 3 6454 3 $ Y : Factor w/ 3 levels "Healthy", "Predict",..:11 3 1 33 1 3 31 > test-datal [11:13,] >train x1 X2 1 4 1 Healthy 2 1 0 Healthy sick 4 3 2 Healthy Sick sick 7 4 3 Healthy Sick sick 10 6 2 Healthy > test x1 X2 11 3 4 Predict 12 4 5 Predict 13 2 2 Predict

data prepared above. Now algo predict below

> reg1-naiveBayes (Y-. ,data-train) > regl Naive Bayes classifier for Discrete Predictors Call: naiveBayes.default(x-X, y-Y, 1aplace1aplace) A-priori probabilities: Healthy Predic sick 0.5 0. 5 0.0 Conditional probabilities: x1 1 23 4 6 Healthy 0.2 0.0 0.2 0.4 0.2 Predict sick 0.2 0.6 0.2 0.0 0.0 0 1 2 3 4 5 Healthy 0.2 0.2 0.4 0.2 0.0 0.0 Predict sick 0.0 0.0 0.2 0.2 0.4 0. 2 > predictedvalue-predict (regi,newdata- test) > predictedvalue [1] sick Healthy Sick

The predicted values are sick,Healty and sick respectively for a , b and c

d)The only problem we can find in the above naive bayes linear classifier is if we have an unknown level of X1 or X2 we will not be able to classify as this is bayesian method where in the train set we don't have that particular value

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!