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- 10. This question should be answered using the Weekly data set, which is part of the ISLR package. This data is similar in nature to the Smarket data from this chapter’s lab, except that it contains 1, 089 weekly returns for 21 years, from the beginning of 1990 to the end of 2010.
- - (a) Produce some numerical and graphical summaries of the Weekly data. Do there appear to be any patterns?
  - (b) Use the full data set to perform a logistic regression with Direction as the response and the five lag variables plus Volume as predictors. Use the summary function to print the results.
  - - Do any of the predictors appear to be statistically significant? If so, which ones?
  - (c) Compute the confusion matrix and overall fraction of correct predictions. Explain what the confusion matrix is telling you about the types of mistakes made by logistic regression.
  - (d) Now fit the logistic regression model using a training data period from 1990 to 2008, with Lag2 as the only predictor. Compute the confusion matrix and the overall fraction of correct predictions for the held out data (that is, the data from 2009 and 2010).
  - (e) Repeat (d) using LDA.
  - (f) Repeat (d) using QDA.
总结

10. This question should be answered using the Weekly data set, which is part of the ISLR package. This data is similar in nature to the Smarket data from this chapter’s lab, except that it contains 1, 089 weekly returns for 21 years, from the beginning of 1990 to the end of 2010.

(a) Produce some numerical and graphical summaries of the Weekly data. Do there appear to be any patterns?

library(ISLR)
library(MASS)
View(Weekly)
# str(Weekly)
summary(Weekly)
attach(Weekly)
#相关阵
cor(Weekly[,-9])

(b) Use the full data set to perform a logistic regression with Direction as the response and the five lag variables plus Volume as predictors. Use the summary function to print the results.

glm.fits <-glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Weekly,family=binomial)
summary(glm.fits)

Do any of the predictors appear to be statistically significant? If so, which ones?

Lag2*显著，具有统计学意义

glm.pred=predict(glm.fits)
glm.pred[1:10]

© Compute the confusion matrix and overall fraction of correct predictions. Explain what the confusion matrix is telling you about the types of mistakes made by logistic regression.

glm.probs <- predict(glm.fits,type = "response")
contrasts(Direction)
glm.pred=rep("Up",length(glm.probs))
glm.pred[glm.probs <.5]="Down"
table(glm.pred ,Direction)
mean(glm.pred==Direction)
54/(48+54)
557/(557+430)

56%的市场动向可以被正确预测
混淆矩阵表明用逻辑斯蒂回归模型预测市场下跌时，只有54/(48+54)=52.9%
混淆矩阵表明用逻辑斯蒂回归模型预测市场上涨时，只有557/(557+430)=56.4%

(d) Now fit the logistic regression model using a training data period from 1990 to 2008, with Lag2 as the only predictor. Compute the confusion matrix and the overall fraction of correct predictions for the held out data (that is, the data from 2009 and 2010).

train = (Year<=2008)
test<- Weekly[!train,] #
dim(test)
Direction_data<-Direction[!train] # glm.fits1 <- glm(Direction~Lag2,data=Weekly,family = binomial,subset = train)
summary(glm.fits1)
glm.probs1 <- predict(glm.fits1,test,type = "response")#
glm.pred1=rep ("Up",length(glm.probs1))
glm.pred1[glm.probs1 <.5]="Down"
table(glm.pred1,Direction_data)
mean(glm.pred1 == Direction_data)9/(9+5)
56/(56+34)

调整后的逻辑回归，62.5%的市场动向可以被正确预测
混淆矩阵表明用逻辑斯蒂回归模型预测市场下跌时，只有9/(9+5)=64.3%
混淆矩阵表明用逻辑斯蒂回归模型预测市场上涨时，只有56/(56+34)=62.2%

(e) Repeat (d) using LDA.

library(MASS)
lda.fit <- lda(Direction~Lag2,data=Weekly,subset = train)
lda.fit
# plot(lda.fit)
lda.pred=predict (lda.fit,test)
names(lda.pred)
lda.class=lda.pred$class
table(lda.class ,Direction_data)
mean(lda.class==Direction_data)# 62.5%

(f) Repeat (d) using QDA.

qda.fit <- qda(Direction~Lag2,data=Weekly,subset = train)
qda.fit
# plot(lda.fit)
qda.pred=predict (qda.fit,test)
names(qda.pred)
qda.class=qda.pred$class
table(qda.class ,Direction_data)
mean(qda.class==Direction_data)# 58.7%

总结

以上均为个人观点，由于个人能力有限，难免有差错，还请多多指教

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