#4.7.1
library(ISLR)
library(GGally)
## Loading required package: ggplot2
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
names(Smarket)
## [1] "Year" "Lag1" "Lag2" "Lag3" "Lag4" "Lag5"
## [7] "Volume" "Today" "Direction"
data("Smarket")
str(Smarket)
## 'data.frame': 1250 obs. of 9 variables:
## $ Year : num 2001 2001 2001 2001 2001 ...
## $ Lag1 : num 0.381 0.959 1.032 -0.623 0.614 ...
## $ Lag2 : num -0.192 0.381 0.959 1.032 -0.623 ...
## $ Lag3 : num -2.624 -0.192 0.381 0.959 1.032 ...
## $ Lag4 : num -1.055 -2.624 -0.192 0.381 0.959 ...
## $ Lag5 : num 5.01 -1.055 -2.624 -0.192 0.381 ...
## $ Volume : num 1.19 1.3 1.41 1.28 1.21 ...
## $ Today : num 0.959 1.032 -0.623 0.614 0.213 ...
## $ Direction: Factor w/ 2 levels "Down","Up": 2 2 1 2 2 2 1 2 2 2 ...
summary(Smarket)
## Year Lag1 Lag2 Lag3
## Min. :2001 Min. :-4.922000 Min. :-4.922000 Min. :-4.922000
## 1st Qu.:2002 1st Qu.:-0.639500 1st Qu.:-0.639500 1st Qu.:-0.640000
## Median :2003 Median : 0.039000 Median : 0.039000 Median : 0.038500
## Mean :2003 Mean : 0.003834 Mean : 0.003919 Mean : 0.001716
## 3rd Qu.:2004 3rd Qu.: 0.596750 3rd Qu.: 0.596750 3rd Qu.: 0.596750
## Max. :2005 Max. : 5.733000 Max. : 5.733000 Max. : 5.733000
## Lag4 Lag5 Volume Today
## Min. :-4.922000 Min. :-4.92200 Min. :0.3561 Min. :-4.922000
## 1st Qu.:-0.640000 1st Qu.:-0.64000 1st Qu.:1.2574 1st Qu.:-0.639500
## Median : 0.038500 Median : 0.03850 Median :1.4229 Median : 0.038500
## Mean : 0.001636 Mean : 0.00561 Mean :1.4783 Mean : 0.003138
## 3rd Qu.: 0.596750 3rd Qu.: 0.59700 3rd Qu.:1.6417 3rd Qu.: 0.596750
## Max. : 5.733000 Max. : 5.73300 Max. :3.1525 Max. : 5.733000
## Direction
## Down:602
## Up :648
##
##
##
##
head(Smarket)
## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction
## 1 2001 0.381 -0.192 -2.624 -1.055 5.010 1.1913 0.959 Up
## 2 2001 0.959 0.381 -0.192 -2.624 -1.055 1.2965 1.032 Up
## 3 2001 1.032 0.959 0.381 -0.192 -2.624 1.4112 -0.623 Down
## 4 2001 -0.623 1.032 0.959 0.381 -0.192 1.2760 0.614 Up
## 5 2001 0.614 -0.623 1.032 0.959 0.381 1.2057 0.213 Up
## 6 2001 0.213 0.614 -0.623 1.032 0.959 1.3491 1.392 Up
cor(Smarket[, -9])
## Year Lag1 Lag2 Lag3 Lag4
## Year 1.00000000 0.029699649 0.030596422 0.033194581 0.035688718
## Lag1 0.02969965 1.000000000 -0.026294328 -0.010803402 -0.002985911
## Lag2 0.03059642 -0.026294328 1.000000000 -0.025896670 -0.010853533
## Lag3 0.03319458 -0.010803402 -0.025896670 1.000000000 -0.024051036
## Lag4 0.03568872 -0.002985911 -0.010853533 -0.024051036 1.000000000
## Lag5 0.02978799 -0.005674606 -0.003557949 -0.018808338 -0.027083641
## Volume 0.53900647 0.040909908 -0.043383215 -0.041823686 -0.048414246
## Today 0.03009523 -0.026155045 -0.010250033 -0.002447647 -0.006899527
## Lag5 Volume Today
## Year 0.029787995 0.53900647 0.030095229
## Lag1 -0.005674606 0.04090991 -0.026155045
## Lag2 -0.003557949 -0.04338321 -0.010250033
## Lag3 -0.018808338 -0.04182369 -0.002447647
## Lag4 -0.027083641 -0.04841425 -0.006899527
## Lag5 1.000000000 -0.02200231 -0.034860083
## Volume -0.022002315 1.00000000 0.014591823
## Today -0.034860083 0.01459182 1.000000000
pairs(Smarket[, -9], col = Smarket$Direction)
plot(Smarket$Year, Smarket$Volume, type = "l", xlab = "Year", ylab = "Volume",
main = "Volume of Shares Traded Over Time")
#4.7.2
if (!requireNamespace("ISLR", quietly = TRUE)) {
install.packages("ISLR")
}
library(ISLR)
data("Smarket")
glm.fits <- glm(Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume,
data = Smarket, family = binomial)
summary(glm.fits)
##
## Call:
## glm(formula = Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 +
## Volume, family = binomial, data = Smarket)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.126000 0.240736 -0.523 0.601
## Lag1 -0.073074 0.050167 -1.457 0.145
## Lag2 -0.042301 0.050086 -0.845 0.398
## Lag3 0.011085 0.049939 0.222 0.824
## Lag4 0.009359 0.049974 0.187 0.851
## Lag5 0.010313 0.049511 0.208 0.835
## Volume 0.135441 0.158360 0.855 0.392
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1731.2 on 1249 degrees of freedom
## Residual deviance: 1727.6 on 1243 degrees of freedom
## AIC: 1741.6
##
## Number of Fisher Scoring iterations: 3
glm.probs <- predict(glm.fits, type = "response")
glm.pred <- ifelse(glm.probs > 0.5, "Up", "Down")
table(glm.pred, Smarket$Direction)
##
## glm.pred Down Up
## Down 145 141
## Up 457 507
mean(glm.pred == Smarket$Direction)
## [1] 0.5216
train <- Smarket$Year < 2005
Smarket.2005 <- Smarket[!train, ]
Direction.2005 <- Smarket$Direction[!train]
glm.fits <- glm(Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume,
data = Smarket, family = binomial, subset = train)
glm.probs <- predict(glm.fits, Smarket.2005, type = "response")
glm.pred <- ifelse(glm.probs > 0.5, "Up", "Down")
table(glm.pred, Direction.2005)
## Direction.2005
## glm.pred Down Up
## Down 77 97
## Up 34 44
train <- Smarket$Year < 2005
Smarket.2005 <- Smarket[!train, ]
Direction.2005 <- Smarket$Direction[!train]
glm.fits <- glm(Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume,
data = Smarket, family = binomial, subset = train)
glm.probs <- predict(glm.fits, Smarket.2005, type = "response")
glm.pred <- ifelse(glm.probs > 0.5, "Up", "Down")
table(glm.pred, Direction.2005)
## Direction.2005
## glm.pred Down Up
## Down 77 97
## Up 34 44
glm.fits <- glm(Direction ~ Lag1 + Lag2,
data = Smarket, family = binomial, subset = train)
glm.probs <- predict(glm.fits, Smarket.2005, type = "response")
glm.pred <- ifelse(glm.probs > 0.5, "Up", "Down")
table(glm.pred, Direction.2005)
## Direction.2005
## glm.pred Down Up
## Down 35 35
## Up 76 106
mean(glm.pred == Direction.2005)
## [1] 0.5595238
predict(glm.fits, newdata = data.frame(Lag1 = c(1.2, 1.5), Lag2 = c(1.1, -0.8)), type = "response")
## 1 2
## 0.4791462 0.4960939