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STATS 782 Statistical Computing
创建日期：2024-05-28 17:41:18
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标签： STATS 782
Statistical Computing

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Department of Statistics

STATS 782 Statistical Computing
Assignment 3 (2023; Semester 1)
Total: 65 marks Due: 10:00 NZDT, May 15, 2023
Notes:
(i) Please do not use any external R packages for this assignment.
(ii) When mimicking the plots given to you, we reserve the right to decide what is close enough.
Also,
– Please include basic information behind how you constructed your plot by a short descrip-
tion in English.
– The dimension of your plot should be very similar or the same as the original. Create
your plot in .pdf and upload it to Canvas. The originals will be made available to you.
– Of course, try to match the colours reasonably closely without spending hours on it.
– As always, marks will be awarded for correctness, simplicity, readability, and the ability
to change certain major features easily, etc.
(iii) Please see Canvas for any other instructions.
1. [15 marks] Consider the equation
y2 (a2 − x2) =
[
x2 + 2ay − a2
]2
(1)
on the plane, where a = (1 + d)/3 and d is the last digit of your UPI (so that a is positive and
no more than 4).
(a) Use R to plot the equation with the x- and y-axes on the same scale. Note: it can be
done in a reasonably basic way. Hint: don’t use contour() and the answer reminds me
of something you might see in the sky. Because of symmetry, only consider what is above
the horizontal axis. [10 marks]
(b) Compute the area numerically using integrate(). It should be accurate to at least five
decimal places. [5 marks]
2. [10 marks] Consider Fig. 1, which was put on https://timesofindia.indiatimes.com as an
optical illusion/brain teaser to help ward off dementia and Alzheimer’s disease. The challenge
is to find the word ‘LARGE’ in the image within 10 seconds.
Use R to reproduce the figure closely. Further notes:
ˆ Feed the last three digits of your UPI into set.seed() to position your word ‘LARGE’.
Its position should be uniformly distributed over the ‘grid’, and there is to be only one
‘LARGE’. That is, your position will probably not match the original.
ˆ You should write a function having at least two arguments, e.g., drawLARGE(width = 8,
height = 11) so that it can easily be changed to a 12 × 9 grid, say, for another Indian
newspaper. Your function should invisibly return the location of your ‘LARGE’ and the
grid size.
ˆ Fonts are very OS-specific but there are sometimes good options, e.g., on macOS you can
try "Arial Narrow" or even better "Futura Condensed Medium" which gets a lot closer.
My solution is so different so that you don’t have to match the font if that’s too difficult.
Figure 1: Scaled original from the internet.
2
3. [10 marks] Consider Fig. 2 which is based on a picture from the internet. Viewers are
supposed to find the (one) star that differs from the others within 16 seconds.
Use R to reproduce the figure closely. Further notes:
ˆ The position of your aberrant star should be uniformly distributed over the ‘grid’ based
on the last three digits of your UPI—input it into set.seed().
ˆ You should write a function having at least two arguments, e.g., drawstars(width = 7,
height = 5) so that it can easily be changed. Your function should invisibly return the
location of your aberrant star and the grid size.
Figure 2: A (scaled) grid of stars. Using my coordinate system, the answer is in position (1, 2).
4. [10 marks] Consider Fig. 3 which is an optical illusion because the horizontal bar is in
fact just one colour—even though it appears to progress from light gray to dark gray.
Use R to reproduce the figure closely. Hint: use pdf(..., height = 4, width = 6)
Figure 3: Scaled original from the internet.

(a) Read the data into R by first downloading the text file. Obtain a summary() of your data
frame and comment. [4 marks]
(b) Plot the data to create a .pdf file that is very similar to Fig. 4. However, [11 marks]
– don’t spend hours on it to make it exactly the same;
– don’t plot the third Lowess column of data—you are to use lowess() to do it yourself!
Hint: use pdf(..., height = 5.2, width = 8)
(c) Continuing from (b) and without doing too much extra work, add some improvements to
the plot. Justify your improvements. Produce a new plot. [5 marks]
Figure 4: Original plot (scaled) in .png given on the NASA website.
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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 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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