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Some Notes from the Book:

Statistical Learning from a Regression Perspective

by Richard A. Berk

John L. Weatherwax

∗

September 12, 200 1

Introduction

Here you’ll ﬁnd some notes that I wrote up as I worked through this excellent book. I’ve

worked hard to make these notes as good as I can, but I have no illusions that they are perfect.

If you feel that that there is a better way to accomplish or explain an exercise or derivation

presented in these notes; or that one or more of t he explanations is unclear, incomplete,

or misleading, please tell me. If you ﬁnd an erro r of any kind – technical, grammatical,

typographical, whatever – please tell me that , too. I’ll gladly add to the acknowledgments

in later printings the name of the ﬁrst person to bring each problem to my attention.

All comments (no matter how small) are much appreciated. In fact, if you ﬁnd these notes

useful I would appreciate a contribution in the form of a solution to a problem that is not yet

worked in these notes. Sort of a “t ake a penny, leave a penny” type of approach. Remember:

pay it forward.

∗

wax@alum.mit.edu

1

Statistic al Learning as a Regr ession Problem

Problem Solutions

Problem 1 ( the airquality dataset)

See the R script chap

1 prob 1.R.

Part (1): When we use the pairs command we get the plot shown in Figure 1. In reading

a plot like this it is helpful to note that the y axis scale in each plot is determined by the

variable denoted in the same horizontal row. The x axis variable is the variable in the same

vertical row. Thus the scatter plot present ed in the (1, 2) location of the grid is a plot of

Ozone considered as a function of Solar.R. The scatter plot presented in the (3, 4) location

is a plot of Wind as a f unction of Temp. Thus plots like this enable one to quickly view

how two variable change in relat ionship to each other. The red curve is a non-parametric

“smoothing” of the data that can given a quick understanding of how the two variables

depend on each other. For example from the output of the pairs function we can see that

from the (1, 3) plot that Ozone decreases as Wind increases. From the (1, 4) plot we see that

Ozone increases a s Temp increases. Comparing the “transpose” plots i.e. (1, 3) and (3, 1) can

give an argument as to which variable should be the response and which variable should be

the explanatory variable. For example in the (3, 1) plot it looks like Wind is almost a linear

function of Ozone while from (1, 3) it does not look like Ozone is a linear function of Wind.

Part (3): Using boxplot to plot Ozone as a function of the categorical variable Month we

get the plot show in Figure 2 (left). Plotting Ozone as a function of Day we get the plot

show in Figure 2 (right). There is a clear pattern in that Ozone concentration seems to peak

during the mont hs of July and August. There is also a much larger range of possible values

during these two months. There does not seem to be much of a pattern in the behaviour of

Ozone as a function of Day. To use these variables in the scatterplots from Part ( 1) earlier

we would have to specify t he set of months or days to study in the scatterplots.

Part (5): When we use the cloud command we get the plot shown in Figure 3. We can see

that Ozone increases as Temp increases and Wind decreases.

Part (6): When we use the coplot command we g et the plot shown in Figure 4 . In that

plot it looks like the way that Wind is kept constant is to break it up into ordered bins and

consider the samples that fall in each bin. From the given plot it looks like that when Wind

is held constant the general trend is for Ozone to be an increasing as Temp.

Problem 2 ( complexity of the ﬁtting function)

See the R script chap

1 prob 2.R. When that script is run we get the result show in Figure 5.

2

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