plot LDA fit using R function plot()

Question

I am doing the lab section: classifying the stock data using LDA in the book "Introduction to Statistical Learning with Applications in R", here is the lab video. Basically, this lab uses LDA to predict the stock Up or Down from Lag1 and Lag2 as following,

 lda.fit = lda(Direction~Lag1+Lag2, data=Smarket, subset=Year<2005)

The coefficients are

Coefficients of linear discriminants:
        LD1
Lag1 -0.6420190
Lag2 -0.5135293

And following the lab steps, plot the LDA fit,

plot(lda.fit)

the plot is like below

I am having difficulties interpreting the plots. In the book it says that The plot() function produces plots of the linear discriminants, obtained by computing −0.642 × Lag1 − 0.514 × Lag2 for each of the training observations. I don't understand what this sentence exactly is meaning here,

1. What's the x and y axis of this plot? And what does the axis mean here?
2. Why the plot is a bar plot?
3. How the computing −0.642 × Lag1 − 0.514 × Lag2 is related to the x and y axis?

Answer 1

The horizontal axis is the linear combination of Lag1 and Lag2. This is the linear combination where the two groups (Up, Down) are most different. What you can see from this plot is that both groups are centered on 0, and have similar spread, which means there is nothing that distinguishes these two groups. You didn't compute the prediction error. If you did, I am guessing it will be close to 50%, which indicates that you cannot distinguish between the groups.