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STAT 441 Assignment

Creation date：2024-04-26 10:40:17

Belonging category：计算机computer science

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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 roˆle 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.)

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FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 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LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 FINC5090 MATH1052 SciComp Elec4622 FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 MAT 237 BISM2201 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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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