We now fit a logistic regression model using only the subset of the observations that correspond to dates before 2005, using the subset argument. We then obtain predicted probabilities of the stock market going up for each of the days in our test set—that is, for the days in 2005.

> 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")

Notice that we have trained and tested our model on two completely separate data sets: training was performed using only the dates before 2005, and testing was performed using only the dates in 2005. Finally, we 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 > .5] <- "Up"
> table(glm.pred, Direction.2005)
Direction.2005
glm.pred Down Up
    Down   77 97
    Up     34 44
> mean(glm.pred == Direction.2005)
[1] 0.48
> mean(glm.pred != Direction.2005)
[1] 0.52

The != notation means not equal to, and so the last command computes the test set error rate. The results are rather disappointing: the test error rate is 52 %, which is worse than random guessing! Of course this result is not all that surprising, given that one would not generally expect to be able to use previous days’ returns to predict future market performance.

Try creating a logistic regression model with a training set for yourself:

Assume that: