lab3 - The following will illustrate some of the concepts...

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# 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 UP-ARROW 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
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lab3 - The following will illustrate some of the concepts...

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