Exercise 4.7.3

library(ISLR2)

library(MASS)

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:ISLR2':
## 
##     Boston

train <- Smarket$Year < 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2 , data = Smarket , subset = train)
lda.fit

## Call:
## lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = train)
## 
## Prior probabilities of groups:
##     Down       Up 
## 0.491984 0.508016 
## 
## Group means:
##             Lag1        Lag2
## Down  0.04279022  0.03389409
## Up   -0.03954635 -0.03132544
## 
## Coefficients of linear discriminants:
##             LD1
## Lag1 -0.6420190
## Lag2 -0.5135293

par(mar = c(4, 4, 2, 2))  # Adjust the margins (bottom, left, top, right)
plot(lda.fit)

Smarket.2005 <- subset(Smarket, Year == 2005)
lda.pred <- predict (lda.fit , Smarket.2005)
names ( lda.pred )

## [1] "class"     "posterior" "x"

lda.class <- lda.pred$class
Direction.2005 <- Smarket$Direction[Smarket$Year == 2005]
table(lda.class , Direction.2005)

##          Direction.2005
## lda.class Down  Up
##      Down   35  35
##      Up     76 106

mean ( lda.class == Direction.2005)

## [1] 0.5595238

sum ( lda.pred$posterior [ , 1] >= .5)

## [1] 70

sum ( lda.pred$posterior [ , 1] < .5)

## [1] 182

lda.pred$posterior [1:20 , 1]

##       999      1000      1001      1002      1003      1004      1005      1006 
## 0.4901792 0.4792185 0.4668185 0.4740011 0.4927877 0.4938562 0.4951016 0.4872861 
##      1007      1008      1009      1010      1011      1012      1013      1014 
## 0.4907013 0.4844026 0.4906963 0.5119988 0.4895152 0.4706761 0.4744593 0.4799583 
##      1015      1016      1017      1018 
## 0.4935775 0.5030894 0.4978806 0.4886331

lda.class [1:20]

##  [1] Up   Up   Up   Up   Up   Up   Up   Up   Up   Up   Up   Down Up   Up   Up  
## [16] Up   Up   Down Up   Up  
## Levels: Down Up

sum ( lda.pred$posterior [ , 1] > .9)

## [1] 0