LogisticRegression.R

#CLASSIFICATION TECHNIQUES USING R


#1) LOGISTIC REGFRESSION using glm() function-Generalized linear Models , followed by
# family = binomial

require(ISLR) #packages with all datasets

#using Smarket dataset

names(Smarket) #Stock Market Data
?Smarket
view(Smarket)
summary(Smarket)

#Direction var -will be used as a Binary Response variable -to predict whether market will
#move Up or Down  on a given day


#Constructing a Scatterplot Matrix
pairs(Smarket,col = Smarket$Direction)
#By looking at the scatterplot matrix we can easily see that there are no Correlations
#between Variables - As it is a Stock market Data- No BIG Surprise!!

#Fitting a Logistic REgression Model
mod1<-glm(Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume ,data =Smarket , family =binomial)

#The model will compute the Prob values of Direction given  these inputs/predictors

summary(mod1)
#Non of the variables have significant p-values , this only means that they are not 
#correlated or very correlated, and also suggest that none of the variables are related
#to the Response(Direction) variable, i.e H0 is true-no relations b/w predictor and Res
#and again for this kind of datasets it is not a big surprise. 

#Still we can make Predictions and calculate Probabilities values
probs<-fitted(mod1,'response')
#probs a vector of fitted Pr(Y=Direction|Inputs) values by the Model
head(probs)
#Prob values nearby 0.5
probs<-ifelse(probs>=0.5,'Up','Down')
#if prob >=0.5 then 'Up' , otherwise Market 'Down'
attach(Smarket)
#Forming a CONFUSION MATRIX to check the number of mismatches(misclassifications)
table(Predicted=probs,True=Direction)
#lots of mismatches
#Accuracy of the model
mean(probs==Direction) 
#i.e The Model performs Slightly Better than chance , ie when Error Rate < 1/2 or 50%
# % of matches  = 52 %  , Error(mismatches)=47%
#We might be OVERFITTING with such high accuracy on TRAINING DATA


#NOW WE SEGREGATE INTO Training and Test Data and see if we do any better?

train = Year < 2005 
mod2<-glm(Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume ,
                        data =Smarket ,subset = train, family =binomial)

summary(mod2)

#Lets check the predictions of this model with Traiing data
#But we will generalize & predict Direction  on TEST DATA
prob1<-predict(mod2,newdata = subset(Smarket,!train),type='response')
mod2.pred<-ifelse(prob1>=0.5,'Up','Down')
head(mod2.pred)
#Dataframe of True Directions and Predicted Direction on TEST Data
pred.df<-data.frame(True_Direction = subset(Smarket,!train)$Direction , Predicted = mod2.pred)

#CONFUSION MATRIX:
table(Predicted = mod2.pred , Ture = Smarket$Direction[!train])
#Accuracy of the Model2-no of matches-correct classifications
mean(mod2.pred==subset(Smarket,!train)$Direction)
#accuracy decreases to 48%

#Hence the model performs poorer than 1st Model and also Overfits




#Smaller Model with Lesser Input variables
mod3<-glm(Direction ~ Lag1 + Lag2,data = Smarket,subset=train , family = binomial)
summary(mod3)
#AIC(mod2,mod3)
#df      AIC
#mod2  7 1395.105
#mod3  3 1387.402
#By looking at the AIC(Infor criterion) we can say that model3 is better and good as
#less information is lost

#PREDICTIONS ON TEST
prob1<-predict(mod3,newdata = subset(Smarket,!train),type='response')
mod3.pred<-ifelse(prob1>=0.5,'Up','Down')
head(mod3.pred)
#Dataframe of True Directions and Predicted Direction on TEST Data
pred.df2<-data.frame(lag1 = Smarket$Lag1[!train] , Lag2 = Smarket$Lag2[!train],True_direction = 
                       Smarket$Direction[!train],Predicted = mod3.pred)

#CONFUSION MATRIX:
table(Predicted = mod3.pred , Ture = Smarket$Direction[!train])
#Accuracy of the Model2-no of matches-correct classifications
mean(mod3.pred==subset(Smarket,!train)$Direction)

#Hence by taking Less predictors the Accuracy of the Model has improved to 56%
predict(mod3,newdata = data.frame(Lag1=0.967,Lag2=0.600),type='response')