STAT 441, ASSIGNMENT 2 1. Return back to the Problem 2 of the
previous homework, Assignment 1. You do not needthe original operational
data, variables Murder and Latitude, if you kept in your R workspacethe
objects for the 3 models you fitted in Assignment 1. Recall those were (i) linear: y = α + βx, (ii) quadratic: y = α + βx+ γx2, (iii) reciprocal: y = 1 α + βx . If
you did not keep the object and need to refit those models for this
assignment those modelsusing Murder and Latitude, then do it—but without
much further ado; make only sure (doublecheck!) that you obtain the
same parameter estimates as in the Assignment 1 (otherwise itsgrading
will have to be revised, and possibly not for the better).And now, here
is your performance evaluation dataset, data for the Canadian provinces
andterritories: m2019 is the murder rate in 2019, and d, m, s are
respectively degrees, minutes,and seconds for the latitude of the center
of corresponding Canadian province or territory.(I’ll make the dataset
available, although typing it down—as I did—does not take too muchtime
either) d m s m2019 AB 55 10 11 2.29 BC 54 45 16 1.78 MN 54 55 46 5.23 NB 46 37 01 1.96 NL 52 53 23 0.96 NS 45 08 45 0.63 ON 50 26 43 1.69 PE 46 23 25 1.31 QC 53 23 34 0.92 SK 54 25 05 4.68 YT 63 37 52 2.52 NT 66 22 49 4.52 NU
71 01 10 17.81Of course, before doing anything with this data, you need
to make them compatible with theUS data first. (How That is a sort of
high school mathematical problem. Thus, no extensivecommentaries needed
on this, just do not forget to do it.) And now:(a) Evaluate the
performance of your fits of all three models on the Canadian data
andcomment on the results. Is the fit you proposed in Assignment 1 a
winner (There is no pointin changing your mind now, it all sits
submitted there. And your grade does not depend onwhether you proposed a
winner or not. It depends on whether the analysis is done right.)(b)
Evaluate the performance of your fits of all three models on the
Canadian data, but nowonly on provinces, not on territories (you know
which are those, don’t you ). Comment againon the result; do not forget
to mention whether your bet in Assignment 1 happens to be awinner in
this case or not. (This assignment has 2 pages.) 22. Lecture 9
says on page 8Scaling of the variables entails that the ro le of the
variance-covariance matrixin principal components is taken over by the
correlation matrix.(a) Explain what it means.(b) Justify it in an “R
experiment”; that is, take some suitable dataset, for instance
USArrestsonce again, and calculate… not the principal components or
directions themselves, but thematrices in your explanation.(c) Once you
achieve success in (b), give a mathematical proof why it works. (It is
fine to workcomponentwise here.)This is neither a pure mathematical, nor
a pure computational exercise. Something of both.Show code and results
for (b), give mathematics for (c), and a mathematical/verbal
explanationfor (a). 3. Consider the dissimilarity matrix of Crime data (page 4 of Lecture 11, also available as crime.R
from the Datasets folder in eClass).(a) Is the dissimilarity
represented by this matrix a metric (b) And how about that on page 1 on
Lecture 11 You may want to look only at the matrix Fairorg, if you
understand the way how Fairmont was produced out of it. (Both are
containedin fairmont.R, also in the Datasets folder.)Use methodology
that you believe should provide you with the correct result in the
mostconvenient way. (Slovak proverb: If it’s not in the head, it’s in
the feet.) Due Wednesday, February 16, 2022
