Semipartial (Part) and Partial Correlation


 Egbert Scot Logan
 2 years ago
 Views:
Transcription
1 Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated 003 edition now). Oveview. Patial and semipatial coelations ovide anothe means of assessing the elative impotance of independent vaiables in detemining Y. Basically, they show how much each vaiable uniquely contibutes to ove and above that which can be accounted fo by the othe IVs. We will use two apoaches fo explaining patial and semipatial coelations. he fist elies imaily on fomulas, while the second uses diagams and gaphics. o save pape shuffling, we will epeat the SPSS intout fo ou income example: egession Desciptive Statistics INCOME EDUC JOBEXP Mean Std. Deviation N Coelations Peason Coelation INCOME EDUC JOBEXP INCOME EDUC JOBEXP Model Model Summay Adjusted Std. Eo of Squae Squae the Estimate.99 a a. Pedictos: (Constant), JOBEXP, EDUC Model egession esidual otal ANOVA b Sum of Squaes df Mean Squae F Sig a a. Pedictos: (Constant), JOBEXP, EDUC b. Dependent Vaiable: INCOME Model (Constant) EDUC JOBEXP Unstandadized Coefficients a. Dependent Vaiable: INCOME Standadi zed Coefficien ts Coefficients a 95% Confidence Inteval fo B t Sig. Lowe Bound Uppe Bound Coelations Zeoode Patial Pat Collineaity Statistics VIF B Std. Eo Beta oleance Semipatial (Pat) and Patial Coelation  Page
2 Apoach : Fomulas. One of the oblems that aises in multiple egession is that of defining the contibution of each IV to the multiple coelation. One answe is ovided by the semipatial coelation s and its squae, s. (NOE: Hayes and SPSS efe to this as the pat coelation.) Patial coelations and the patial coelation squaed ( and ) ae also sometimes used. Semipatial coelations. Semipatial coelations (also called pat coelations) indicate the unique contibution of an independent vaiable. Specifically, the squaed semipatial coelation fo a vaiable tells us how much will decease if that vaiable is emoved fom the egession equation. Let H the set of all the X (independent) vaiables, G the set of all the X vaiables except X Some elevant fomulas fo the semipatial and squaed semipatial coelations ae then s b * X G b * ol s YG b *( X G ) b * ol hat is, to get X s unique contibution to, fist egess Y on all the X s. hen egess Y on all the X s except X. he diffeence between the values is the squaed semipatial coelation. O altenatively, the standadized coefficients and the oleances can be used to compute the semipatials and squaed semipatials. Note that he moe toleant a vaiable is (i.e. the less highly coelated it is with the othe IVs), the geate its unique contibution to will be. Once one vaiable is added o emoved fom an equation, all the othe semipatial coelations can change. he semipatial coelations only tell you about changes to fo one vaiable at a time. Semipatial coelations ae used in Stepwise egession Pocedues, whee the compute (athe than the analyst) decides which vaiables should go into the final equation. We will discuss Stepwise egession in moe detail shotly. Fo now, we will note that, in a fowad stepwise egession, the vaiable which would add the lagest incement to (i.e. the vaiable which would have the lagest semipatial coelation) is added next (ovided it is statistically significant). In a bacwads stepwise egession, the vaiable which would oduce the smallest decease in (i.e. the vaiable with the smallest semipatial coelation) is dopped next (ovided it is not statistically significant.) Semipatial (Pat) and Patial Coelation  Page
3 Fo computational puposes, hee ae some othe fomulas fo the two IV case only: s Y  Y  Y  Y ol b  b ol s Y Y Y Y ol b b ol Fo ou income example, s Y  Y * (.07 ).8797 b ol * , s Y  Y , s Y Y * (.07 ).3606 b ol.366* s Y  Y Compae these esults with the column SPSS labels pat co. Anothe notational fom of s used is y( ). Also, efeing bac to ou geneal fomula, it may be useful to note that YG + s, YG hat is, when Y is egessed on all the Xs, is equal to the squaed coelation of Y egessed on all the Xs except X plus the squaed semipatial coelation fo X ; and, if we would lie to now what would be if a paticula vaiable wee excluded fom the equation, just subtact s fom. Fo example, if we want to now what would be if X wee eliminated fom the equation, just compute  s Y ; and, if we want to now what would be if X wee eliminated fom the equation, compute  s Y.  s Semipatial (Pat) and Patial Coelation  Page 3
4 Patial Coelation Coefficients. Anothe ind of solution to the oblem of descibing each IV s paticipation in detemining is given by the patial coelation coefficient, and its squae,. he squaed patial answes the question How much of the Y vaiance which is not estimated by the othe IVs in the equation is estimated by this vaiable? he fomulas ae s s s s, s YG + s YG Note that, since the denominato cannot be geate than, patial coelations will be lage than semipatial coelations, except in the limiting case when othe IVs ae coelated 0 with Y in which case s. In the two IV case, may be found via s  Y s  Y + s, s Y s Y + s In the case of ou income example, s  Y , , s Y , (o confim these esults, loo at the column SPSS labels patial.) hese esults imply that 46% of the vaiation in Y (income) that was left unexplained by the simple egession of Y on X (education) has been explained by the addition hee of X (job expeience) as an explanatoy vaiable. Similaly, 83% of the vaiation in income that is left unexplained by the simple egession of Y on X is explained by the addition of X as an explanatoy vaiable. A fequently employed fom of notation to exess the patial is Y is also sometimes called the patial coefficient of detemination fo X. WANING. In a multiple egession, the metic coefficients ae sometimes efeed to as the patial egession coefficients. hese should not be confused with the patial coelation coefficients we ae discussing hee. Semipatial (Pat) and Patial Coelation  Page 4
5 Altenative fomulas fo semipatial and patial coelations: s * N K + ( N K ) Note that the only pat of the calculations that will change acoss X vaiables is the value; theefoe the X vaiable with the lagest patial and semipatial coelations will also have the lagest value (in magnitude). Examples: * s N K 9.09 * s * N K 3.77* ( N K ) ( N K ) Besides maing obvious how the patials and semipatials ae elated to, these fomulas may be useful if you want the patials and semipatials and they have not been epoted, but the othe infomation equied by the fomulas has been. Once I figued it out (which wasn t easy!) I used the fomula fo the semipatial in the pco outine I wote fo Stata. Semipatial (Pat) and Patial Coelation  Page 5
6 Apoach : Diagams and Gaphics. Hee is an altenative, moe visually oiented discussion of what semipatial and patial coelations ae and what they mean. Following ae gaphic eesentations of semipatial and patial coelations. Assume we have independent vaiables X, X, X 3, and X 4, and dependent vaiable Y. (Assume that all vaiables ae in standadized fom, i.e. have mean 0 and vaiance.) o get the semipatial coelation of X with Y, egess X on X, X 3, and X 4. he esidual fom this egession (i.e. the diffeence between the edicted value of X and the actual value) is e. he semipatial coelation, then, is the coelation between e and Y. It is called a semipatial coelation because the effects of X, X 3, and X 4 have been emoved (i.e. patialled out ) fom X but not fom Y. Semipatial (Pat) Coelation o get the patial coelation of X with Y, egess X on X, X 3, and X 4. he esidual fom this egession is again e. hen, egess Y on X, X 3, and X 4 (but NO X ). he esidual fom this egession is e y. he patial coelation is the coelation between e and e y. It is called a patial coelation because the effects of X, X 3, and X 4 have been patialled out fom both X and Y. Patial Coelation Semipatial (Pat) and Patial Coelation  Page 6
7 Semipatial (Pat) Coelations. o bette undestand the meaning of semipatial and squaed semipatial coelations, it will be helpful to conside the following diagam (called a ballantine ). [NOE: his ballantine descibes ou cuent oblem etty well. Section 3.4 of the 975 edition of Cohen and Cohen gives seveal othe examples of how the Xs and Y can be inteelated, e.g. X and X might be uncoelated with each othe, o they might be negatively coelated with each othe but positively coelated with Y.] In this diagam, the vaiance of each vaiable is eesented by a cicle of unit aea (i.e. each vaiable is standadized to have a vaiance of ). Hence, A + B + C + D s y yy, (B + C)/ (A + B + C + D) B + C Y, (C + D)/ (A + B + C + D) C + D Y, (C + F)/ (B + C + E + F) (C + F)/ (C + D + F + G) C + F, (B + C + D) / (A + B + C + D) B + C + D Y hat is, the ovelapping of cicles eesents thei squaed coelation, e.g.. he total aea of Y coveed by the X and X aeas eesents the opotion of Y s vaiance accounted fo by the two IVs, Y. he figue shows that this aea is equal to the sum of the aeas designated B, C, and D. (NOE: Don t confuse the A and B used in the diagam with the a and b we use fo egession coefficients!) he aeas B and D eesent those potions of Y ovelapped uniquely by X and X, espectively, wheeas aea C eesents thei simultaneous ovelap with Y. he unique aeas, exessed as opotions of Y vaiance, ae squaed semipatial coelation coefficients, and each equals the incease in the squaed multiple coelation which occus when the vaiable is added to the othe IV. hus, Semipatial (Pat) and Patial Coelation  Page 7
8 s B (B +C + D)  (C + D) Y  Y, s D (B + C + D)  (B +C) he semipatial coelation s is the coelation between all of Y and X fom which X has been patialled. It is a semipatial coelation since the effects of X have been emoved fom X but not fom Y. emoving the effect is equivalent to subtacting fom X the X values estimated fom X, that is, to woing with x  x^ (whee x^ is estimated by egessing X on X ). hat is, x  x^ is the esidual obtained by egessing X on X. We will denote this as e. Hence, s ye. s is the amount that is inceased by including X in the multiple egession equation (o altenatively, it is the amount that would go down if X wee eliminated fom the equation.) In tems of ou diagam, s y A + B + C + D, (because Y is standadized) y (B + C)/ (A + B + C + D) B + C, s B / (A + B + C + D) B. hus, we emove the aea C fom X but not fom Y. Y  Y Anothe notational fom of s used is y( ), the being a shothand way of exessing X fom which X has been patialled. Patial Coelation Coefficients. Anothe ind of solution to the oblem of descibing each IV s paticipation in detemining is given by the patial coelation coefficient, and its squae,. he squaed patial coelation may be undestood best as the opotion of the vaiance of Y not associated with X which is associated with X. hat is, B (B +C + D)  (C + D) Y  A+ B (A+ B +C + D)  (C + D)  Y Y s  Y D A+ D Moe geneally, we can say that (B + C + D) (B +C) (A+ B + C + D) (B +C) Y Y Y s  s s s s, s YG + s YG Y Semipatial (Pat) and Patial Coelation  Page 8
9 he numeato fo is the squaed semipatial coelation coefficient; howeve, the base includes not all of the vaiance as in s, but only that potion of Y vaiance which is not associated with X, that is,  Y. hus, the squaed patial answes the question How much of the Y vaiance which is not estimated by the othe IVs in the equation is estimated by this vaiable? Note that, since the denominato cannot be geate than, patial coelations will be lage than semipatial coelations, except in the limiting case when othe IVs ae coelated 0 with Y in which case s. Anothe way of viewing the patial coelation is that is the coelation between X fom which X has been patialled and Y fom which X has also been patialled (i.e., the coelation between x^ and y^ ). A fequently employed fom of notation to exess the patial is Y, which conveys that X is being patialled fom both Y and X, in contast to the semipatial, which is eesented as Y( ). is also sometimes called the patial coefficient of detemination fo X. In tems of ou diagam, s y A + B + C + D, (because Y is standadized) y (B + C)/ (A + B + C + D) B + C, s B / (A + B + C + D) B B / (A + B) hus, in the squaed semipatial coelation, aeas which belong to X and which ovelap eithe X o Y (C and D) ae emoved fom X but not Y. In the squaed patial coelation, aeas which belong to X ae emoved fom both X and Y. Semipatial (Pat) and Patial Coelation  Page 9
Chapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationPower and Sample Size Calculations for the 2Sample ZStatistic
Powe and Sample Size Calculations fo the Sample ZStatistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.
More information2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90
. Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationSymmetric polynomials and partitions Eugene Mukhin
Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More information2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES
. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an
More informationLAL Update. Letter From the President. Dear LAL User:
LAL Update ASSOCIATES OF CAPE COD, INCORPORATED OCTOBER 00 VOLUME 0, NO. Lette Fom the Pesident Dea LAL Use: This Update will claify some of the statistics used with tubidimetic and chomogenic LAL tests.
More informationPsychology 282 Lecture #2 Outline. Review of Pearson correlation coefficient:
Psychology 282 Lectue #2 Outline Review of Peason coelation coefficient: z z ( n 1) Measue of linea elationship. Magnitude Stength Sign Diection Bounded by +1.0 and 1.0. Independent of scales of measuement.
More informationEconomics 326: Input Demands. Ethan Kaplan
Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationStandardized Coefficients
Standadized Coefficient Ta. How do ou decide which of the X ae mot impotant fo detemining? In thi handout, we dicu one poile (and contoveial) anwe to thi quetion  the tandadized egeion coefficient. Fomula.
More informationOn Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables.
C.Candan EE3/53METU On Coelation Coefficient The coelation coefficient indicates the degee of linea dependence of two andom vaiables. It is defined as ( )( )} σ σ Popeties: 1. 1. (See appendi fo the poof
More information(3) Bipolar Transistor Current Sources
B73 lectonics Analysis & Design (3) Bipola Tansisto Cuent Souces Leaning utcome Able to descibe and: Analyze and design a simple twotansisto BJT cuentsouce cicuit to poduce a given bias cuent. Analyze
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More informationAlternative Formulas for Rating Prediction Using Collaborative Filtering
Altenative Fomulas fo Rating Pediction Using Collaboative Filteing Ama Saic, Misad Hadziadic, David Wilson College of Computing and Infomatics The Univesity of Noth Caolina at Chalotte, 901 Univesity City
More informationLecture 8 Topic 5: Multiple Comparisons (means separation)
Lectue 8 Topic 5: Multiple Compaisons (means sepaation) ANOVA: H 0 : µ 1 = µ =... = µ t H 1 : The mean of at least one teatment goup is diffeent If thee ae moe than two teatments in the expeiment, futhe
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationModel Question Paper Mathematics Class XII
Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat
More information1ST INTERNATIONAL CONFERENCE ON SUPPLY CHAINS
Examination of the inteelation among the ice of the fuel, the cost of tansot feight and the ofit magin Angeliki Paana 1, Aiadni Paana 2, Michael Dagiasis 3, Dimitios Folinas 4, Eaminontas Diamantooulos
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationReview of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction.
Appendi A Review of Vectos This appendi is a summa of the mathematical aspects of vectos used in electicit and magnetism. Fo a moe detailed intoduction to vectos, see Chapte 1. A.1 DESCRIBING THE 3D WORLD:
More informationGravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
More informationPerformance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation
Cicuits and Systems, 013, 4, 1171 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0
More informationLoyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
More informationChapter 5 Review  Part I
Math 17 Chate Review Pat I Page 1 Chate Review  Pat I I. Tyes of Polynomials A. Basic Definitions 1. In the tem b m, b is called the coefficient, is called the vaiable, and m is called the eonent on the
More informationConcept and Experiences on using a Wikibased System for Softwarerelated Seminar Papers
Concept and Expeiences on using a Wikibased System fo Softwaeelated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wthaachen.de,
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationTrigonometric Functions of Any Angle
Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationLATIN SQUARE DESIGN (LS) With the Latin Square design you are able to control variation in two directions.
Facts about the LS Design LATIN SQUARE DESIGN (LS) With the Latin Squae design you ae able to contol vaiation in two diections. Teatments ae aanged in ows and columns Each ow contains evey teatment.
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationSamples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationChapter 4: Matrix Norms
EE448/58 Vesion.0 John Stensby Chate 4: Matix Noms The analysis of matixbased algoithms often equies use of matix noms. These algoithms need a way to quantify the "size" of a matix o the "distance" between
More information92.131 Calculus 1 Optimization Problems
9 Calculus Optimization Poblems ) A Noman window has the outline of a semicicle on top of a ectangle as shown in the figue Suppose thee is 8 + π feet of wood tim available fo all 4 sides of the ectangle
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationThe Critical Angle and Percent Efficiency of Parabolic Solar Cookers
The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More information0.9 Radicals and Equations
0.9 Radicals and Equations 0.9 Radicals and Equations In tis section we eview simlifying exessions and solving equations involving adicals. In addition to te oduct, quotient and owe ules stated in Teoem
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationLife Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More informationIn order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Radians At school we usually lean to measue an angle in degees. Howeve, thee ae othe ways of measuing an angle. One that we ae going to have a look at hee is measuing angles in units called adians. In
More informationSIMULATION OF GAS TURBINES OPERATING IN OFFDESIGN CONDITION
SIMULAION OF GAS URBINES OPERAING IN OFFDESIGN CONDIION Analdo Walte: awalte@fem.unicamp.b Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box 6122  ZIP code 13083970  Bazil Abstact. In many
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationUniversal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool
Univesal Cycles 2011 Yu She Wial Gamma School fo Gils Depatment of Mathematical Sciences Univesity of Livepool Supeviso: Pofesso P. J. Giblin Contents 1 Intoduction 2 2 De Buijn sequences and Euleian Gaphs
More informationIn the lecture on double integrals over nonrectangular domains we used to demonstrate the basic idea
Double Integals in Pola Coodinates In the lectue on double integals ove nonectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example
More informationmv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !
Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationOpen Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
More informationBA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS
BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment
More informationFigure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
More informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationCapital Asset Pricing Model (CAPM) at Work
Capital Asset Picing Model (CAPM) at Wok Some o the Intuition behind CAPM Applications o CAPM Estimation and Testing o CAPM Intuition behind Equilibium Suppose you obseved the ollowing chaacteistics o
More informationCIRCUITS LABORATORY EXPERIMENT 7
CIRCUITS LABORATORY EXPERIMENT 7 Design of a Single Tansisto Amplifie 7. OBJECTIVES The objectives of this laboatoy ae to: (a) Gain expeience in the analysis and design of an elementay, single tansisto
More informationSimple Harmonic Motion
Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,
More informationThere is considerable variation in health care utilization and spending. Geographic Variation in Health Care: The Role of Private Markets
TOMAS J. PHILIPSON Univesity of Chicago SETH A. SEABUY AND Copoation LEE M. LOCKWOOD Univesity of Chicago DANA P. GOLDMAN Univesity of Southen Califonia DAIUS N. LAKDAWALLA Univesity of Southen Califonia
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationSo we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)
Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing
More informationLesson C3 2. Exploring Genetics. Performance Standard: 2. Discuss the implications of genetic variation.
Lesson C3 2 Exploing Genetics Unit C. Basic Pinciples of Agicultual/Hoticultual Science Poblem Aea 3. Undestanding Cells, Genetics, and Repoduction Lesson 2. Exploing Genetics New Mexico Content Standad:
More informationCRRC1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the
More informationChapter 6. GraduallyVaried Flow in Open Channels
Chapte 6 GaduallyVaied Flow in Open Channels 6.. Intoduction A stea nonunifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gaduallyvaied flow (GVF). The backwate
More informationThank you for participating in Teach It First!
Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Suppot Coach, Foundational Mathematics teache lesson followed by the coesponding student lesson. We ae confident
More informationJapan s trading losses reach JPY20 trillion
IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup
More informationSome text, some maths and going loopy. This is a fun chapter as we get to start real programming!
Chapte Two Some text, some maths and going loopy In this Chapte you ae going to: Lean how to do some moe with text. Get Python to do some maths fo you. Lean about how loops wok. Lean lots of useful opeatos.
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationRoad tunnel. Road tunnel information sheet. Think about. Using the information
Road tunnel This activity is about using a gaphical o algebaic method to solve poblems in eal contets that can be modelled using quadatic epessions. The fist poblem is about a oad tunnel. The infomation
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationExam I. Spring 2004 Serway & Jewett, Chapters 15. Fill in the bubble for the correct answer on the answer sheet. next to the number.
Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 15 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE
More informationInternational Monetary Economics Note 1
36632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More information