R Notebook

An Introduction to Statistical Leraning: Labs 4.6.1 and 4.6.2

##Lab Section 4.6.1
library (ISLR)
names(Smarket )

[1] "Year"      "Lag1"      "Lag2"      "Lag3"      "Lag4"      "Lag5"      "Volume"    "Today"    
[9] "Direction"

dim(Smarket )

[1] 1250    9

summary (Smarket )

      Year           Lag1                Lag2                Lag3                Lag4          
 Min.   :2001   Min.   :-4.922000   Min.   :-4.922000   Min.   :-4.922000   Min.   :-4.922000  
 1st Qu.:2002   1st Qu.:-0.639500   1st Qu.:-0.639500   1st Qu.:-0.640000   1st Qu.:-0.640000  
 Median :2003   Median : 0.039000   Median : 0.039000   Median : 0.038500   Median : 0.038500  
 Mean   :2003   Mean   : 0.003834   Mean   : 0.003919   Mean   : 0.001716   Mean   : 0.001636  
 3rd Qu.:2004   3rd Qu.: 0.596750   3rd Qu.: 0.596750   3rd Qu.: 0.596750   3rd Qu.: 0.596750  
 Max.   :2005   Max.   : 5.733000   Max.   : 5.733000   Max.   : 5.733000   Max.   : 5.733000  
      Lag5              Volume           Today           Direction 
 Min.   :-4.92200   Min.   :0.3561   Min.   :-4.922000   Down:602  
 1st Qu.:-0.64000   1st Qu.:1.2574   1st Qu.:-0.639500   Up  :648  
 Median : 0.03850   Median :1.4229   Median : 0.038500             
 Mean   : 0.00561   Mean   :1.4783   Mean   : 0.003138             
 3rd Qu.: 0.59700   3rd Qu.:1.6417   3rd Qu.: 0.596750             
 Max.   : 5.73300   Max.   :3.1525   Max.   : 5.733000             

pairs(Smarket )

cor(Smarket [,-9])

             Year         Lag1         Lag2         Lag3         Lag4         Lag5      Volume
Year   1.00000000  0.029699649  0.030596422  0.033194581  0.035688718  0.029787995  0.53900647
Lag1   0.02969965  1.000000000 -0.026294328 -0.010803402 -0.002985911 -0.005674606  0.04090991
Lag2   0.03059642 -0.026294328  1.000000000 -0.025896670 -0.010853533 -0.003557949 -0.04338321
Lag3   0.03319458 -0.010803402 -0.025896670  1.000000000 -0.024051036 -0.018808338 -0.04182369
Lag4   0.03568872 -0.002985911 -0.010853533 -0.024051036  1.000000000 -0.027083641 -0.04841425
Lag5   0.02978799 -0.005674606 -0.003557949 -0.018808338 -0.027083641  1.000000000 -0.02200231
Volume 0.53900647  0.040909908 -0.043383215 -0.041823686 -0.048414246 -0.022002315  1.00000000
Today  0.03009523 -0.026155045 -0.010250033 -0.002447647 -0.006899527 -0.034860083  0.01459182
              Today
Year    0.030095229
Lag1   -0.026155045
Lag2   -0.010250033
Lag3   -0.002447647
Lag4   -0.006899527
Lag5   -0.034860083
Volume  0.014591823
Today   1.000000000

attach(Smarket)

The following objects are masked from Smarket (pos = 3):

    Direction, Lag1, Lag2, Lag3, Lag4, Lag5, Today, Volume, Year

The following objects are masked from Smarket (pos = 5):

    Direction, Lag1, Lag2, Lag3, Lag4, Lag5, Today, Volume, Year

plot(Volume)

##Lab Section 4.6.2
glm.fit=glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume, data=Smarket,family=binomial )
summary (glm.fit)

Call:
glm(formula = Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + 
    Volume, family = binomial, data = Smarket)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-1.446  -1.203   1.065   1.145   1.326  

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

coef(glm.fit)

 (Intercept)         Lag1         Lag2         Lag3         Lag4         Lag5       Volume 
-0.126000257 -0.073073746 -0.042301344  0.011085108  0.009358938  0.010313068  0.135440659 

summary (glm.fit)$coef

                Estimate Std. Error    z value  Pr(>|z|)
(Intercept) -0.126000257 0.24073574 -0.5233966 0.6006983
Lag1        -0.073073746 0.05016739 -1.4565986 0.1452272
Lag2        -0.042301344 0.05008605 -0.8445733 0.3983491
Lag3         0.011085108 0.04993854  0.2219750 0.8243333
Lag4         0.009358938 0.04997413  0.1872757 0.8514445
Lag5         0.010313068 0.04951146  0.2082966 0.8349974
Volume       0.135440659 0.15835970  0.8552723 0.3924004

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

(Intercept)        Lag1        Lag2        Lag3        Lag4        Lag5      Volume 
  0.6006983   0.1452272   0.3983491   0.8243333   0.8514445   0.8349974   0.3924004 

glm.probs=predict(glm.fit ,type="response")
glm.probs [1:10]

        1         2         3         4         5         6         7         8         9        10 
0.5070841 0.4814679 0.4811388 0.5152224 0.5107812 0.5069565 0.4926509 0.5092292 0.5176135 0.4888378 

contrasts (Direction )

     Up
Down  0
Up    1

glm.pred=rep("Down",1250)
glm.pred[glm.probs >.5]=" Up"
table(glm.pred ,Direction )

        Direction
glm.pred Down  Up
     Up   457 507
    Down  145 141

(507+145) /1250

[1] 0.5216

mean(glm.pred==Direction )

[1] 0.116

train=(Year <2005)
Smarket.2005= Smarket [!train ,]
dim(Smarket.2005)

[1] 252   9

Direction.2005= 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")
glm.pred=rep("Down",252)
glm.pred[glm.probs >.5]=" Up"
table(glm.pred ,Direction.2005)

        Direction.2005
glm.pred Down Up
     Up    34 44
    Down   77 97

mean(glm.pred==Direction.2005)

[1] 0.3055556

mean(glm.pred!=Direction.2005)

[1] 0.6944444

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 >.5]=" Up"
table(glm.pred ,Direction.2005)

        Direction.2005
glm.pred Down  Up
     Up    76 106
    Down   35  35

mean(glm.pred==Direction.2005) 

[1] 0.1388889

106/(106+76)

[1] 0.5824176

predict (glm.fit,newdata=data.frame(Lag1=c(1.2,1.5),Lag2=c(1.1,-0.8)),type="response")

        1         2 
0.4791462 0.4960939