The bibliography and corresponding authors are cited at all times and this posts series is a way of honoring and giving them the credit they deserve for their work.

We will develop a logistic regression example. The exercise was originally published in

**.**

*"An Introduction to Statistical Learning. With applications in R"*by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. Springer 2015The example we will develop is about predicting when the market value will rise (UP) or fall (Down).

We will carry out the exercise verbatim as published in the aforementioned reference and only with slight changes in the coding style.

For more details on the models, algorithms and parameters interpretation, it is recommended to check the aforementioned reference or any other bibliography of your choice.

**### "An Introduction to Statistical Learning.**

### With applications in R" by Gareth James,

### Daniela Witten, Trevor Hastie and Robert Tibshirani.

### Springer 2015.

### install and load required packages

### With applications in R" by Gareth James,

### Daniela Witten, Trevor Hastie and Robert Tibshirani.

### Springer 2015.

### install and load required packages

library(ISLR)

library(psych)

**### explore the dataset**

names(Smarket)

dim(Smarket)

summary(Smarket)

**### correlation matrix**

cor(Smarket[,-9])

**### correlations between th lag variables and today**

### returns are close to zero

### the only substantial correlation is between $Year

### and $Volume

### returns are close to zero

### the only substantial correlation is between $Year

### and $Volume

plot(Smarket$Volume, main= "Stock Market Data",

ylab = "Volume")

**### scatterplots, distributions and correlations**

pairs.panels(Smarket)

**### fit a logistic regression model to predict $Direction**

### using $Lag1 through $Lag5 and $Volume

### glm(): generalized linear model function

### family=binomial => logistic regression

### using $Lag1 through $Lag5 and $Volume

### glm(): generalized linear model function

### family=binomial => logistic regression

glm.fit <- glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,

data = Smarket, family = binomial)

summary(glm.fit)

**### the smallest p_value is associated with Lag1**

### the negative coefficient for this predictor suggests

### that if the market had a positive return yesterday,

### then it is less likely to go up today

### at a value of 0.15, the p-value is still relatively large,

### and so there is no clear evidence of a real association

### between $Lag1 and $Direction

### the negative coefficient for this predictor suggests

### that if the market had a positive return yesterday,

### then it is less likely to go up today

### at a value of 0.15, the p-value is still relatively large,

### and so there is no clear evidence of a real association

### between $Lag1 and $Direction

**### explore fitted model coefficients**

coef(glm.fit)

summary(glm.fit)$coef

summary(glm.fit)$coef[ ,4]

**### predict the probability that the market will go up,**

### given values of the predictors

### given values of the predictors

glm.probs <- predict(glm.fit, type="response")

glm.probs[1:10]

contrasts(Smarket$Direction)

**### these values correspond to the probability of the market**

### going up, rather than down, because the contrasts()

### function indicates that R has created a dummy variable with

### a 1 for Up

### create a vector of class predictions based on whether the

### predicted probability of a market increase is greater than

### or less than 0.5

### going up, rather than down, because the contrasts()

### function indicates that R has created a dummy variable with

### a 1 for Up

### create a vector of class predictions based on whether the

### predicted probability of a market increase is greater than

### or less than 0.5

glm.pred <- rep ("Down", 1250)

glm.pred[glm.probs > .5] <- "Up"

**### confusion matrix in order to determine how many observations**

### were correctly or incorrectly classified

### were correctly or incorrectly classified

table(glm.pred, Smarket$Direction)

mean(glm.pred == Smarket$Direction)

**### model correctly predicted that the market would go up on 507**

### days and that it would go down on 145 days, for a total of

### 507 + 145 = 652 correct predictions

### ogistic regression correctly predicted the movement of the

### market 52.2 % of the time

### to better assess the accuracy of the logistic regression model

### in this setting, we can fit the model using part of the data,

### and then examine how well it predicts the held out data

### days and that it would go down on 145 days, for a total of

### 507 + 145 = 652 correct predictions

### ogistic regression correctly predicted the movement of the

### market 52.2 % of the time

### to better assess the accuracy of the logistic regression model

### in this setting, we can fit the model using part of the data,

### and then examine how well it predicts the held out data

train <- (Smarket$Year < 2005)

Smarket.2005 <- Smarket[!train, ]

dim(Smarket.2005)

Direction.2005 <- Smarket$Direction[!train]

glm.fit <- glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,

data = Smarket, family = binomial, subset = train)

glm.probs <- predict(glm.fit, Smarket.2005, type = "response")

**### compute the predictions for 2005 and compare them to the**

**### actual movements of the market over that time period**

glm.pred <- rep("Down", 252)

glm.pred[glm.probs > 0.5] <- "Up"

table(glm.pred, Direction.2005)

mean(glm.pred == Direction.2005)

mean(glm.pred != Direction.2005)

**### not generally expect to be able to use previous days returns ### to predict future market performance**

### refit the logistic regression using just $Lag1 and $Lag2,

### refit the logistic regression using just $Lag1 and $Lag2,

**### which seemed to have the highest predictive power in the**

**### original logistic regression model**

glm.fit <- glm(Direction ~ Lag1 + Lag2 , data = Smarket,

family = binomial, subset = train)

glm.probs <- predict(glm.fit, Smarket.2005 , type = "response")

glm.pred <- rep("Down", 252)

glm.pred[glm.probs > 0.5] <- "Up"

table(glm.pred, Direction.2005)

mean(glm.pred == Direction.2005)

**### results appear to be a little better: 56%**

### if we want to predict the returns associated with particular

### values of $Lag1 and $Lag2

### if we want to predict the returns associated with particular

### values of $Lag1 and $Lag2

predict(glm.fit, newdata = data.frame(Lag1 = c (1.2 ,1.5),

Lag2 = c(1.1, -0.8)) , type = "response")

You can get the example in:

https://github.com/pakinja/Data-R-Value