GEOMETRY of LDA and QDA

There is a nice Field Goal data among the data sets on our course web site. We’ll read this text file directly from the site.

> FG = read.table(url("http://fs2.american.edu/~baron/624/R/Field%20goals.txt"))

> attach(FG)

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

V1, V2, V3

> distance = V1; made = V2; week = V3;

> plot( week, distance, col = made+2 ) # Adding 2, the colors become green and red for made and missed field goals.

# Apply LDA and QDA to predict success of a field goal attempt

> GF.lda = lda( made ~ distance + week, CV=TRUE )

> mean( GF.lda$class == made )

[1] 0.8090717 # Classification rate of 80.9%

> plot( week, distance, col = as.numeric(GF.lda$class)+1 )

# We see a linear decision boundary for LDA.

> GF.qda = qda ( made ~ distance + week, CV=TRUE )

> plot( week, distance, col = as.numeric(GF.qda$class)+1 )

# A curvy boundary.