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STAT2008 Regression Modelling
创建日期：2024-05-14 16:41:57
所属分类：统计学statistics
标签： STAT2008
Regression Modelling

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STAT2008 Regression Modelling
Examination/Writing Time Duration: 180 minutes
Reading Time: 15 minutes
Exam Conditions:
Central Examination. This examination paper is not available to the ANU Library archives.
Students must return the examination paper at the end of the examination.
Materials permitted in the exam venue: (No electronic aids are permitted e.g. laptops, phones)
Unannotated paper-based dictionary (no approval required),
One A4 page with notes on both side, Calculator
Materials to be supplied to Students:
Scribble Paper
Instructions to Students:
1. This examination paper comprises a total of twenty (20) pages and there is a separate handout of
R output which also has a total of twenty (20) pages. During the reading time preceding the exam,
please check that both documents have the correct number of pages.
2. All answers are to be written on this exam paper, which is to be handed in at the end of the exam.
You may make notes on scribble paper (or on the R handout) during the reading time, but
do NOT write on this exam paper until after the start of the writing time. If you need additional
space, use the rear of the previous page and clearly indicate the part of the question that your
answer refers to. The R handout and any scribble paper will be collected at the end of the
examination and destroyed, they will not be marked.
3. There are a total of four questions, which are worth 15 marks each, for a total of 60 marks.
The parts of each question are of unequal value, with the marks indicated for each part.
You should attempt to answer each and every part of all four questions. This examination
counts towards 60% of your final assessment.
4. Please write your student number in the space provided at the top of this page.
5. Include a clear statement of the formulae you use to answer each question.
6. Statistical tables (generated using R) are provided on pages 19 and 20 at the end of the handout of
R output. Unless otherwise indicated, use a significance level of 5% and note that log x refers to the
natural logarithm of x.
Q1 Q2 Q3 Q4 Total
Pages 2 to 6 7 to 11 12 to 15 16 to 20
Marks 15 15 15 15 60
Score

Venue _________________________________________

STUDENT
NUMBER U

Final Examination, Semester 1, 2017 STAT2008 Regression Modelling
Page 2 of 20
Question 1 (15 marks)
The faraway library includes a data frame called cheddar, which contains data from a study of
cheddar cheese from the La Trobe Valley in Victoria. The concentration of Lactic acid, along
with the concentrations (on a log scale) of both Acetic acid and H2S (hydrogen sulphide) were
measured from 30 samples of cheese, which were then subjected to taste tests. Overall taste
scores were obtained by combining the scores from several tasters.
(a) A multiple regression model (cheddar.lm) has been fitted to these data and the summary
output from this model is given at the top of page 2 of the R output, but the analysis of
variance (ANOVA) table is not shown. Fill in the details of the ANOVA table in the
spaces shown below:
Df Sum Sq Mean Sq F value Pr(>F)
H2S

Lactic

Residuals

(3 marks – 1 for each row of the ANOVA table)
[Hint: rounding errors will accumulate as you derive entries in this table from other
values shown in the R output, so do NOT round the results of intermediate
calculations. DO round all your final answers in the above table to 2 decimal places.
You may also have to use the statistical tables to estimate one or more of the
p-values, or you can receive the marks for showing appropriate critical values.]
Working
Final Examination, Semester 1, 2017 STAT2008 Regression Modelling
Page 3 of 20
Question 1 continued
(b) Residual plots for the model in part (a) are shown on pages 2 and 3 of the R output.
Do these plots suggest any problems with the underlying assumptions?
What is your overall assessment? (select just ONE of the following options)
□ Residuals are not independent (obvious pattern)
□ Residuals do not have constant variance (heteroscedasticity)
□ Residuals are not normally distributed
□ There are possible outliers and/or influential observations
□ More than one of the above problems
□ No obvious problems
(2 marks – 0.5 for each section)
Are there any problem(s) shown on the “Residuals vs Fitted” plot on page 2?
If so describe the problem(s):
Are there any problem(s) shown on the “Cook’s distance” plot on page 3?
If so describe the problem(s):
Are there any problem(s) shown on the “Normal Q-Q” plot on page 3?
If so describe the problem(s):
Final Examination, Semester 1, 2017 STAT2008 Regression Modelling
Page 4 of 20
Question 1 continued
(c) For each of the following five diagnostic measures shown on page 4 of the R output,
calculate the relevant cut-off value suggested in the lecture notes and discuss whether or
not this cut-off is appropriate in this instance. Which observations, if any, exceed each
of the cut-off values?
(see the next page for more answer spaces for part (c) of Question 1)

The leverage or hat values (hii)
DFFITS
The externally studentised residuals (ti)
Final Examination, Semester 1, 2017 STAT2008 Regression Modelling
Page 5 of 20
Question 1, part (c) continued
(7 marks – 1 for each of the first 5 sections and 2 for the last summary section)
Given your answers above and considering the residual plots in part (b), are there
any observations that are vertical outliers and/or highly influential observations?
Should some observations be removed and the model re-fit to the remaining data?
COVRATIO
DFBETAS
Final Examination, Semester 1, 2017 STAT2008 Regression Modelling
Page 6 of 20
Question 1 continued
(d) Output for a second model (cheddar.lm2) is shown on page 5 of the R output, which
includes an additional term added to the initial model described in the earlier parts of
this question. Is the term involving Acetic a significant addition to a model which
already includes H2S and Lactic? Give full details of an appropriate hypothesis test.
(3 marks)

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CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 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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