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ENVS3023/6034 Quantitative Methods
Creation date：2024-04-11 16:14:05
Belonging category：统计学statistics
Quantitative Methods

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ENVS3023/6034 –Advanced

Quantitative Methods
Long answer question practise – some tips
Last edited 5 May 2021
1
Quail.xls
 The quail dataset provides records of presence or
absence (coded as 1 or 0 in variable Presence).
You have been asked by a hunting group who like
to shoot quail (a small game bird) whether
topographic variation (variables coded topov1 to
topov10 for fine to large scale variations) affects
quail presence. Their plan is to make the ground
more variable so that they have places to hide
when shooting the bird but they don’t want to do
this if the quail will avoid the area. What is your
advice to them?
2
What the questions says
 …records of presence or absence
 …variables coded topov1 to topov10 for
fine to large scale variations
 [want] …places to hide when shooting
the bird
 What is your advice to them?
3
Creating a research question
 Is the presence of quail influenced by
topographic variation when everything else
is taken into account?
 We are just asked for advice, not a model
or equation
 Interpretation is important but mainly by
the researcher, not the hunter
4
Possible approaches?
 GLM – if assumptions can be met
 GAM – good but possibly slow
 MARS –binomial response is possible (read the
earth pdf)
 CART – not suitable as single tree
 RF and SGB – possible because n = 2154 – but you
need to know how to specify in RF
 NN – not really interpretable unless you add PDPs
5
Results from GLM model
6
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 5.7954362 0.9979657 5.807 6.35e-09 ***
meanNDVI -0.0789547 0.0096221 -8.206 2.30e-16 ***
spriNDVI 0.0564619 0.0052579 10.739 < 2e-16 ***
wintNDVI -0.0281757 0.0070006 -4.025 5.70e-05 ***
topov1 0.2092300 0.3059940 0.684 0.494120
topov2 1.0601105 0.7800388 1.359 0.174131
topov5 -1.0383771 1.4579828 -0.712 0.476340
topov10 -2.5709852 1.2681614 -2.027 0.042628 *
alt 0.0018815 0.0001809 10.401 < 2e-16 ***
townden -2.7884717 0.7536330 -3.700 0.000216 ***
rivden -1.1856096 0.4275608 -2.773 0.005555 **
Running randomForest on binary
response
7
randomForest(as.factor(Presence) ~
meanNDVI...
To answer the question
 It’s easy to forget this!
 Go back and read it again to check
 What would your advice be to the hunters?
8
Body fat in men.csv
Excess body fat is bad for health but is not simple to
measure directly because the worst place to carry it
is around the internal organs, hidden from view.
Your task is to explore the data provided to see
whether it is possible to predict body fat (variable
Percent body fat) from various characteristics and
body measurements (variables Age to Wrist
circumference). The aim is to develop a simple way
(perhaps a rule of thumb?) for medical practitioners
and affected individuals to assess body fat.
9
What the questions says
 … explore the data provided to see whether
it is possible to predict body fat
 The aim is to develop a simple way for
medical practitioners and affected
individuals to assess body fat
10
Creating a research question
 Can we predict body fat from the variables
provided?
 We need to do this simply enough to be able
to communicate the results
 What two techniques stand out as
appropriate?
11
Possible approaches?
 (G)LM – if assumptions can be met. Link is identity
function so = linear regression. n = 252
 GAM – too complex
 MARS – possible but complex
 CART – good for visualization but low predictive
power?
 RF and SGB – too complex
 NN - too complex
12
Run as LM
 % body fat = 0.996*abdomen + 0.473* forearm –
1.506 wrist – 0.136*weight – 34.854
 Why not round coefficients to simplify?
 % body fat = abdomen + ½ forearm – 1½ wrist –
1½ (weight/10) – 35
 Correlations in both cases are r = 0.857
 My simplified formula is much easier for
practictioners to use.
13
Speeding violations.csv
These are data from the US and the focus is
on the police allegedly stopping people on the
basis of race. Your task is to discover
whether there is evidence for a difference in
tendency to drive too fast (variables Speed
and Overlimit) according to race (variable
Race).
14
What the questions says
 …discover whether there is evidence for a
difference in tendency to drive too fast
according to race...
 In other words, is race a significant
predictor of speed (the response)
 There are four categorical predictors plus
date and time. Speed could also be a
continuous predictor but it must be related
to “overlimit” so probably best to omit.
15
Data cleaning
 Possible problem here is that missing
values have been assigned **
 Cannot search and replace in Excel so use
the .csv directly and do it in Notepad
 Or in R use Speedy_clean <-
Speeders[(Speeders$Speed!="**"),]
 Otherwise leave it and rely on listwise
deletion to take care of it.
16
Possible approaches?
 GLM – possible using dummy coding (automatic
in R)
 GAM - possible using dummy coding (automatic in R)
 MARS – also possible if no missing values
 CART – not suitable as single tree
 RF and SGB – possible if we specify categorical
predictors as factors (n = 6929)
 NN – possible if predictors standardized.
17
Example prediction from lm in R
18
Conclusion
 Linear model and even neural nets have low
predictive power for this problem
 Little evidence that race has an effect on
speeding over the limit
 Might suggest that the observed
disproportionate stopping of certain groups
is racism.
19
Mammal sleep.xlsx
How much do different species of mammal
sleep and why are there differences? Explore
the data provided to determine which
variables seem to influence sleep duration
(three possible variables) and come up with
hypotheses to explain your findings.
20
What the questions says
 …explore the data provided to determine
which variables seem to influence sleep
duration
 …come up with hypotheses to explain your
findings
21
Creating a research question
 How well can we predict sleep duration
from the variables provided?
 Which variables are most important as
predictors?
 So we need both predictive power and
interpretability to some extent (enough to
create hypotheses).
22
Possible approaches?
 (G)LM – best if assumptions can be met
 GAM – slow and at the limit as n = 62
 MARS – possible even with n = 62
 CART – not suitable (unreliable) as single tree
 RF and SGB – too few points
 NN – too few points
 We should try a linear model because it is the
most interpretable and n is small. 23
Issues
 Information on two datasheets so awkward
and needs tidying
 Excel is good for sorting this out and
getting a feel for the data
 Remember: we need to check for linearity if
we are to build a simple linear model, so
make some plots.
24
General tips
 Make sure you read and then answer the question!
 Answers need to include text, R code, plots etc.
 Use resampling techniques (e.g. cross-validation)
wherever appropriate
 Look at model fits and residuals when appropriate
 Interpret any output as fully as you can
 Write a conclusion.
Case category
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CMP7000A CMP-7038B Math 263 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 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. 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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