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MATH363 mathematics

创建日期：2024-06-08 16:23:07

所属分类：数学mathematics

标签： MATH363

mathematics

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MATH363: Group Project part 2

Group project contributes 60% to your mark for Math363.
Part 1 = 15 marks; part 2 = 85 marks
You will work on all parts of this project as a group and submit your answers as a group. In
addition to the project you need to submit minutes from your meetings and provide the peer as-
sessment of everyone’s contribution through Buddycheck. The final mark for each member of the
group will be adjusted according to these peer scores.
The project needs to be submitted on Canvas and will be checked for potential plagiarism using
turnitin. A high similarity score might result in the project being investigated for suspected plagia-
rism; see Code of Practice on Assessment Appendix L.
DATA SETS FOR EACH GROUP ARE DIFFERENT and THEREFORE
YOUR RESULTS AND ANSWERS SHOULD BE DIFFERENT
Please only discuss your project with your group members. Any similarity between different
project submission might be investigated for suspected plagiarism.
You must include your minutes [10 marks] and include all relevant code in the appendix [10
marks].
Part II
1. [25 marks] A six minute walking test (6MWT) is used to assess functional exercise perfor-
mance. In this test the subject is asked to walk for 6 minutes on a level course and the distance
covered is recorded in meters (m). The pace is set by the subject and breaks are allowed if
needed. The data were collected on healthy subjects and includes information about
sex (Female = 1; Male = 0 );
age (in years);
height (cm);
weight (kg);
BMI (= body mass index);
resting heart rate (beats per minute, bmp);
heart rate at the end of the 6 minutes;
current smoking status (1 if smoker);
1
if the person ever smoked;
usual activity level: 0 =sedentary (less then 30 min physical activity a day), 1 = moder-
ately active ( 30-60 min physical activity a day), 2 = active ( more than 60 min physical
activity a day);
You are asked to find a model for dependance of the distance travelled in 6MWT on explanatory
variables provided. The model will be used to predict the average distance for a person and
should only include variables available before the test is taken (that is, not their heart rate at
the end of the test).
(a) Use appropriate plots to help suggest possible models. You should consider here which
of the explanatory variables are covariates and which are factors.
(b) Fit different linear models as suggested by the plots in (a) and decide which model is most
appropriate. Examples of things that you could consider here are models with quadratic
or cubic terms, interactions, other transformations of variables are also possible.
(c) For the model chosen in (b), perform residual analysis and decide if the model fits well.
If it does not, suggest changes that can be made to the model to address these issues.
2. [10 marks] Based on the analysis in Q1, recommend a model which should be used to predict
distance travelled in 6MWT and interpret the parameters of your model. Explain any limita-
tions of your model. Discuss what information about the patient is needed to use your model
and provide examples of predicted values including confidence and prediction intervals. You
can use some of the subjects included in your data set for these examples. Indicative word
count: 500
3. [15 marks] Choosing a model for large data sets can be a very complex task but there are
a few different methods which help researchers to decide on the best set of variables to be
included in a model in a systematic way. Three commonly used methods are forward selec-
tion, backward elimination and stepwise regression. Research one of these methods and write
a short explanation in your own words of how this method works. Apply this method to your
data on 6WMT. Discuss similarities and differences between the model obtained here and the
model you choose in 1(b). You should use published resources to in this part and cite any
books or articles used. A good source here is Applied regression analysis by H. Smith, and
N.R. Draper (on reading lists).Indicative word count: 750
4. [15 marks] It is also of interest to model the probability that a subject reached the threshold
heart rate (HR) for vigorous-intensity physical activity (VIPA), that is a heart rate of at
least 77% of maximum HR. Maximum HR is calculated as 220 minus age. For example,
for a person who is 35, maximum HR is 185 bpm and VIPA is when their HR is at least
0.77(220− 35) ≈ 143bpm. The researchers want to use the data set used in Q1 to estimate
a probability of VIPA during 6MWT. The distance travelled should be one of the explanatory
variables in this case.
(a) Create a new variable which is 1 if a person’s HR reached VIPA, and 0 otherwise (you
might want to first create a variable with maximum HR for each person).
2
(b) Propose a model for the probability of VIPA. You do not need to consider interactions
or higher order terms in this case but you need to consider which link function is most
appropriate.
(c) Interpret your model parameters, discuss its fit and any limitations.

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MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 EARN 5 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 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 MATH20602 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ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 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