REGRESSION DISCONTINUITY (RD) Technical Track Session V. Dhushyanth Raju Julieta Trias The World Bank

Size: px
Start display at page:

Download "REGRESSION DISCONTINUITY (RD) Technical Track Session V. Dhushyanth Raju Julieta Trias The World Bank"

Transcription

1 REGRESSION DISCONTINUITY (RD) Technical Track Sessin V Dhushyanth Raju Julieta Trias The Wrld Bank These slides cnstitute supprting material t the Impact Evaluatin in Practice Handbk : Gertler, P. J.; Martinez, S., Premand, P., Rawlings, L. B. and Christel M. J. Vermeersch, 2010, Impact Evaluatin in Practice: Ancillary Material, The Wrld Bank, Washingtn DC ( The cntent f this presentatin reflects the views f the authrs and nt necessarily thse f the Wrld Bank.

2 Intrductin Many times randm assignment is nt pssible Universal take-up Nn-excludable interventin Treatment already assigned When randmizatin is nt feasible, hw can we explit implementatin features f the prgram t measure its impact? Answer: Quasi-experiments Example: Regressin Discntinuity Design.

3 Regressin Discntinuity Design (RDD) RDD clser t randmized experiments than ther quasiexperimental methds Relies n knwledge f the selectin prcess Need t knw quantifiable selectin criteria a cntinuus scre r index Assignment t treatment depends discntinuusly n this scre at a threshld r cutff Intuitin The ptential beneficiaries (units) just abve the cut-ff pint are very similar t the ptential beneficiaries just belw the cut-ff. Within narrw bandwidth arund cut-ff, treatment assignment apprximates randmizatin Cmparing final utcmes f thse just abve cutff t thse just belw can apprximate treatment effect

4 Indexes are cmmn in targeting f scial prgrams Anti-pverty prgrams Pensin prgrams Schlarships Cmmunity Driven Develpment prgrams targeted t husehlds belw a given pverty index. targeted t ppulatin abve a certain age. targeted t students with highest scres n standardized test r with lwest scre f pverty index. awarded t NGOs that achieve highest scres.

5 An example US minimum legal age fr drinking alchl is 21 illegal fr peple yunger than 21 Cnsider tw grups Peple aged 20 years, 11 mnths and 29 days 21 year lds Tw grups treated differently under plicy because f arbitrary age cut ff But nt inherently different (likelihd t g t parties, bedience, prpensity t engage in risky behavir, etc)

6 Effect f alchl n mrtality Plicy rule assigns peple t treatment and cmparisn grups Treatment grup: Peple between ages 20 years and 11 mnths and 20 years 11 mnths and 29 days Cmparisn grup: individuals wh just turned 21 and can nw legally drink alchl. Grups shuld be similar in terms f bservable and unbservable characteristics that affect utcmes (mrtality rates) but dissimilar n legality f their alchl cnsumptin Pssible t estimate impact f legality f alchl cnsumptin n mrtality rates Als pssible t islate the causal impact f actual alchl cnsumptin n mrtality rates

7 Graphical depictin

8 All deaths Increased alchl cnsumptin causes higher mrtality rates arund the age f 21 All deaths assciated with injuries, alchl r drug use All ther deaths

9 Sharp and fuzzy discntinuities Sharp discntinuity Discntinuity precisely determines treatment status All peple 21 and lder drink alchl and n ne else des Fuzzy discntinuity Percentage f participants changes discntinuusly at cut-ff, but nt frm 0% t 100% (r frm 100% t 0%) Sme peple yunger than 21 end up cnsuming alchl and/r sme lder than 21 dn t cnsume at all Need t use scre as an instrumental variable fr cnsumptin

10 Example: Effect f cash transfer n cnsumptin Gal Methd Target transfer t prest husehlds Cnstruct pverty index frm 1 t 100 with preinterventin characteristics Husehlds with a scre 50 are pr Husehlds with a scre >50 are nn-pr Implementatin Cash transfer t pr husehlds Evaluatin Measure utcmes (i.e. cnsumptin, schl attendance rates) befre and after transfer, cmparing husehlds just abve and belw the cut-ff pint.

11 Regressin Discntinuity Design-Baseline Pr Nn pr Index

12 Regressin Discntinuity Design-Fllw-up Pr Nn pr Treatment effect Index

13 Identificatin fr sharp discntinuity y i = β 0 + β 1 D i + δ(scre i ) + ε i D i = 1 If husehld i receives transfer 0 If husehld i des nt receive transfer δ(scre i ) = Functin that is cntinuus arund the cut-ff pint Assignment rule under sharp discntinuity: D i = 1 D i = 0 scre i 50 scre i > 50

14 Identificatin fr fuzzy discntinuity y i = β 0 + β 1 D i + δ(scre i ) + ε i D i = 1 If husehld receives transfer 0 If husehld des nt receive transfer But Treatment depends n whether scre i > r< 50 And Endgenus factrs

15 Estimatin fr fuzzy discntinuity IV estimatin y i = β 0 + β 1 D i + δ(scre i ) + ε i First stage: D i = γ 0 + γ 1 I(scre i > 50) + η i Dummy variable Secnd stage: ^ y i = β 0 + β 1 D i + δ(scre i ) + ε i Cntinuus functin

16 Internal validity If cut-ff is arbitrary, individuals t the immediate left and right f the cut-ff shuld be very similar pre-interventin Pst-interventin: Differences in utcmes can be attributed t the plicy. Baseline Fllw-up utcme assignment variable assignment variable

17 Internal Validity Majr assumptin Nthing else is happening: in absence f plicy, we wuld nt bserve a discntinuity in the utcmes arund this particular cut ff. Might nt be the case if cutff meaningful fr ther plicies Bike-helmet plicy stps als stps applying at age 21. Majr data requirement Requires many bservatins arund cut-ff All bservatins away frm the cut-ff have less weight

18 Internal Validity Crucial that participants d nt knw much abut frmula fr determining cut-ffs Otherwise, they can adjust their behavir in ways that undermine validity Example 1: Pupil teacher ratis and student achievement in Chile Enrllment cutff (X) determined required number f classrms Schl with X students and schl with X+1 students wuld have different number f classrms Very little difference in enrllment Big difference in Pupil/Teacher Rati Once enrllment reached a trigger pint, sme schls began t increase fees t decrease enrllment and avid requirement fr new classrm Schls with X and X+1 students, where X is the cut-ff, culd be very different

19 Internal Validity Crucial that participants d nt knw much abut frmula fr determining cut-ffs Otherwise, they can adjust their behavir in ways that undermine validity Example 2: SISBEN index in Clmbia Pverty index used t determine eligibility in many public prgrams Evidence f clumping at index-threshlds ver time

20 External validity Wuld the results generalize past the tw grups yu are cmparing? Cunterfactual grup in RDD Individuals marginally excluded frm benefits Example: peple less than 21 but lder than 20 years and 10 mnths Causal cnclusins are limited t individuals, husehlds, villages, near the cut-ff The estimated impact fr units marginally r just eligible fr benefits Extraplatin beynd this pint needs additinal, ften unwarranted, assumptins (r multiple cut-ffs)

21 Advantages f RD fr evaluatin RD yields an unbiased estimate f treatment effect at the discntinuity Can take advantage f a knwn rule fr assigning the benefit This is cmmn in the design f scial interventins N need t exclude a grup f eligible husehlds/ individuals frm treatment

22 Ptential disadvantages f RD Lcal average treatment effects: We estimate the effect f the prgram arund the cut-ff pint This is nt always generalizable Pwer: The effect is estimated at the discntinuity, s we generally have fewer bservatins than in a randmized experiment with the same sample size. Specificatin can be sensitive t functinal frm: Make sure the relatinship between the assignment variable and the utcme variable is crrectly mdeled, including: (1) Nnlinear Relatinships and (2) Interactins.

23 References Christpher Carpenter and Carls Dbkin (2009), The Effect f Alchl Access n Cnsumptin and Mrtality: Regressin Discntinuity Evidence frm the Minimum Drinking Age, American Ecnmic Jurnal: Applied Ecnmics, Vl. 1, Issue 1, pp Miguel Urquila and Eric Verhgen (2009), Class-Size Caps, Srting, and the Regressin Discntinuity Design, American Ecnmic Review, v. 99 n. 1, pp , March Adriana Camach and Emily Cnver (2009), Manipulatin f Scial Prgram Eligibility: Detectin, Explanatins and Cnsequences fr Empirical Research, UNIVERSIDAD DE LOS ANDES-CEDE Discussin Paper

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank

CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal

More information

INSTRUMENTAL VARIABLES

INSTRUMENTAL VARIABLES INSTRUMENTAL VARIABLES Technical Track Sessin IV Sergi Urzua University f Maryland Instrumental Variables and IE Tw main uses f IV in impact evaluatin: 1. Crrect fr difference between assignment f treatment

More information

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank

MATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank MATCHING TECHNIQUES Technical Track Sessin VI Emanuela Galass The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Emanuela Galass fr the purpse f this wrkshp When can we use

More information

MATCHING TECHNIQUES Technical Track Session VI Céline Ferré The World Bank

MATCHING TECHNIQUES Technical Track Session VI Céline Ferré The World Bank MATCHING TECHNIQUES Technical Track Sessin VI Céline Ferré The Wrld Bank When can we use matching? What if the assignment t the treatment is nt dne randmly r based n an eligibility index, but n the basis

More information

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9. Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.

More information

Evaluating enterprise support: state of the art and future challenges. Dirk Czarnitzki KU Leuven, Belgium, and ZEW Mannheim, Germany

Evaluating enterprise support: state of the art and future challenges. Dirk Czarnitzki KU Leuven, Belgium, and ZEW Mannheim, Germany Evaluating enterprise supprt: state f the art and future challenges Dirk Czarnitzki KU Leuven, Belgium, and ZEW Mannheim, Germany Intrductin During the last decade, mircecnmetric ecnmetric cunterfactual

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

A Quick Overview of the. Framework for K 12 Science Education

A Quick Overview of the. Framework for K 12 Science Education A Quick Overview f the NGSS EQuIP MODULE 1 Framewrk fr K 12 Science Educatin Mdule 1: A Quick Overview f the Framewrk fr K 12 Science Educatin This mdule prvides a brief backgrund n the Framewrk fr K-12

More information

Eric Klein and Ning Sa

Eric Klein and Ning Sa Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure

More information

Five Whys How To Do It Better

Five Whys How To Do It Better Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex

More information

EASTERN ARIZONA COLLEGE Introduction to Statistics

EASTERN ARIZONA COLLEGE Introduction to Statistics EASTERN ARIZONA COLLEGE Intrductin t Statistics Curse Design 2014-2015 Curse Infrmatin Divisin Scial Sciences Curse Number PSY 220 Title Intrductin t Statistics Credits 3 Develped by Adam Stinchcmbe Lecture/Lab

More information

How do scientists measure trees? What is DBH?

How do scientists measure trees? What is DBH? Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between

More information

Kepler's Laws of Planetary Motion

Kepler's Laws of Planetary Motion Writing Assignment Essay n Kepler s Laws. Yu have been prvided tw shrt articles n Kepler s Three Laws f Planetary Mtin. Yu are t first read the articles t better understand what these laws are, what they

More information

Associated Students Flacks Internship

Associated Students Flacks Internship Assciated Students Flacks Internship 2016-2017 Applicatin Persnal Infrmatin: Name: Address: Phne #: Years at UCSB: Cumulative GPA: E-mail: Majr(s)/Minr(s): Units Cmpleted: Tw persnal references (Different

More information

Functional Form and Nonlinearities

Functional Form and Nonlinearities Sectin 6 Functinal Frm and Nnlinearities This is a gd place t remind urselves f Assumptin #0: That all bservatins fllw the same mdel. Levels f measurement and kinds f variables There are (at least) three

More information

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck

More information

PSU GISPOPSCI June 2011 Ordinary Least Squares & Spatial Linear Regression in GeoDa

PSU GISPOPSCI June 2011 Ordinary Least Squares & Spatial Linear Regression in GeoDa There are tw parts t this lab. The first is intended t demnstrate hw t request and interpret the spatial diagnstics f a standard OLS regressin mdel using GeDa. The diagnstics prvide infrmatin abut the

More information

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) > Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);

More information

4th Indian Institute of Astrophysics - PennState Astrostatistics School July, 2013 Vainu Bappu Observatory, Kavalur. Correlation and Regression

4th Indian Institute of Astrophysics - PennState Astrostatistics School July, 2013 Vainu Bappu Observatory, Kavalur. Correlation and Regression 4th Indian Institute f Astrphysics - PennState Astrstatistics Schl July, 2013 Vainu Bappu Observatry, Kavalur Crrelatin and Regressin Rahul Ry Indian Statistical Institute, Delhi. Crrelatin Cnsider a tw

More information

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.

Lesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method. Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

Unit 1: Introduction to Biology

Unit 1: Introduction to Biology Name: Unit 1: Intrductin t Bilgy Theme: Frm mlecules t rganisms Students will be able t: 1.1 Plan and cnduct an investigatin: Define the questin, develp a hypthesis, design an experiment and cllect infrmatin,

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

Professional Development. Implementing the NGSS: High School Physics

Professional Development. Implementing the NGSS: High School Physics Prfessinal Develpment Implementing the NGSS: High Schl Physics This is a dem. The 30-min vide webinar is available in the full PD. Get it here. Tday s Learning Objectives NGSS key cncepts why this is different

More information

SIZE BIAS IN LINE TRANSECT SAMPLING: A FIELD TEST. Mark C. Otto Statistics Research Division, Bureau of the Census Washington, D.C , U.S.A.

SIZE BIAS IN LINE TRANSECT SAMPLING: A FIELD TEST. Mark C. Otto Statistics Research Division, Bureau of the Census Washington, D.C , U.S.A. SIZE BIAS IN LINE TRANSECT SAMPLING: A FIELD TEST Mark C. Ott Statistics Research Divisin, Bureau f the Census Washingtn, D.C. 20233, U.S.A. and Kenneth H. Pllck Department f Statistics, Nrth Carlina State

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information

Excessive Social Imbalances and the Performance of Welfare States in the EU. Frank Vandenbroucke, Ron Diris and Gerlinde Verbist

Excessive Social Imbalances and the Performance of Welfare States in the EU. Frank Vandenbroucke, Ron Diris and Gerlinde Verbist Excessive Scial Imbalances and the Perfrmance f Welfare States in the EU Frank Vandenbrucke, Rn Diris and Gerlinde Verbist Child pverty in the Eurzne, SILC 2008 35.00 30.00 25.00 20.00 15.00 10.00 5.00.00

More information

Apply Discovery Teaching Model to Instruct Engineering Drawing Course: Sketch a Regular Pentagon

Apply Discovery Teaching Model to Instruct Engineering Drawing Course: Sketch a Regular Pentagon Available nline at www.sciencedirect.cm Prcedia - Scial and Behaviral Sciences 6 ( 01 ) 7 66 INTERNATIONAL EDUCATIONAL TECHNOLOGY CONFERENCE IETC01 Apply Discvery Teaching Mdel t Instruct Engineering Drawing

More information

Modelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA

Modelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA Mdelling f Clck Behaviur Dn Percival Applied Physics Labratry University f Washingtn Seattle, Washingtn, USA verheads and paper fr talk available at http://faculty.washingtn.edu/dbp/talks.html 1 Overview

More information

Checking the resolved resonance region in EXFOR database

Checking the resolved resonance region in EXFOR database Checking the reslved resnance regin in EXFOR database Gttfried Bertn Sciété de Calcul Mathématique (SCM) Oscar Cabells OECD/NEA Data Bank JEFF Meetings - Sessin JEFF Experiments Nvember 0-4, 017 Bulgne-Billancurt,

More information

BASD HIGH SCHOOL FORMAL LAB REPORT

BASD HIGH SCHOOL FORMAL LAB REPORT BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines

AP Literature and Composition. Summer Reading Packet. Instructions and Guidelines AP Literature and Cmpsitin Summer Reading Packet Instructins and Guidelines Accrding t the Cllege Bard Advanced Placement prgram: "The AP English curse in Literature and Cmpsitin shuld engage students

More information

Bios 6648: Design & conduct of clinical research

Bios 6648: Design & conduct of clinical research Bis 6648: Design & cnduct f clinical research Sectin 3 - Essential principle 3.1 Masking (blinding) 3.2 Treatment allcatin (randmizatin) 3.3 Study quality cntrl : Interim decisin and grup sequential :

More information

In the OLG model, agents live for two periods. they work and divide their labour income between consumption and

In the OLG model, agents live for two periods. they work and divide their labour income between consumption and 1 The Overlapping Generatins Mdel (OLG) In the OLG mdel, agents live fr tw perids. When ung the wrk and divide their labur incme between cnsumptin and savings. When ld the cnsume their savings. As the

More information

A Regression Solution to the Problem of Criterion Score Comparability

A Regression Solution to the Problem of Criterion Score Comparability A Regressin Slutin t the Prblem f Criterin Scre Cmparability William M. Pugh Naval Health Research Center When the criterin measure in a study is the accumulatin f respnses r behavirs fr an individual

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Emphases in Common Core Standards for Mathematical Content Kindergarten High School

Emphases in Common Core Standards for Mathematical Content Kindergarten High School Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

Analysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network

Analysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:

More information

Optimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants

Optimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants Internatinal Jurnal f Engineering Science Inventin ISSN (Online): 9 67, ISSN (Print): 9 676 www.ijesi.rg Vlume 5 Issue 8 ugust 06 PP.0-07 Optimizatin Prgramming Prblems Fr Cntrl nd Management Of Bacterial

More information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

This project has received funding from the European Union s Horizon 2020 research and innovation programme under grant agreement number

This project has received funding from the European Union s Horizon 2020 research and innovation programme under grant agreement number This prject has received funding frm the Eurpean Unin s Hrizn 2020 research and innvatin prgramme under grant agreement number 727524. Credit t & http://www.h3uni.rg/ https://ec.eurpa.eu/jrc/en/publicatin/eur-scientific-andtechnical-research-reprts/behaviural-insights-appliedplicy-eurpean-reprt-2016

More information

Relationships Between Frequency, Capacitance, Inductance and Reactance.

Relationships Between Frequency, Capacitance, Inductance and Reactance. P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead

More information

ChE 471: LECTURE 4 Fall 2003

ChE 471: LECTURE 4 Fall 2003 ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.

More information

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky

BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns

More information

1b) =.215 1c).080/.215 =.372

1b) =.215 1c).080/.215 =.372 Practice Exam 1 - Answers 1. / \.1/ \.9 (D+) (D-) / \ / \.8 / \.2.15/ \.85 (T+) (T-) (T+) (T-).080.020.135.765 1b).080 +.135 =.215 1c).080/.215 =.372 2. The data shwn in the scatter plt is the distance

More information

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised

More information

8 th Grade Math: Pre-Algebra

8 th Grade Math: Pre-Algebra Hardin Cunty Middle Schl (2013-2014) 1 8 th Grade Math: Pre-Algebra Curse Descriptin The purpse f this curse is t enhance student understanding, participatin, and real-life applicatin f middle-schl mathematics

More information

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Causal inference using regression on the treatment variable

Causal inference using regression on the treatment variable CHAPTER 9 Causal inference using regressin n the treatment variable 9.1 Causal inference and predictive cmparisns S far, we have been interpreting regressins predictively: given the values f several inputs,

More information

Statistics Statistical method Variables Value Score Type of Research Level of Measurement...

Statistics Statistical method Variables Value Score Type of Research Level of Measurement... Lecture 1 Displaying data... 12 Statistics... 13 Statistical methd... 13 Variables... 13 Value... 15 Scre... 15 Type f Research... 15 Level f Measurement... 15 Numeric/Quantitative variables... 15 Ordinal/Rank-rder

More information

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions Guide t Using the Rubric t Scre the Klf4 PREBUILD Mdel fr Science Olympiad 2010-2011 Natinal Cmpetitins These instructins are t help the event supervisr and scring judges use the rubric develped by the

More information

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm

Determining Optimum Path in Synthesis of Organic Compounds using Branch and Bound Algorithm Determining Optimum Path in Synthesis f Organic Cmpunds using Branch and Bund Algrithm Diastuti Utami 13514071 Prgram Studi Teknik Infrmatika Seklah Teknik Elektr dan Infrmatika Institut Teknlgi Bandung,

More information

University of Wollongong Economics Working Paper Series 2003

University of Wollongong Economics Working Paper Series 2003 University f Wllngng Ecnmics Wrking Paper Series 003 http://www.uw.edu.au/cmmerce/ecn/wplist.html Measuring Overweight: A te Amnn Levy WP 03-11 August 003 Measuring Overweight: A te Amnn Levy University

More information

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning

Admin. MDP Search Trees. Optimal Quantities. Reinforcement Learning Admin Reinfrcement Learning Cntent adapted frm Berkeley CS188 MDP Search Trees Each MDP state prjects an expectimax-like search tree Optimal Quantities The value (utility) f a state s: V*(s) = expected

More information

CESAR Science Case The differential rotation of the Sun and its Chromosphere. Introduction. Material that is necessary during the laboratory

CESAR Science Case The differential rotation of the Sun and its Chromosphere. Introduction. Material that is necessary during the laboratory Teacher s guide CESAR Science Case The differential rtatin f the Sun and its Chrmsphere Material that is necessary during the labratry CESAR Astrnmical wrd list CESAR Bklet CESAR Frmula sheet CESAR Student

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

IAML: Support Vector Machines

IAML: Support Vector Machines 1 / 22 IAML: Supprt Vectr Machines Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester 1 2 / 22 Outline Separating hyperplane with maimum margin Nn-separable training data Epanding the input int

More information

Large Sample Hypothesis Tests for a Population Proportion

Large Sample Hypothesis Tests for a Population Proportion Ntes-10.3a Large Sample Hypthesis Tests fr a Ppulatin Prprtin ***Cin Tss*** 1. A friend f yurs claims that when he tsses a cin he can cntrl the utcme. Yu are skeptical and want him t prve it. He tsses

More information

Chapter 5: The Keynesian System (I): The Role of Aggregate Demand

Chapter 5: The Keynesian System (I): The Role of Aggregate Demand LECTURE NOTES Chapter 5: The Keynesian System (I): The Rle f Aggregate Demand 1. The Prblem f Unemplyment Keynesian ecnmics develped in the cntext f the Great Depressin Sharp fall in GDP High rate f unemplyment

More information

We say that y is a linear function of x if. Chapter 13: The Correlation Coefficient and the Regression Line

We say that y is a linear function of x if. Chapter 13: The Correlation Coefficient and the Regression Line Chapter 13: The Crrelatin Cefficient and the Regressin Line We begin with a sme useful facts abut straight lines. Recall the x, y crdinate system, as pictured belw. 3 2 1 y = 2.5 y = 0.5x 3 2 1 1 2 3 1

More information

UNIV1"'RSITY OF NORTH CAROLINA Department of Statistics Chapel Hill, N. C. CUMULATIVE SUM CONTROL CHARTS FOR THE FOLDED NORMAL DISTRIBUTION

UNIV1'RSITY OF NORTH CAROLINA Department of Statistics Chapel Hill, N. C. CUMULATIVE SUM CONTROL CHARTS FOR THE FOLDED NORMAL DISTRIBUTION UNIV1"'RSITY OF NORTH CAROLINA Department f Statistics Chapel Hill, N. C. CUMULATIVE SUM CONTROL CHARTS FOR THE FOLDED NORMAL DISTRIBUTION by N. L. Jlmsn December 1962 Grant N. AFOSR -62..148 Methds f

More information

The Law of Total Probability, Bayes Rule, and Random Variables (Oh My!)

The Law of Total Probability, Bayes Rule, and Random Variables (Oh My!) The Law f Ttal Prbability, Bayes Rule, and Randm Variables (Oh My!) Administrivia Hmewrk 2 is psted and is due tw Friday s frm nw If yu didn t start early last time, please d s this time. Gd Milestnes:

More information

Curriculum Development Overview Unit Planning for 8 th Grade Mathematics MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2

Curriculum Development Overview Unit Planning for 8 th Grade Mathematics MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2 Unit Title It s All Greek t Me Length f Unit 5 weeks Fcusing Lens(es) Cnnectins Standards and Grade Level Expectatins Addressed in this Unit MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2 Inquiry Questins (Engaging-

More information

B. Definition of an exponential

B. Definition of an exponential Expnents and Lgarithms Chapter IV - Expnents and Lgarithms A. Intrductin Starting with additin and defining the ntatins fr subtractin, multiplicatin and divisin, we discvered negative numbers and fractins.

More information

Determining the Accuracy of Modal Parameter Estimation Methods

Determining the Accuracy of Modal Parameter Estimation Methods Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system

More information

Ecology 302 Lecture III. Exponential Growth (Gotelli, Chapter 1; Ricklefs, Chapter 11, pp )

Ecology 302 Lecture III. Exponential Growth (Gotelli, Chapter 1; Ricklefs, Chapter 11, pp ) Eclgy 302 Lecture III. Expnential Grwth (Gtelli, Chapter 1; Ricklefs, Chapter 11, pp. 222-227) Apcalypse nw. The Santa Ana Watershed Prject Authrity pulls n punches in prtraying its missin in apcalyptic

More information

A Matrix Representation of Panel Data

A Matrix Representation of Panel Data web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins

More information

UlNIVLKSIIt OJT tuunols UBRARY STACKS

UlNIVLKSIIt OJT tuunols UBRARY STACKS UlNIVLKSIIt OJT tuunols UBRARY STACKS Digitized by the Internet Archive in 2011 with funding frm University f Illinis Urbana-Champaign http://www.archive.rg/details/humaninfrmatin614brw "^ "^ r'y 6%^-

More information

7 TH GRADE MATH STANDARDS

7 TH GRADE MATH STANDARDS ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,

More information

ENSC Discrete Time Systems. Project Outline. Semester

ENSC Discrete Time Systems. Project Outline. Semester ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding

More information

CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS

CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS CHAPTER 4 DIAGNOSTICS FOR INFLUENTIAL OBSERVATIONS 1 Influential bservatins are bservatins whse presence in the data can have a distrting effect n the parameter estimates and pssibly the entire analysis,

More information

Biplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint

Biplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint Biplts in Practice MICHAEL GREENACRE Prfessr f Statistics at the Pmpeu Fabra University Chapter 13 Offprint CASE STUDY BIOMEDICINE Cmparing Cancer Types Accrding t Gene Epressin Arrays First published:

More information

Please Stop Laughing at Me and Pay it Forward Final Writing Assignment

Please Stop Laughing at Me and Pay it Forward Final Writing Assignment Kirk Please Stp Laughing at Me and Pay it Frward Final Writing Assignment Our fcus fr the past few mnths has been n bullying and hw we treat ther peple. We ve played sme games, read sme articles, read

More information

West Deptford Middle School 8th Grade Curriculum Unit 4 Investigate Bivariate Data

West Deptford Middle School 8th Grade Curriculum Unit 4 Investigate Bivariate Data West Deptfrd Middle Schl 8th Grade Curriculum Unit 4 Investigate Bivariate Data Office f Curriculum and Instructin West Deptfrd Middle Schl 675 Grve Rd, Paulsbr, NJ 08066 wdeptfrd.k12.nj.us (856) 848-1200

More information

Lab #3: Pendulum Period and Proportionalities

Lab #3: Pendulum Period and Proportionalities Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the

More information

AP Statistics Notes Unit Two: The Normal Distributions

AP Statistics Notes Unit Two: The Normal Distributions AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).

More information

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions.

o o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions. BASD High Schl Frmal Lab Reprt GENERAL INFORMATION 12 pt Times New Rman fnt Duble-spaced, if required by yur teacher 1 inch margins n all sides (tp, bttm, left, and right) Always write in third persn (avid

More information

Chapter 8: The Binomial and Geometric Distributions

Chapter 8: The Binomial and Geometric Distributions Sectin 8.1: The Binmial Distributins Chapter 8: The Binmial and Gemetric Distributins A randm variable X is called a BINOMIAL RANDOM VARIABLE if it meets ALL the fllwing cnditins: 1) 2) 3) 4) The MOST

More information

THE LIFE OF AN OBJECT IT SYSTEMS

THE LIFE OF AN OBJECT IT SYSTEMS THE LIFE OF AN OBJECT IT SYSTEMS Persns, bjects, r cncepts frm the real wrld, which we mdel as bjects in the IT system, have "lives". Actually, they have tw lives; the riginal in the real wrld has a life,

More information

BASIC DIRECT-CURRENT MEASUREMENTS

BASIC DIRECT-CURRENT MEASUREMENTS Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard

More information

Lifting a Lion: Using Proportions

Lifting a Lion: Using Proportions Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They

More information

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical). Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -

More information

A Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus

A Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus A Crrelatin f Suth Carlina Academic Standards fr Mathematics Precalculus INTRODUCTION This dcument demnstrates hw Precalculus (Blitzer), 4 th Editin 010, meets the indicatrs f the. Crrelatin page references

More information

The standards are taught in the following sequence.

The standards are taught in the following sequence. B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

Comparing Several Means: ANOVA. Group Means and Grand Mean

Comparing Several Means: ANOVA. Group Means and Grand Mean STAT 511 ANOVA and Regressin 1 Cmparing Several Means: ANOVA Slide 1 Blue Lake snap beans were grwn in 12 pen-tp chambers which are subject t 4 treatments 3 each with O 3 and SO 2 present/absent. The ttal

More information

Subject description processes

Subject description processes Subject representatin 6.1.2. Subject descriptin prcesses Overview Fur majr prcesses r areas f practice fr representing subjects are classificatin, subject catalging, indexing, and abstracting. The prcesses

More information

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y ) (Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

Chapter 3: Cluster Analysis

Chapter 3: Cluster Analysis Chapter 3: Cluster Analysis } 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries } 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA

More information

End of Course Algebra I ~ Practice Test #2

End of Course Algebra I ~ Practice Test #2 End f Curse Algebra I ~ Practice Test #2 Name: Perid: Date: 1: Order the fllwing frm greatest t least., 3, 8.9, 8,, 9.3 A. 8, 8.9,, 9.3, 3 B., 3, 8, 8.9,, 9.3 C. 9.3, 3,,, 8.9, 8 D. 3, 9.3,,, 8.9, 8 2:

More information

Math 10 - Exam 1 Topics

Math 10 - Exam 1 Topics Math 10 - Exam 1 Tpics Types and Levels f data Categrical, Discrete r Cntinuus Nminal, Ordinal, Interval r Rati Descriptive Statistics Stem and Leaf Graph Dt Plt (Interpret) Gruped Data Relative and Cumulative

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date

AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares

More information