Multiple Regressions and Correlation Analysis
|
|
- Arleen Campbell
- 5 years ago
- Views:
Transcription
1 Mulple Regreon and Correlaon Analy Chaper 4 McGraw-Hll/Irwn Copyrgh 2 y The McGraw-Hll Compane, Inc. All rgh reerved.
2 GOALS. Decre he relaonhp eween everal ndependen varale and a dependen varale ung mulple regreon analy. 2. Se up, nerpre, and apply an ANOVA ale 3. Compue and nerpre he mulple andard error of emae, he coeffcen of mulple deermnaon, and he adjued coeffcen of mulple deermnaon. 4. Conduc a e of hypohe o deermne wheher regreon coeffcen dffer from zero. 5. Conduc a e of hypohe on each of he regreon coeffcen. 6. Ue redual analy o evaluae he aumpon of mulple regreon analy. 7. Evaluae he effec of correlaed ndependen varale. 8. Ue and underand qualave ndependen varale. 9. Underand and nerpre he epwe regreon mehod.. Underand and nerpre pole neracon among ndependen varale. 4-2
3 Mulple Regreon Analy The general mulple regreon wh k ndependen varale gven y: X X k are he ndependen varale. a he Y-nercep he ne change n Y for each un change n X holdng X 2 X k conan. I called a paral regreon coeffcen or ju a regreon coeffcen. The lea quare creron ued o develop h equaon. Deermnng, 2, ec. very edou, a ofware package uch a Excel or MINITAB recommended. 4-3
4 Mulple Lnear Regreon - Example ^ Y X X 2 X 3 Salerry Realy ell home along he ea coa of he Uned Sae. One of he queon mo frequenly aked y propecve uyer : If we purchae h home, how much can we expec o pay o hea durng he wner? The reearch deparmen a Salerry ha een aked o develop ome gudelne regardng heang co for nglefamly home. Three varale are hough o relae o he heang co: () he mean daly oude emperaure, (2) he numer of nche of nulaon n he ac, and (3) he age n year of he furnace. To nvegae, Salerry reearch deparmen eleced a random ample of 2 recenly old home. I deermned he co o hea each home la January, a well 4-4
5 Mulple Lnear Regreon Mna Example Regreon oupu produced y Mna and Excel a
6 The Mulple Regreon Equaon Inerpreng he Regreon Coeffcen and Applyng he Model for Emaon Inerpreng he Regreon Coeffcen The regreon coeffcen for mean oude emperaure, X, The coeffcen negave a he oude emperaure ncreae, he co o hea he home decreae. For every un ncreae n emperaure, holdng he oher wo ndependen varale conan, monhly heang co expeced o decreae y $ Applyng he Model for Emaon Wha he emaed heang co for a home f he mean oude emperaure 3 degree, here are 5 nche of nulaon n he ac, and he furnace year old? The ac nulaon varale, X 2, alo how an nvere relaonhp (negave coeffcen). The more nulaon n he ac, he le he co o hea he home. For each addonal nch of nulaon, he co o hea he home expeced o declne y $4.83 per monh. 4-6 The age of he furnace varale how a drec relaonhp. Wh an older furnace, he co o hea he home ncreae. For each addonal year older he furnace, he co expeced o ncreae y $6. per monh.
7 Mulple Sandard Error of Emae The mulple andard error of emae a meaure of he effecvene of he regreon equaon. I meaured n he ame un a he dependen varale. I dffcul o deermne wha a large value and wha a mall value of he andard error. 4-7
8 Mulple Regreon and Correlaon Aumpon The ndependen varale and he dependen varale have a lnear relaonhp. The dependen varale mu e connuou and a lea nervalcale. The redual mu e he ame for all value of Y. When h he cae, we ay he dfference exh homocedacy. The redual hould follow he normal drued wh mean. Succeve value of he dependen varale mu e uncorrelaed. 4-8
9 Coeffcen of Mulple Deermnaon (r 2 ) Coeffcen of Mulple Deermnaon:. Symolzed y R Range from o. 3. Canno aume negave value. 4. Eay o nerpre. The Adjued R 2. The numer of ndependen varale n a mulple regreon equaon make he coeffcen of deermnaon larger. 2. If he numer of varale, k, and he ample ze, n, are equal, he coeffcen of deermnaon.. 3. To alance he effec ha he numer of ndependen varale ha on he coeffcen of mulple deermnaon, adjued R 2 ued nead. 4-9
10 Gloal Te: Teng he Mulple Regreon Model The gloal e ued o nvegae wheher any of he ndependen varale have gnfcan coeffcen. The hypohee are: H H : 2... : No all equal k Decon Rule: Rejec H f F > F,k,n-k- 4-
11 Fndng he Compued and Crcal F F,k,n-k- F.5,3,6 4-
12 Inerpreaon The compued value of F 2.9, whch n he rejecon regon. The null hypohe ha all he mulple regreon coeffcen are zero herefore rejeced. Inerpreaon: ome of he ndependen varale (amoun of nulaon, ec.) do have he aly o explan he varaon n he dependen varale (heang co). Logcal queon whch one?
13 Evaluang Indvdual Regreon Coeffcen (β = ) Th e ued o deermne whch ndependen varale have nonzero regreon coeffcen. The varale ha have zero regreon coeffcen are uually dropped from he analy. The e ac he druon wh n-(k+) degree of freedom. The hypohe e a follow: H : β = H : β Rejec H f > /2,n-k- or < - /2,n-k- 4-3
14 4-4 Crcal for he Slope : f Rejec H.25,6.25,6 3 2,2.5/ 3 2,2.5/ 2, / 2, / 2, / 2, / k n k n k n k n
15 4-5 Compued for he Slope
16 Concluon on Sgnfcance of Slope (Temp) -3.9 (Inulaon).52 (Age) 4-6
17 4-7 New Regreon Model whou Varale Age Mna
18 4-8 New Regreon Model whou Varale Age Mna
19 Teng he New Model for Sgnfcance d.f. (2,7) 3.59 Compued F =
20 4-2 Crcal -a for he New Slope : f Rejec H.25,7.25,7 2 2,2.5/ 2 2,2.5/ 2, / 2, / 2, / 2, / k n k n k n k n
21 Concluon on Sgnfcance of New Slope (Temp) Inulaon
22 Evaluang he Aumpon of Mulple Regreon. There a lnear relaonhp. Tha, here a ragh-lne relaonhp eween he dependen varale and he e of ndependen varale. 2. The varaon n he redual he ame for oh large and mall value of he emaed Y To pu anoher way, he redual unrelaed wheher he emaed Y large or mall. 3. The redual follow he normal proaly druon. 4. The ndependen varale hould no e correlaed. Tha, we would lke o elec a e of ndependen varale ha are no hemelve correlaed. 5. The redual are ndependen. Th mean ha ucceve oervaon of he dependen varale are no correlaed. Th aumpon ofen volaed when me nvolved wh he ampled oervaon. A redual he dfference eween he acual value of Y and he predced value of Y. 4-22
23 Scaer and Redual Plo A plo of he redual and her correpondng Y value ued for howng ha here are no rend or paern n he redual. 4-23
24 Druon of Redual Boh MINITAB and Excel offer anoher graph ha help o evaluae he aumpon of normally drued redual. I a called a normal proaly plo and hown o he rgh of he hogram. 4-24
25 Mulcollneary Mulcollneary ex when ndependen varale (X ) are correlaed. Effec of Mulcollneary on he Model:. An ndependen varale known o e an mporan predcor end up havng a regreon coeffcen ha no gnfcan. 2. A regreon coeffcen ha hould have a pove gn urn ou o e negave, or vce vera. 3. When an ndependen varale added or removed, here a drac change n he value of he remanng regreon coeffcen. However, correlaed ndependen varale do no affec a mulple regreon equaon aly o predc he dependen varale (Y). 4-25
26 Varance Inflaon Facor A general rule f he correlaon eween wo ndependen varale eween -.7 and.7 here lkely no a prolem ung oh of he ndependen varale. A more prece e o ue he varance nflaon facor (VIF). A VIF > unafacory. Remove ha ndependen varale from he analy. The value of VIF found a follow: VIF 2 R j The erm R 2 j refer o he coeffcen of deermnaon, where he eleced ndependen varale ued a a dependen varale and he remanng ndependen varale are ued a ndependen varale. 4-26
27 Mulcollneary Example Refer o he daa n he ale, whch relae he heang co o he ndependen varale oude emperaure, amoun of nulaon, and age of furnace. Develop a correlaon marx for all he ndependen varale. Doe appear here a prolem wh mulcollneary? Correlaon Marx of he Varale Fnd and nerpre he varance nflaon facor for each of he ndependen varale. 4-27
28 VIF Mna Example Coeffcen of Deermnaon The VIF value of.32 le han he upper lm of. Th ndcae ha he ndependen varale emperaure no rongly correlaed wh he oher ndependen varale. 4-28
29 Independence Aumpon The ffh aumpon aou regreon and correlaon analy ha ucceve redual hould e ndependen. When ucceve redual are correlaed we refer o h condon a auocorrelaon. Auocorrelaon frequenly occur when he daa are colleced over a perod of me. 4-29
30 Redual Plo veru Fed Value: Teng he Independence Aumpon When ucceve redual are correlaed we refer o h condon a auocorrelaon, whch frequenly occur when he daa are colleced over a perod of me. Noe he run of redual aove he mean of he redual, followed y a run elow he mean. A caer plo uch a h would ndcae pole auocorrelaon. 4-3
31 Qualave Varale - Example Frequenly we wh o ue nomnal-cale varale uch a gender, wheher he home ha a wmmng pool, or wheher he por eam wa he home or he vng eam n our analy. Thee are called qualave varale. To ue a qualave varale n regreon analy, we ue a cheme of dummy varale n whch one of he wo pole condon coded and he oher. EXAMPLE Suppoe n he Salerry Realy example ha he ndependen varale garage added. For hoe home whou an aached garage, ued; for home wh an aached garage, a ued. We wll refer o he garage varale a The daa from Tale 4 2 are enered no he MINITAB yem. 4-3
32 Qualave Varale - Mna Garage a dummy varale 4-32
33 Ung he Model for Emaon Wha he effec of he garage varale? Suppoe we have wo houe exacly alke nex o each oher n Buffalo, New York; one ha an aached garage, and he oher doe no. Boh home have 3 nche of nulaon, and he mean January emperaure n Buffalo 2 degree. For he houe whou an aached garage, a uued for n he regreon equaon. The emaed heang co $28.9, found y: Whou garage For he houe wh an aached garage, a uued for n he regreon equaon. The emaed heang co $358.3, found y: Wh garage 4-33
34 Evaluang Indvdual Regreon Coeffcen (β = ) Th e ued o deermne whch ndependen varale have nonzero regreon coeffcen. The varale ha have zero regreon coeffcen are uually dropped from he analy. The e ac he druon wh n-(k+) or n-k-degree of freedom. The hypohe e a follow: H : β = H : β Rejec H f > /2,n-k- or < - /2,n-k- 4-34
35 4-35 Teng Varale Garage for Sgnfcance : f Rejec H.25,6.25,6 3 2,2.5/ 3 2,2.5/ 2, / 2, / 2, / 2, / k n k n k n k n Concluon: The regreon coeffcen no zero. The ndependen varale garage hould e ncluded n he analy.
36 Sepwe Regreon The advanage o he epwe mehod are:. Only ndependen varale wh gnfcan regreon coeffcen are enered no he equaon. 2. The ep nvolved n uldng he regreon equaon are clear. 3. I effcen n fndng he regreon equaon wh only gnfcan regreon coeffcen. 4. The change n he mulple andard error of emae and he coeffcen of deermnaon are hown. 4-36
37 Sepwe Regreon Mna Example The epwe MINITAB oupu for he heang co prolem follow. Temperaure eleced fr. Th varale explan more of he varaon n heang co han any of he oher hree propoed ndependen varale. Garage eleced nex, followed y Inulaon. 4-37
38 Regreon Model wh Ineracon In Chaper 2 neracon among ndependen varale wa covered. Suppoe we are udyng wegh lo and aume, a he curren leraure ugge, ha de and exerce are relaed. So he dependen varale amoun of change n wegh and he ndependen varale are: de (ye or no) and exerce (none, moderae, gnfcan). We are nereed n eeng f hoe uded who mananed her de and exerced gnfcanly ncreaed he mean amoun of wegh lo? In regreon analy, neracon can e examned a a eparae ndependen varale. An neracon predcon varale can e developed y mulplyng he daa value n one ndependen varale y he value n anoher ndependen varale, herey creang a new ndependen varale. A wo-varale model ha nclude an neracon erm : Refer o he heang co example. I here an neracon eween he oude emperaure and he amoun of nulaon? If oh varale are ncreaed, he effec on heang co greaer han he um of avng from warmer emperaure and he avng from ncreaed nulaon eparaely? 4-38
39 Regreon Model wh Ineracon - Example 4-39 Creang he Ineracon Varale Ung he nformaon from he ale n he prevou lde, an neracon varale creaed y mulplyng he emperaure varale y he nulaon. For he fr ampled home he value emperaure 35 degree and nulaon 3 nche o he value of he neracon varale 35 X 3 = 5. The value of he oher neracon produc are found n a mlar fahon.
40 Regreon Model wh Ineracon - Example The regreon equaon : I he neracon varale gnfcan a.5 gnfcance level? 4-4
A Demand System for Input Factors when there are Technological Changes in Production
A Demand Syem for Inpu Facor when here are Technologcal Change n Producon Movaon Due o (e.g.) echnologcal change here mgh no be a aonary relaonhp for he co hare of each npu facor. When emang demand yem
More information(,,, ) (,,, ). In addition, there are three other consumers, -2, -1, and 0. Consumer -2 has the utility function
MACROECONOMIC THEORY T J KEHOE ECON 87 SPRING 5 PROBLEM SET # Conder an overlappng generaon economy le ha n queon 5 on problem e n whch conumer lve for perod The uly funcon of he conumer born n perod,
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationGraduate Macroeconomics 2 Problem set 5. - Solutions
Graduae Macroeconomcs 2 Problem se. - Soluons Queson 1 To answer hs queson we need he frms frs order condons and he equaon ha deermnes he number of frms n equlbrum. The frms frs order condons are: F K
More informationEcon107 Applied Econometrics Topic 5: Specification: Choosing Independent Variables (Studenmund, Chapter 6)
Econ7 Appled Economercs Topc 5: Specfcaon: Choosng Independen Varables (Sudenmund, Chaper 6 Specfcaon errors ha we wll deal wh: wrong ndependen varable; wrong funconal form. Ths lecure deals wh wrong ndependen
More informationCooling of a hot metal forging. , dt dt
Tranen Conducon Uneady Analy - Lumped Thermal Capacy Model Performed when; Hea ranfer whn a yem produced a unform emperaure drbuon n he yem (mall emperaure graden). The emperaure change whn he yem condered
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More informationANALYSIS AND MODELING OF HYDROLOGIC TIME SERIES. Wasserhaushalt Time Series Analysis and Stochastic Modelling Spring Semester
ANALYSIS AND MODELING OF HYDROLOGIC TIME SERIES Waerhauhal Tme Sere Analy and Sochac Modellng Sprng Semeer 8 ANALYSIS AND MODELING OF HYDROLOGIC TIME SERIES Defnon Wha a me ere? Leraure: Sala, J.D. 99,
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationExample: MOSFET Amplifier Distortion
4/25/2011 Example MSFET Amplfer Dsoron 1/9 Example: MSFET Amplfer Dsoron Recall hs crcu from a prevous handou: ( ) = I ( ) D D d 15.0 V RD = 5K v ( ) = V v ( ) D o v( ) - K = 2 0.25 ma/v V = 2.0 V 40V.
More informationt = s D Overview of Tests Two-Sample t-test: Independent Samples Independent Samples t-test Difference between Means in a Two-sample Experiment
Overview of Te Two-Sample -Te: Idepede Sample Chaper 4 z-te Oe Sample -Te Relaed Sample -Te Idepede Sample -Te Compare oe ample o a populaio Compare wo ample Differece bewee Mea i a Two-ample Experime
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Lnear Response Theory: The connecon beween QFT and expermens 3.1. Basc conceps and deas Q: ow do we measure he conducvy of a meal? A: we frs nroduce a weak elecrc feld E, and hen measure
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationRandomized Perfect Bipartite Matching
Inenive Algorihm Lecure 24 Randomized Perfec Biparie Maching Lecurer: Daniel A. Spielman April 9, 208 24. Inroducion We explain a randomized algorihm by Ahih Goel, Michael Kapralov and Sanjeev Khanna for
More informationFall 2009 Social Sciences 7418 University of Wisconsin-Madison. Problem Set 2 Answers (4) (6) di = D (10)
Publc Affars 974 Menze D. Chnn Fall 2009 Socal Scences 7418 Unversy of Wsconsn-Madson Problem Se 2 Answers Due n lecure on Thursday, November 12. " Box n" your answers o he algebrac quesons. 1. Consder
More informationu(t) Figure 1. Open loop control system
Open loop conrol v cloed loop feedbac conrol The nex wo figure preen he rucure of open loop and feedbac conrol yem Figure how an open loop conrol yem whoe funcion i o caue he oupu y o follow he reference
More informationF-Tests and Analysis of Variance (ANOVA) in the Simple Linear Regression Model. 1. Introduction
ECOOMICS 35* -- OTE 9 ECO 35* -- OTE 9 F-Tess and Analyss of Varance (AOVA n he Smple Lnear Regresson Model Inroducon The smple lnear regresson model s gven by he followng populaon regresson equaon, or
More informationNotes on cointegration of real interest rates and real exchange rates. ρ (2)
Noe on coinegraion of real inere rae and real exchange rae Charle ngel, Univeriy of Wiconin Le me ar wih he obervaion ha while he lieraure (mo prominenly Meee and Rogoff (988) and dion and Paul (993))
More informationDepartment of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationOrdinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s
Ordnary Dfferenal Equaons n Neuroscence wh Malab eamples. Am - Gan undersandng of how o se up and solve ODE s Am Undersand how o se up an solve a smple eample of he Hebb rule n D Our goal a end of class
More informationA. Inventory model. Why are we interested in it? What do we really study in such cases.
Some general yem model.. Inenory model. Why are we nereed n? Wha do we really udy n uch cae. General raegy of machng wo dmlar procee, ay, machng a fa proce wh a low one. We need an nenory or a buffer or
More informationTHEORETICAL AUTOCORRELATIONS. ) if often denoted by γ. Note that
THEORETICAL AUTOCORRELATIONS Cov( y, y ) E( y E( y))( y E( y)) ρ = = Var( y) E( y E( y)) =,, L ρ = and Cov( y, y ) s ofen denoed by whle Var( y ) f ofen denoed by γ. Noe ha γ = γ and ρ = ρ and because
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationLecture 11 SVM cont
Lecure SVM con. 0 008 Wha we have done so far We have esalshed ha we wan o fnd a lnear decson oundary whose margn s he larges We know how o measure he margn of a lnear decson oundary Tha s: he mnmum geomerc
More informationData Collection Definitions of Variables - Conceptualize vs Operationalize Sample Selection Criteria Source of Data Consistency of Data
Apply Sascs and Economercs n Fnancal Research Obj. of Sudy & Hypoheses Tesng From framework objecves of sudy are needed o clarfy, hen, n research mehodology he hypoheses esng are saed, ncludng esng mehods.
More informationLecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination
Lecure 3 Topc : Drbuo, hypohe eg, ad ample ze deermao The Sude - drbuo Coder a repeaed drawg of ample of ze from a ormal drbuo of mea. For each ample, compue,,, ad aoher ac,, where: The ac he devao of
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More informationPanel Data Regression Models
Panel Daa Regresson Models Wha s Panel Daa? () Mulple dmensoned Dmensons, e.g., cross-secon and me node-o-node (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy (c) Pongsa Pornchawseskul,
More informationChapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
More informationRobustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
More informationAdvanced time-series analysis (University of Lund, Economic History Department)
Advanced me-seres analss (Unvers of Lund, Economc Hsor Dearmen) 3 Jan-3 Februar and 6-3 March Lecure 4 Economerc echnues for saonar seres : Unvarae sochasc models wh Box- Jenns mehodolog, smle forecasng
More informationSSRG International Journal of Thermal Engineering (SSRG-IJTE) Volume 4 Issue 1 January to April 2018
SSRG Inernaonal Journal of Thermal Engneerng (SSRG-IJTE) Volume 4 Iue 1 January o Aprl 18 Opmal Conrol for a Drbued Parameer Syem wh Tme-Delay, Non-Lnear Ung he Numercal Mehod. Applcaon o One- Sded Hea
More informationPubH 7405: REGRESSION ANALYSIS DIAGNOSTICS IN MULTIPLE REGRESSION
PubH 7405: REGRESSION ANALYSIS DIAGNOSTICS IN MULTIPLE REGRESSION The daa are n he form : {( y ; x, x,, x k )},, n Mulple Regresson Model : Y β 0 β x β x β k x k ε ε N (0, σ ) The error erms are dencally
More informationLecture 6: Learning for Control (Generalised Linear Regression)
Lecure 6: Learnng for Conrol (Generalsed Lnear Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure 6: RLSC - Prof. Sehu Vjayakumar Lnear Regresson
More informationPolymerization Technology Laboratory Course
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon Polymerzaon Technology Laboraory Course Resdence Tme Dsrbuon of Chemcal Reacors If molecules or elemens of a flud are akng dfferen
More information6.302 Feedback Systems Recitation : Phase-locked Loops Prof. Joel L. Dawson
6.32 Feedback Syem Phae-locked loop are a foundaional building block for analog circui deign, paricularly for communicaion circui. They provide a good example yem for hi cla becaue hey are an excellen
More informationChapters 2 Kinematics. Position, Distance, Displacement
Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen
More informationDiscussion Session 2 Constant Acceleration/Relative Motion Week 03
PHYS 100 Dicuion Seion Conan Acceleraion/Relaive Moion Week 03 The Plan Today you will work wih your group explore he idea of reference frame (i.e. relaive moion) and moion wih conan acceleraion. You ll
More informationLecture 18: The Laplace Transform (See Sections and 14.7 in Boas)
Lecure 8: The Lalace Transform (See Secons 88- and 47 n Boas) Recall ha our bg-cure goal s he analyss of he dfferenal equaon, ax bx cx F, where we emloy varous exansons for he drvng funcon F deendng on
More informationDiebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles
Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance
More informationMath 10B: Mock Mid II. April 13, 2016
Name: Soluions Mah 10B: Mock Mid II April 13, 016 1. ( poins) Sae, wih jusificaion, wheher he following saemens are rue or false. (a) If a 3 3 marix A saisfies A 3 A = 0, hen i canno be inverible. True.
More informationH = d d q 1 d d q N d d p 1 d d p N exp
8333: Sacal Mechanc I roblem Se # 7 Soluon Fall 3 Canoncal Enemble Non-harmonc Ga: The Hamlonan for a ga of N non neracng parcle n a d dmenonal box ha he form H A p a The paron funcon gven by ZN T d d
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
More informationJ i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.
umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal
More information. The geometric multiplicity is dim[ker( λi. number of linearly independent eigenvectors associated with this eigenvalue.
Lnear Algebra Lecure # Noes We connue wh he dscusson of egenvalues, egenvecors, and dagonalzably of marces We wan o know, n parcular wha condons wll assure ha a marx can be dagonalzed and wha he obsrucons
More informationCHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING
CHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING 4. Inroducon The repeaed measures sudy s a very commonly used expermenal desgn n oxcy esng because no only allows one o nvesgae he effecs of he oxcans,
More informationBiol. 356 Lab 8. Mortality, Recruitment, and Migration Rates
Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationAlgorithmic Discrete Mathematics 6. Exercise Sheet
Algorihmic Dicree Mahemaic. Exercie Shee Deparmen of Mahemaic SS 0 PD Dr. Ulf Lorenz 7. and 8. Juni 0 Dipl.-Mah. David Meffer Verion of June, 0 Groupwork Exercie G (Heap-Sor) Ue Heap-Sor wih a min-heap
More informationUNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 2017 EXAMINATION
INTERNATIONAL TRADE T. J. KEHOE UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 27 EXAMINATION Please answer wo of he hree quesons. You can consul class noes, workng papers, and arcles whle you are workng on he
More informationJanuary Examinations 2012
Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons
More informationLecture 11: Stereo and Surface Estimation
Lecure : Sereo and Surface Emaon When camera poon have been deermned, ung rucure from moon, we would lke o compue a dene urface model of he cene. In h lecure we wll udy he o called Sereo Problem, where
More informationLecture VI Regression
Lecure VI Regresson (Lnear Mehods for Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure VI: MLSC - Dr. Sehu Vjayakumar Lnear Regresson Model M
More information5.2 GRAPHICAL VELOCITY ANALYSIS Polygon Method
ME 352 GRHICL VELCITY NLYSIS 52 GRHICL VELCITY NLYSIS olygon Mehod Velociy analyi form he hear of kinemaic and dynamic of mechanical yem Velociy analyi i uually performed following a poiion analyi; ie,
More information2. SPATIALLY LAGGED DEPENDENT VARIABLES
2. SPATIALLY LAGGED DEPENDENT VARIABLES In hs chaper, we descrbe a sascal model ha ncorporaes spaal dependence explcly by addng a spaally lagged dependen varable y on he rgh-hand sde of he regresson equaon.
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More information1) According to the article, what is the main reason investors in US government bonds grow less optimistic?
4.02 Quz 3 Soluon Fall 2004 Mulple-Choce Queon Accordng o he arcle, wha he man reaon nveor n US governmen bond grow le opmc? A They are concerned abou he declne (deprecaon of he dollar, whch, n he long
More informationMacroeconomics 1. Ali Shourideh. Final Exam
4780 - Macroeconomic 1 Ali Shourideh Final Exam Problem 1. A Model of On-he-Job Search Conider he following verion of he McCall earch model ha allow for on-he-job-earch. In paricular, uppoe ha ime i coninuou
More information. The geometric multiplicity is dim[ker( λi. A )], i.e. the number of linearly independent eigenvectors associated with this eigenvalue.
Mah E-b Lecure #0 Noes We connue wh he dscusson of egenvalues, egenvecors, and dagonalzably of marces We wan o know, n parcular wha condons wll assure ha a marx can be dagonalzed and wha he obsrucons are
More informationFTCS Solution to the Heat Equation
FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationComparing Means: t-tests for One Sample & Two Related Samples
Comparing Means: -Tess for One Sample & Two Relaed Samples Using he z-tes: Assumpions -Tess for One Sample & Two Relaed Samples The z-es (of a sample mean agains a populaion mean) is based on he assumpion
More informationChapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
More informationCONSTRUCTING AN INFORMATION MATRIX FOR MULTIVARIATE DCC-MGARCH (1, 1) METHOD
VOL 13 NO 8 APRIL 018 ISSN 1819-6608 ARPN Journal of Engneerng and Appled Scence 006-018 Aan Reearch Pulhng Nework (ARPN) All rgh reerved wwwarpnjournalcom CONSRUCING AN INFORMAION MARIX FOR MULIVARIAE
More informationNON-HOMOGENEOUS SEMI-MARKOV REWARD PROCESS FOR THE MANAGEMENT OF HEALTH INSURANCE MODELS.
NON-HOOGENEOU EI-AKO EWA POCE FO THE ANAGEENT OF HEATH INUANCE OE. Jacque Janen CEIAF ld Paul Janon 84 e 9 6 Charlero EGIU Fax: 32735877 E-mal: ceaf@elgacom.ne and amondo anca Unverà a apenza parmeno d
More informationPractice Final Exam (corrected formulas, 12/10 11AM)
Ecoomc Meze. Ch Fall Socal Scece 78 Uvery of Wco-Mado Pracce Fal Eam (correced formula, / AM) Awer all queo he (hree) bluebook provded. Make cera you wre your ame, your ude I umber, ad your TA ame o all
More information2) Of the following questions, which ones are thermodynamic, rather than kinetic concepts?
AP Chemisry Tes (Chaper 12) Muliple Choice (40%) 1) Which of he following is a kineic quaniy? A) Enhalpy B) Inernal Energy C) Gibb s free energy D) Enropy E) Rae of reacion 2) Of he following quesions,
More informationNetwork Flows: Introduction & Maximum Flow
CSC 373 - lgorihm Deign, nalyi, and Complexiy Summer 2016 Lalla Mouaadid Nework Flow: Inroducion & Maximum Flow We now urn our aenion o anoher powerful algorihmic echnique: Local Search. In a local earch
More informationCS626 Speech, Web and natural Language Processing End Sem
CS626 Speech, Web and naural Language Proceng End Sem Dae: 14/11/14 Tme: 9.30AM-12.30PM (no book, lecure noe allowed, bu ONLY wo page of any nformaon you deem f; clary and precon are very mporan; read
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More informationChapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws
Chaper 5: Phenomena Phenomena: The reacion (aq) + B(aq) C(aq) was sudied a wo differen emperaures (98 K and 35 K). For each emperaure he reacion was sared by puing differen concenraions of he 3 species
More informationPredator - Prey Model Trajectories and the nonlinear conservation law
Predaor - Prey Model Trajecories and he nonlinear conservaion law James K. Peerson Deparmen of Biological Sciences and Deparmen of Mahemaical Sciences Clemson Universiy Ocober 28, 213 Ouline Drawing Trajecories
More informationChapter Floating Point Representation
Chaper 01.05 Floaing Poin Represenaion Afer reading his chaper, you should be able o: 1. conver a base- number o a binary floaing poin represenaion,. conver a binary floaing poin number o is equivalen
More informationComb Filters. Comb Filters
The smple flers dscussed so far are characered eher by a sngle passband and/or a sngle sopband There are applcaons where flers wh mulple passbands and sopbands are requred Thecomb fler s an example of
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signal & Syem Prof. Mark Fowler Noe Se #27 C-T Syem: Laplace Tranform Power Tool for yem analyi Reading Aignmen: Secion 6.1 6.3 of Kamen and Heck 1/18 Coure Flow Diagram The arrow here how concepual
More informationThe Residual Graph. 12 Augmenting Path Algorithms. Augmenting Path Algorithm. Augmenting Path Algorithm
Augmening Pah Algorihm Greedy-algorihm: ar wih f (e) = everywhere find an - pah wih f (e) < c(e) on every edge augmen flow along he pah repea a long a poible The Reidual Graph From he graph G = (V, E,
More informationFundamentals of PLLs (I)
Phae-Locked Loop Fundamenal of PLL (I) Chng-Yuan Yang Naonal Chung-Hng Unvery Deparmen of Elecrcal Engneerng Why phae-lock? - Jer Supreon - Frequency Synhe T T + 1 - Skew Reducon T + 2 T + 3 PLL fou =
More informationAssignment 16. Malaria does not affect the red cell count in the lizards.
ignmen 16 7.3.5 If he null hypohei i no rejeced ha he wo ample are differen, hen he Type of Error would be ype II 7.3.9 Fale. The cieni rejeced baed on a bad calculaion, no baed upon ample ha yielded an
More informationL N O Q. l q l q. I. A General Case. l q RANDOM LAGRANGE MULTIPLIERS AND TRANSVERSALITY. Econ. 511b Spring 1998 C. Sims
Econ. 511b Sprng 1998 C. Sm RAD AGRAGE UPERS AD RASVERSAY agrange mulpler mehod are andard fare n elemenary calculu coure, and hey play a cenral role n economc applcaon of calculu becaue hey ofen urn ou
More information5th International Conference on Advanced Design and Manufacturing Engineering (ICADME 2015)
5h Inernaonal onference on Advanced Desgn and Manufacurng Engneerng (IADME 5 The Falure Rae Expermenal Sudy of Specal N Machne Tool hunshan He, a, *, La Pan,b and Bng Hu 3,c,,3 ollege of Mechancal and
More informationTime series Decomposition method
Time series Decomposiion mehod A ime series is described using a mulifacor model such as = f (rend, cyclical, seasonal, error) = f (T, C, S, e) Long- Iner-mediaed Seasonal Irregular erm erm effec, effec,
More informationControl Systems. Mathematical Modeling of Control Systems.
Conrol Syem Mahemacal Modelng of Conrol Syem chbum@eoulech.ac.kr Oulne Mahemacal model and model ype. Tranfer funcon model Syem pole and zero Chbum Lee -Seoulech Conrol Syem Mahemacal Model Model are key
More informationAlgorithms and Data Structures 2011/12 Week 9 Solutions (Tues 15th - Fri 18th Nov)
Algorihm and Daa Srucure 2011/ Week Soluion (Tue 15h - Fri 18h No) 1. Queion: e are gien 11/16 / 15/20 8/13 0/ 1/ / 11/1 / / To queion: (a) Find a pair of ube X, Y V uch ha f(x, Y) = f(v X, Y). (b) Find
More informationSterilization D Values
Seriliaion D Values Seriliaion by seam consis of he simple observaion ha baceria die over ime during exposure o hea. They do no all live for a finie period of hea exposure and hen suddenly die a once,
More informationEconomics 120C Final Examination Spring Quarter June 11 th, 2009 Version A
Suden Name: Economcs 0C Sprng 009 Suden ID: Name of Suden o your rgh: Name of Suden o your lef: Insrucons: Economcs 0C Fnal Examnaon Sprng Quarer June h, 009 Verson A a. You have 3 hours o fnsh your exam.
More informationTHE UNIVERSITY OF TEXAS AT AUSTIN McCombs School of Business
THE UNIVERITY OF TEXA AT AUTIN McCombs chool of Business TA 7.5 Tom hively CLAICAL EAONAL DECOMPOITION - MULTIPLICATIVE MODEL Examples of easonaliy 8000 Quarerly sales for Wal-Mar for quarers a l e s 6000
More informationLinear Circuit Elements
1/25/2011 inear ircui Elemens.doc 1/6 inear ircui Elemens Mos microwave devices can be described or modeled in erms of he hree sandard circui elemens: 1. ESISTANE () 2. INDUTANE () 3. APAITANE () For he
More informationLags from Money to Inflation in a Monetary Integrated Economy: Evidence from the Extreme Case of Puerto Rico. Abstract
Lag from oney o Inflaon n a oneary Inegraed Economy: Evdence from he Exreme Cae of Puero Rco Carlo A. Rodríguez * Abrac Th paper ude he me lengh of he long and hor run effec of money growh over nflaon
More informationReview - Week 10. There are two types of errors one can make when performing significance tests:
Review - Week Read: Chaper -3 Review: There are wo ype of error oe ca make whe performig igificace e: Type I error The ull hypohei i rue, bu we miakely rejec i (Fale poiive) Type II error The ull hypohei
More informationCHEMICAL KINETICS: 1. Rate Order Rate law Rate constant Half-life Temperature Dependence
CHEMICL KINETICS: Rae Order Rae law Rae consan Half-life Temperaure Dependence Chemical Reacions Kineics Chemical ineics is he sudy of ime dependence of he change in he concenraion of reacans and producs.
More informationComputing Relevance, Similarity: The Vector Space Model
Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are
More informationEcon107 Applied Econometrics Topic 7: Multicollinearity (Studenmund, Chapter 8)
I. Definiions and Problems A. Perfec Mulicollineariy Econ7 Applied Economerics Topic 7: Mulicollineariy (Sudenmund, Chaper 8) Definiion: Perfec mulicollineariy exiss in a following K-variable regression
More informationLet. x y. denote a bivariate time series with zero mean.
Linear Filer Le x y : T denoe a bivariae ime erie wih zero mean. Suppoe ha he ime erie {y : T} i conruced a follow: y a x The ime erie {y : T} i aid o be conruced from {x : T} by mean of a Linear Filer.
More information6. Solve by applying the quadratic formula.
Dae: Chaper 7 Prerequisie Skills BLM 7.. Apply he Eponen Laws. Simplify. Idenify he eponen law ha you used. a) ( c) ( c) ( c) ( y)( y ) c) ( m)( n ). Simplify. Idenify he eponen law ha you used. 8 w a)
More informationProblem Set If all directed edges in a network have distinct capacities, then there is a unique maximum flow.
CSE 202: Deign and Analyi of Algorihm Winer 2013 Problem Se 3 Inrucor: Kamalika Chaudhuri Due on: Tue. Feb 26, 2013 Inrucion For your proof, you may ue any lower bound, algorihm or daa rucure from he ex
More information[Link to MIT-Lab 6P.1 goes here.] After completing the lab, fill in the following blanks: Numerical. Simulation s Calculations
Chaper 6: Ordnary Leas Squares Esmaon Procedure he Properes Chaper 6 Oulne Cln s Assgnmen: Assess he Effec of Sudyng on Quz Scores Revew o Regresson Model o Ordnary Leas Squares () Esmaon Procedure o he
More information