Exercise04 Sarantuya Sharavsambuu(113035128) Financial Software

Q1: Example from Website

library(MASS)
library(ggplot2)
library(caret)

## Loading required package: lattice

# Define colors for each species
lookup <- c(setosa = 'blue', versicolor = 'green', virginica = 'orange')

# Assign colors based on species
col.ind <- lookup[iris$Species]

# Scatterplot matrix with colored points
pairs(iris[-5], pch = 21, col = "gray", bg = col.ind)

# Perform LDA on the iris dataset
lda.fit <- lda(Species ~ ., data = iris)
lda.fit

## Call:
## lda(Species ~ ., data = iris)
## 
## Prior probabilities of groups:
##     setosa versicolor  virginica 
##  0.3333333  0.3333333  0.3333333 
## 
## Group means:
##            Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa            5.006       3.428        1.462       0.246
## versicolor        5.936       2.770        4.260       1.326
## virginica         6.588       2.974        5.552       2.026
## 
## Coefficients of linear discriminants:
##                     LD1         LD2
## Sepal.Length  0.8293776  0.02410215
## Sepal.Width   1.5344731  2.16452123
## Petal.Length -2.2012117 -0.93192121
## Petal.Width  -2.8104603  2.83918785
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9912 0.0088

# Make predictions
lda.pred <- predict(lda.fit)
head(lda.pred$x)

##        LD1        LD2
## 1 8.061800  0.3004206
## 2 7.128688 -0.7866604
## 3 7.489828 -0.2653845
## 4 6.813201 -0.6706311
## 5 8.132309  0.5144625
## 6 7.701947  1.4617210

# Plot the first two discriminant functions
plot(LD2 ~ LD1, data = lda.pred$x, pch=21, col="gray", bg=col.ind)

``` r
set.seed(123)
data <- data.frame(
  X1 = rnorm(100),
  X2 = rnorm(100),
  Y = factor(sample(c("Class1", "Class2"), 100, replace = TRUE))
)

lda_model <- lda(Y ~ X1 + X2, data = data)
lda_model

## Call:
## lda(Y ~ X1 + X2, data = data)
## 
## Prior probabilities of groups:
## Class1 Class2 
##    0.5    0.5 
## 
## Group means:
##                X1          X2
## Class1 -0.0725385 -0.15998212
## Class2  0.2533503 -0.05511148
## 
## Coefficients of linear discriminants:
##          LD1
## X1 1.0650581
## X2 0.3499439

data$lda <- predict(lda_model)$x

ggplot(data, aes(x = X1, y = X2, color = Y)) +
  geom_point() +
  labs(title = "LDA Classification")

---

Q2: Section 4.7.3 Example

library(ISLR)
data(Smarket)

lda_fit <- lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = Year < 2005)
lda_fit

## Call:
## lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = Year < 
##     2005)
## 
## 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

# Make predictions for 2005 data
lda_pred <- predict(lda_fit, Smarket[Smarket$Year == 2005, ])
lda_class <- lda_pred$class

# Create confusion matrix
table(lda_class, Smarket$Direction[Smarket$Year == 2005])

##          
## lda_class Down  Up
##      Down   35  35
##      Up     76 106

# Calculate accuracy
mean(lda_class == Smarket$Direction[Smarket$Year == 2005])

## [1] 0.5595238