# The following will illustrate some of the concepts we introduced during last
# week.
# 1) Let's get a feeling of what a Normal qqplot looks like for
# different kinds of distributions. Recall, that if the data comes from a
# Normal distribution, then it's qqplot should look line a straight line,
# at least in the bulk of the plot; the tails usually deviate from a straight
# line, because there are usually few cases there anyway. This
# is a visual method for checking whether your data is normally distributed.
# Also, if linear, then the intercept and slope of the line can be used as
# estimates of the mu and sigma of the normal distribution.
# The answers you get on your screen may look different from what your TA
# shows on screen, but that's because of the different random samples.
x = rnorm(500,0,1)
# Sample of size 500 from a normal dist with mu=0, sigma=1.
hist(x)
qqnorm(x)
x = rexp(500,1)
# Sample of size 500 from an exponential dist with lambda=1.
hist(x)
# Use UPARROW
qqnorm(x)
# So, as you can see, that a normal sample will produce a linear pattern
# in qqnorm(), but an exponential sample will not. Clearly, that's
# because qqnorm() checks the data against a normal distribution.
# But how do we identify if some data comes from some other distribution,
# say, from the exponential distribution? Answer: use analog of qqnorm
# for the exponential distribution. In R, the function qqmath() allows
# for a large number of theoretical distributions.
# Let me just show you that it succeeds in identifying the above exponential
# data as being from an exponential distribution?
library(lattice)
# This is the library that contains qqmath().
x = rexp(500,1)
hist(x)
qqmath(x, dist = qexp)
############################################################################
# 2) Scatterplots:
# Let's pick a 100 random x values, and corresponding y values that have
# some linear association with x. We'll change the amount of linear association
# by adding different amounts of noise to y. Look:
# Cut/paste the following 2 blocks from
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Normal Distribution, (x,y)

Click to edit the document details