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Applied Regression
Creation date：2024-07-16 16:36:49
Belonging category：计算机computer science
Tag Applied
Applied Regression
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1. Suppose X1, X2, . . . , X9 are iid N(μ, 4) variables. We wish to test H0 :
μ = 1 against H1 : μ = 3
(a) Calculate the size and power of the test with rejection region X >ˉ
2.
(b) Find k so that the test with rejection region X > k ˉ has size 0.05.
Calculate the power of this test.
2. The data set big.mac is part of a larger data set described in Cook and
Weisberg, “Applied Regression Including Computing and Graphics,”
Wiley, 1999.
Download the data file, the data is available on moodle. Read the data
into R.
The Big Mac hamburger is a simple commodity that is virtually identical
throughout the world. One might expect that the price of a Big
Mac should be the same everywhere, but of course it is not the same.
The Economist magazine has published a Big Mac parity index, which
compares the costs of a Big Mac in various places, as a measure of
inefficiency in currency exchange. We will use these data to study how
the cost of a Big Mac varies with economic indicators that describe
each city. The variables in the data are logBigMac (log of minutes of
labour required by an average worker to buy a Big Mac and french fries)
logBusFare (log of lowest cost of 10km public transit in US dollars)
logTeachSal (log of annual salary of a primary teacher in US dollars)
and logTeachTax (log of tax rate paid by a primary teacher).
For the following, please provide R scripts that you use and the corresponding
output, including any relevant graphs to support your answers.
(a) Fit a linear model with logBigMac as the response and the remaining
variables as predictors.
(b) Is there any evidence that any of the assumptions of the linear
regression model is not satisfied?
(c) Examine residuals and other diagnostics for the fitted model. Are
there any unusual or influential points?
2(d) Examine the summary output: based on the summary output, do
you think that any of the predictors could be deleted from the
model? Please state any relevant statistical tests you used to base
your conclusion on.
(e) Consider two alternative models: the model including all predictors,
and the model where the predictor logBusFare and logTeachTax
are deleted. Use the F statistic, stating clearly any hypothesis
being tested, and the conclusions reached regarding the two predictors.
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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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