Statistical Analysis-Examples

Statistical Analysis consists of code from the Chapter Lab Sections 4.6.1 and 4.6.2(Induction to Statitical book)

library (ISLR)

## Warning: package 'ISLR' was built under R version 3.3.3

names(Smarket )

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

dim(Smarket )

## [1] 1250    9

summary (Smarket )

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

pairs(Smarket )

#cor(Smarket )

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

attach (Smarket )
plot(Volume )

Following code runs the logististic Regression labcode 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 
## -0.126000257 -0.073073746 -0.042301344  0.011085108  0.009358938 
##         Lag5       Volume 
##  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 
##   0.6006983   0.1452272   0.3983491   0.8243333   0.8514445   0.8349974 
##      Volume 
##   0.3924004

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

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

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

mean(glm.pred!= Direction.2005)

## [1] 1

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
##    Down    35  35
##    Up      76 106

mean(glm.pred== Direction.2005)

## [1] 0.4206349

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

Reference: An Introduction to Statistical Learning with Applications in R Authors: James, G., Witten, D., Hastie, T., Tibshirani, R.