: At least two means differ SST

Size: px
Start display at page:

Download ": At least two means differ SST"

Transcription

1 Formula Card for Eam 3 STA33 ANOVA F-Test: Completely Radomzed Desg ( total umber of observatos, k = Number of treatmets,& T = total for treatmet ) Step : Epress the Clam Step : The ypotheses: :... 0 A : At least two meas dffer k Step 3: Work wth the data Correcto Factor: CF y Sum of all observatos Sum of Squares Total: ( Total) y CF = (Square each observato the add them up) CF T T Tk Sum of Squares for Treatmets: T CF k = (Square each treatmet total ad dvded by the umber of observatos each treatmet the add those results up) CF Sum of Square for Error: E ( Total ) T Mea Square Treatmet: T k Mea Square Error: MSE E k Step 4: the Test Statstc: F MSE Step 5: the Crtcal Value: I order to properly form our cocluso, we eed ether a p-value or a crtcal value. To get the crtcal value, we wll cosder how our F-test stat s formed. It s the rato of ad MSE. The s o top, so ts degrees of freedom wll be the umerator degrees of freedom. The degree of freedom for MSE wll serve as the deomator degree of freedom (we eed these quattes for the F-table). The, we eed a alpha value. Step 6: Ital Cocluso: If F > fk, k,, we reject the ull. *Note the F-test for ANOVA s MSE always rght-taled sce s always the top of the fracto whch forms our F-statstc. Step 7: Word the Fal Cocluso Put all of these calculatos to the ANOVA table:

2 Source Df MS F Treatmets K T = T/k- /MSE Error N k E MSE = E/-k Total N (total) Multple Comparsos of the Meas k k! k k Number of comparsos = k!! where k = umber of treatmets Cofdece terval for a treatmet mea: X t S where S MSE, = umber of repettos for the treatmet, ad t has T / / T degrees of freedom = k The Radomzed Block Desg Step : Epress the Clam: For eample, all of the treatmet meas are the same. Step : The ypotheses: :... 0 A : At least two meas dffer k Step 3: Work wth the data Correcto Factor: CF y Sum of all observatos Sum of Squares Total: ( Total) y CF = (Square each observato the add them up) CF T T Tk Sum of Squares for Treatmets: T CF = (Sum of squared Treatmet totals b b b dvded by the umber of observatos each treatmet) CF B B Bk Sum of Squares for Blocks: B CF = (Sum of squared block totals dvded k k k by the umber of observatos each block) CF Sum of Square for Error: E ( Total ) T B T Mea Square Treatmet: k B Mea Square for Blocks: MSB b

3 E Mea Square Error: MSE k b MSB Step 4: the Test Statstcs: F & F MSE MSE Step 5: the Crtcal Value: I order to properly form our cocluso, we eed ether a p-value or a crtcal value. To get the crtcal value, we wll cosder our how our F-test stat s formed. If t s the rato of ad MSE, the we use the degrees of freedom for treatmets as the umerator degrees of freedom ad the degree of freedom for Error wll serve as the deomator degree of freedom (we would use the df for blocks as our umerator degrees of freedom f our rato was MSB/MSE). MSB Step 6: Ital Cocluso: If F > fk, bk,, we reject the ull. If F > MSE MSE fb, bk,, we coclude the blocks are sgfcatly dfferet. Step 7: Word the Fal Cocluso Place the aswers to our calculatos a ANOVA table: Source Df MS F Treatmet K T /MSE Block B B MSB MSB/MSE Error N k b + E MSE Total N (total) Fttg the Model: The Least Squares Approach ŷ ˆ ˆ 0 Step : fll out the followg table Prelmary computatos table y y Totals y y y y Step : Calculate y Step 3: Calculate the Slope: ˆ y Step 4: Calculate the y-tercept: ˆ ˆ 0 y ad

4 Fdg a estmate for Steps to fdg S a estmate of :. Create ad fll the prelmary calculato table below: y y y Totals. Calculate y y y y y y 3. Calculate y 4. y 5. Fd ˆ y 6. Calculate E ˆ y E 7. Fally, S Testg the Model s Utlty by Testg the Slope Oe Taled Test o : 0 or ( a : 0) a : 0 or ( a : 0) ˆ ˆ Test Statstc: t = s s / ˆ Rejecto rego: t < -t a Or ( t ta whe a : 0) Where t a s based o (-) degrees of freedom Two Taled Test : 0 o : 0 a Test Statstc: t = ˆ ˆ s s / ˆ Rejecto rego: t t a / Where t a / s based o (-) degrees of freedom

5 Step : Form the clam symbolcally Step : Get your ypotheses Step 3: Fd,, y, ˆ y, E ˆ y, s Step 4: Fd the Test Stat t = ˆ ˆ ˆ s s / E, ad s ˆ Step 5: Fd your crtcal t-value by lookg up o the t-table wth d.f. s Step 6: Form your tal cocluso Step 7: State your fal cocluso A 00(-a)% Cofdece Iterval for the Sample Lear Regresso Slope ˆ t a / s ˆ Where the estmated stadard error of ˆ s s calculated by s ˆ ad t a / s based o (-) degrees of freedom. The Coeffcet of Correlato The coeffcet of correlato, r y s a measure of the stregth of the lear relatoshp betwee two varables ad y. The coeffcet of determato s E E Eplaed sample varablty r Total sample varablty Steps to fdg r ad r :. Create ad fll the prelmary calculato table below: y y y Totals. Calculate 3. Calculate y y y y y y

6 y 4. y 5. Fd ˆ y 6. Calculate E ˆ y y 7. Calculate r ad calculate r E Usg the model for estmato ad predcto. Our estmato tervals to estmate the average value of y for a specfc value of ˆ p y t /S where t /s based o - degrees of freedom.. Our predcto terval to estmate a specfc y value for a gve value yˆ t /S p where t /s based o - degrees of freedom. Steps to formg a predcto terval (the steps are early the same for the estmato terval): Step : Use the least squares le to fd ŷ by pluggg to the equato Step : Fd t /usg degrees of freedom s Step 3: Fd S p Step 4: Fd the Marg of Error = ME = / S Step 5: Fsh by gettg: [ yˆme, yˆ ME] p t = t / (the result from step 3)

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The

More information

b. There appears to be a positive relationship between X and Y; that is, as X increases, so does Y.

b. There appears to be a positive relationship between X and Y; that is, as X increases, so does Y. .46. a. The frst varable (X) s the frst umber the par ad s plotted o the horzotal axs, whle the secod varable (Y) s the secod umber the par ad s plotted o the vertcal axs. The scatterplot s show the fgure

More information

Statistics MINITAB - Lab 5

Statistics MINITAB - Lab 5 Statstcs 10010 MINITAB - Lab 5 PART I: The Correlato Coeffcet Qute ofte statstcs we are preseted wth data that suggests that a lear relatoshp exsts betwee two varables. For example the plot below s of

More information

Chapter 13 Student Lecture Notes 13-1

Chapter 13 Student Lecture Notes 13-1 Chapter 3 Studet Lecture Notes 3- Basc Busess Statstcs (9 th Edto) Chapter 3 Smple Lear Regresso 4 Pretce-Hall, Ic. Chap 3- Chapter Topcs Types of Regresso Models Determg the Smple Lear Regresso Equato

More information

ENGI 3423 Simple Linear Regression Page 12-01

ENGI 3423 Simple Linear Regression Page 12-01 ENGI 343 mple Lear Regresso Page - mple Lear Regresso ometmes a expermet s set up where the expermeter has cotrol over the values of oe or more varables X ad measures the resultg values of aother varable

More information

Multiple Linear Regression Analysis

Multiple Linear Regression Analysis LINEA EGESSION ANALYSIS MODULE III Lecture - 4 Multple Lear egresso Aalyss Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Cofdece terval estmato The cofdece tervals multple

More information

Lecture Notes Types of economic variables

Lecture Notes Types of economic variables Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte

More information

Chapter 13, Part A Analysis of Variance and Experimental Design. Introduction to Analysis of Variance. Introduction to Analysis of Variance

Chapter 13, Part A Analysis of Variance and Experimental Design. Introduction to Analysis of Variance. Introduction to Analysis of Variance Chapter, Part A Aalyss of Varace ad Epermetal Desg Itroducto to Aalyss of Varace Aalyss of Varace: Testg for the Equalty of Populato Meas Multple Comparso Procedures Itroducto to Aalyss of Varace Aalyss

More information

Summary of the lecture in Biostatistics

Summary of the lecture in Biostatistics Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the

More information

Simple Linear Regression

Simple Linear Regression Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato

More information

STA302/1001-Fall 2008 Midterm Test October 21, 2008

STA302/1001-Fall 2008 Midterm Test October 21, 2008 STA3/-Fall 8 Mdterm Test October, 8 Last Name: Frst Name: Studet Number: Erolled (Crcle oe) STA3 STA INSTRUCTIONS Tme allowed: hour 45 mutes Ads allowed: A o-programmable calculator A table of values from

More information

Simple Linear Regression and Correlation. Applied Statistics and Probability for Engineers. Chapter 11 Simple Linear Regression and Correlation

Simple Linear Regression and Correlation. Applied Statistics and Probability for Engineers. Chapter 11 Simple Linear Regression and Correlation 4//6 Appled Statstcs ad Probablty for Egeers Sth Edto Douglas C. Motgomery George C. Ruger Chapter Smple Lear Regresso ad Correlato CHAPTER OUTLINE Smple Lear Regresso ad Correlato - Emprcal Models -8

More information

residual. (Note that usually in descriptions of regression analysis, upper-case

residual. (Note that usually in descriptions of regression analysis, upper-case Regresso Aalyss Regresso aalyss fts or derves a model that descres the varato of a respose (or depedet ) varale as a fucto of oe or more predctor (or depedet ) varales. The geeral regresso model s oe of

More information

Multiple Choice Test. Chapter Adequacy of Models for Regression

Multiple Choice Test. Chapter Adequacy of Models for Regression Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to

More information

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn: Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear:

More information

Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades

Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos

More information

Chapter Two. An Introduction to Regression ( )

Chapter Two. An Introduction to Regression ( ) ubject: A Itroducto to Regresso Frst tage Chapter Two A Itroducto to Regresso (018-019) 1 pg. ubject: A Itroducto to Regresso Frst tage A Itroducto to Regresso Regresso aalss s a statstcal tool for the

More information

Example: Multiple linear regression. Least squares regression. Repetition: Simple linear regression. Tron Anders Moger

Example: Multiple linear regression. Least squares regression. Repetition: Simple linear regression. Tron Anders Moger Example: Multple lear regresso 5000,00 4000,00 Tro Aders Moger 0.0.007 brthweght 3000,00 000,00 000,00 0,00 50,00 00,00 50,00 00,00 50,00 weght pouds Repetto: Smple lear regresso We defe a model Y = β0

More information

Linear Regression with One Regressor

Linear Regression with One Regressor Lear Regresso wth Oe Regressor AIM QA.7. Expla how regresso aalyss ecoometrcs measures the relatoshp betwee depedet ad depedet varables. A regresso aalyss has the goal of measurg how chages oe varable,

More information

Objectives of Multiple Regression

Objectives of Multiple Regression Obectves of Multple Regresso Establsh the lear equato that best predcts values of a depedet varable Y usg more tha oe eplaator varable from a large set of potetal predctors {,,... k }. Fd that subset of

More information

Simple Linear Regression - Scalar Form

Simple Linear Regression - Scalar Form Smple Lear Regresso - Scalar Form Q.. Model Y X,..., p..a. Derve the ormal equatos that mmze Q. p..b. Solve for the ordary least squares estmators, p..c. Derve E, V, E, V, COV, p..d. Derve the mea ad varace

More information

Simple Linear Regression and Correlation.

Simple Linear Regression and Correlation. Smple Lear Regresso ad Correlato. Correspods to Chapter 0 Tamhae ad Dulop Sldes prepared b Elzabeth Newto (MIT) wth some sldes b Jacquele Telford (Johs Hopks Uverst) Smple lear regresso aalss estmates

More information

Chapter 11 The Analysis of Variance

Chapter 11 The Analysis of Variance Chapter The Aalyss of Varace. Oe Factor Aalyss of Varace. Radomzed Bloc Desgs (ot for ths course) NIPRL . Oe Factor Aalyss of Varace.. Oe Factor Layouts (/4) Suppose that a expermeter s terested populatos

More information

Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes

Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes coometrcs, CON Sa Fracsco State Uversty Mchael Bar Sprg 5 Mdterm am, secto Soluto Thursday, February 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes eam.. No calculators of ay kd are allowed..

More information

Reaction Time VS. Drug Percentage Subject Amount of Drug Times % Reaction Time in Seconds 1 Mary John Carl Sara William 5 4

Reaction Time VS. Drug Percentage Subject Amount of Drug Times % Reaction Time in Seconds 1 Mary John Carl Sara William 5 4 CHAPTER Smple Lear Regreo EXAMPLE A expermet volvg fve ubject coducted to determe the relatohp betwee the percetage of a certa drug the bloodtream ad the legth of tme t take the ubject to react to a tmulu.

More information

ESS Line Fitting

ESS Line Fitting ESS 5 014 17. Le Fttg A very commo problem data aalyss s lookg for relatoshpetwee dfferet parameters ad fttg les or surfaces to data. The smplest example s fttg a straght le ad we wll dscuss that here

More information

12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model

12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model 1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed

More information

Statistics: Unlocking the Power of Data Lock 5

Statistics: Unlocking the Power of Data Lock 5 STAT 0 Dr. Kar Lock Morga Exam 2 Grades: I- Class Multple Regresso SECTIONS 9.2, 0., 0.2 Multple explaatory varables (0.) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (0.2) Exam 2 Re- grades Re-

More information

Chapter 8. Inferences about More Than Two Population Central Values

Chapter 8. Inferences about More Than Two Population Central Values Chapter 8. Ifereces about More Tha Two Populato Cetral Values Case tudy: Effect of Tmg of the Treatmet of Port-We tas wth Lasers ) To vestgate whether treatmet at a youg age would yeld better results tha

More information

Mean is only appropriate for interval or ratio scales, not ordinal or nominal.

Mean is only appropriate for interval or ratio scales, not ordinal or nominal. Mea Same as ordary average Sum all the data values ad dvde by the sample sze. x = ( x + x +... + x Usg summato otato, we wrte ths as x = x = x = = ) x Mea s oly approprate for terval or rato scales, ot

More information

REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION

REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION I lear regreo, we coder the frequecy dtrbuto of oe varable (Y) at each of everal level of a ecod varable (X). Y kow a the depedet varable. The

More information

Econometric Methods. Review of Estimation

Econometric Methods. Review of Estimation Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators

More information

Lecture 8: Linear Regression

Lecture 8: Linear Regression Lecture 8: Lear egresso May 4, GENOME 56, Sprg Goals Develop basc cocepts of lear regresso from a probablstc framework Estmatg parameters ad hypothess testg wth lear models Lear regresso Su I Lee, CSE

More information

STA 105-M BASIC STATISTICS (This is a multiple choice paper.)

STA 105-M BASIC STATISTICS (This is a multiple choice paper.) DCDM BUSINESS SCHOOL September Mock Eamatos STA 0-M BASIC STATISTICS (Ths s a multple choce paper.) Tme: hours 0 mutes INSTRUCTIONS TO CANDIDATES Do ot ope ths questo paper utl you have bee told to do

More information

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON430 Statstcs Date of exam: Frday, December 8, 07 Grades are gve: Jauary 4, 08 Tme for exam: 0900 am 00 oo The problem set covers 5 pages Resources allowed:

More information

Midterm Exam 1, section 2 (Solution) Thursday, February hour, 15 minutes

Midterm Exam 1, section 2 (Solution) Thursday, February hour, 15 minutes coometrcs, CON Sa Fracsco State Uverst Mchael Bar Sprg 5 Mdterm xam, secto Soluto Thursda, Februar 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes exam.. No calculators of a kd are allowed..

More information

Regresso What s a Model? 1. Ofte Descrbe Relatoshp betwee Varables 2. Types - Determstc Models (o radomess) - Probablstc Models (wth radomess) EPI 809/Sprg 2008 9 Determstc Models 1. Hypothesze

More information

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postpoed exam: ECON430 Statstcs Date of exam: Jauary 0, 0 Tme for exam: 09:00 a.m. :00 oo The problem set covers 5 pages Resources allowed: All wrtte ad prted

More information

Previous lecture. Lecture 8. Learning outcomes of this lecture. Today. Statistical test and Scales of measurement. Correlation

Previous lecture. Lecture 8. Learning outcomes of this lecture. Today. Statistical test and Scales of measurement. Correlation Lecture 8 Emprcal Research Methods I434 Quattatve Data aalss II Relatos Prevous lecture Idea behd hpothess testg Is the dfferece betwee two samples a reflecto of the dfferece of two dfferet populatos or

More information

The Randomized Block Design

The Randomized Block Design Statstcal Methods I (EXST 75) Page 131 A factoral s a way of eterg two or more treatmets to a aalyss. The descrpto of a factoral usually cludes a measure of sze, a by, 3 by 4, 6 by 3 by 4, by by, etc.

More information

Suggested Answers, Problem Set 4 ECON The R 2 for the unrestricted model is by definition u u u u

Suggested Answers, Problem Set 4 ECON The R 2 for the unrestricted model is by definition u u u u Da Hgerma Fall 9 Sggested Aswers, Problem Set 4 ECON 333 The F-test s defed as ( SSEr The R for the restrcted model s by defto SSE / ( k ) R ( SSE / SST ) so therefore, SSE SST ( R ) ad lkewse SSEr SST

More information

Fundamentals of Regression Analysis

Fundamentals of Regression Analysis Fdametals of Regresso Aalyss Regresso aalyss s cocered wth the stdy of the depedece of oe varable, the depedet varable, o oe or more other varables, the explaatory varables, wth a vew of estmatg ad/or

More information

Probability and. Lecture 13: and Correlation

Probability and. Lecture 13: and Correlation 933 Probablty ad Statstcs for Software ad Kowledge Egeers Lecture 3: Smple Lear Regresso ad Correlato Mocha Soptkamo, Ph.D. Outle The Smple Lear Regresso Model (.) Fttg the Regresso Le (.) The Aalyss of

More information

Applied Statistics and Probability for Engineers, 5 th edition February 23, b) y ˆ = (85) =

Applied Statistics and Probability for Engineers, 5 th edition February 23, b) y ˆ = (85) = Appled Statstcs ad Probablty for Egeers, 5 th edto February 3, y.8.7.6.5.4.3.. -5 5 5 x b) y ˆ.3999 +.46(85).6836 c) y ˆ.3999 +.46(9).744 d) ˆ.46-3 a) Regresso Aalyss: Ratg Pots versus Meters per Att The

More information

Regression. Linear Regression. A Simple Data Display. A Batch of Data. The Mean is 220. A Value of 474. STAT Handout Module 15 1 st of June 2009

Regression. Linear Regression. A Simple Data Display. A Batch of Data. The Mean is 220. A Value of 474. STAT Handout Module 15 1 st of June 2009 STAT Hadout Module 5 st of Jue 9 Lear Regresso Regresso Joh D. Sork, M.D. Ph.D. Baltmore VA Medcal Ceter GRCC ad Uversty of Marylad School of Medce Claude D. Pepper Older Amercas Idepedece Ceter Reducg

More information

Mu Sequences/Series Solutions National Convention 2014

Mu Sequences/Series Solutions National Convention 2014 Mu Sequeces/Seres Solutos Natoal Coveto 04 C 6 E A 6C A 6 B B 7 A D 7 D C 7 A B 8 A B 8 A C 8 E 4 B 9 B 4 E 9 B 4 C 9 E C 0 A A 0 D B 0 C C Usg basc propertes of arthmetc sequeces, we fd a ad bm m We eed

More information

Lecture 3. Sampling, sampling distributions, and parameter estimation

Lecture 3. Sampling, sampling distributions, and parameter estimation Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called

More information

Statistics. Correlational. Dr. Ayman Eldeib. Simple Linear Regression and Correlation. SBE 304: Linear Regression & Correlation 1/3/2018

Statistics. Correlational. Dr. Ayman Eldeib. Simple Linear Regression and Correlation. SBE 304: Linear Regression & Correlation 1/3/2018 /3/08 Sstems & Bomedcal Egeerg Departmet SBE 304: Bo-Statstcs Smple Lear Regresso ad Correlato Dr. Ama Eldeb Fall 07 Descrptve Orgasg, summarsg & descrbg data Statstcs Correlatoal Relatoshps Iferetal Geeralsg

More information

Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions.

Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions. Ordary Least Squares egresso. Smple egresso. Algebra ad Assumptos. I ths part of the course we are gog to study a techque for aalysg the lear relatoshp betwee two varables Y ad X. We have pars of observatos

More information

Simulation Output Analysis

Simulation Output Analysis Smulato Output Aalyss Summary Examples Parameter Estmato Sample Mea ad Varace Pot ad Iterval Estmato ermatg ad o-ermatg Smulato Mea Square Errors Example: Sgle Server Queueg System x(t) S 4 S 4 S 3 S 5

More information

STK3100 and STK4100 Autumn 2017

STK3100 and STK4100 Autumn 2017 SK3 ad SK4 Autum 7 Geeralzed lear models Part III Covers the followg materal from chaters 4 ad 5: Sectos 4..5, 4.3.5, 4.3.6, 4.4., 4.4., ad 4.4.3 Sectos 5.., 5.., ad 5.5. Ørulf Borga Deartmet of Mathematcs

More information

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1 STA 08 Appled Lear Models: Regresso Aalyss Sprg 0 Soluto for Homework #. Let Y the dollar cost per year, X the umber of vsts per year. The the mathematcal relato betwee X ad Y s: Y 300 + X. Ths s a fuctoal

More information

Lecture 2: Linear Least Squares Regression

Lecture 2: Linear Least Squares Regression Lecture : Lear Least Squares Regresso Dave Armstrog UW Mlwaukee February 8, 016 Is the Relatoshp Lear? lbrary(car) data(davs) d 150) Davs$weght[d]

More information

Simple Linear Regression

Simple Linear Regression Correlato ad Smple Lear Regresso Berl Che Departmet of Computer Scece & Iformato Egeerg Natoal Tawa Normal Uversty Referece:. W. Navd. Statstcs for Egeerg ad Scetsts. Chapter 7 (7.-7.3) & Teachg Materal

More information

THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 2

THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 2 THE ROYAL STATISTICAL SOCIETY 06 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE The Socety s provdg these solutos to assst caddates preparg for the examatos 07. The solutos are teded as learg ads ad should

More information

Comparison of Dual to Ratio-Cum-Product Estimators of Population Mean

Comparison of Dual to Ratio-Cum-Product Estimators of Population Mean Research Joural of Mathematcal ad Statstcal Sceces ISS 30 6047 Vol. 1(), 5-1, ovember (013) Res. J. Mathematcal ad Statstcal Sc. Comparso of Dual to Rato-Cum-Product Estmators of Populato Mea Abstract

More information

Using Statistics To Make Inferences 9

Using Statistics To Make Inferences 9 Usg tatstcs To Make Ifereces 9 xtee radomly selected mce of the same age ad stra were radomly assged to oe of four treatmet groups. The varous treatmets were varous dets: Cheeros (0 cal), Cor Flakes (0

More information

Simple Linear Regression Analysis

Simple Linear Regression Analysis LINEAR REGREION ANALYSIS MODULE II Lecture - 5 Smple Lear Regreo Aaly Dr Shalabh Departmet of Mathematc Stattc Ida Ittute of Techology Kapur Jot cofdece rego for A jot cofdece rego for ca alo be foud Such

More information

Special Instructions / Useful Data

Special Instructions / Useful Data JAM 6 Set of all real umbers P A..d. B, p Posso Specal Istructos / Useful Data x,, :,,, x x Probablty of a evet A Idepedetly ad detcally dstrbuted Bomal dstrbuto wth parameters ad p Posso dstrbuto wth

More information

Correlation and Simple Linear Regression

Correlation and Simple Linear Regression Correlato ad Smple Lear Regresso Berl Che Departmet of Computer Scece & Iformato Egeerg Natoal Tawa Normal Uverst Referece:. W. Navd. Statstcs for Egeerg ad Scetsts. Chapter 7 (7.-7.3) & Teachg Materal

More information

STK3100 and STK4100 Autumn 2018

STK3100 and STK4100 Autumn 2018 SK3 ad SK4 Autum 8 Geeralzed lear models Part III Covers the followg materal from chaters 4 ad 5: Cofdece tervals by vertg tests Cosder a model wth a sgle arameter β We may obta a ( α% cofdece terval for

More information

The equation is sometimes presented in form Y = a + b x. This is reasonable, but it s not the notation we use.

The equation is sometimes presented in form Y = a + b x. This is reasonable, but it s not the notation we use. INTRODUCTORY NOTE ON LINEAR REGREION We have data of the form (x y ) (x y ) (x y ) These wll most ofte be preseted to us as two colum of a spreadsheet As the topc develops we wll see both upper case ad

More information

Sum Mean n

Sum Mean n tatstcal Methods I (EXT 75) Page 147 ummary data Itermedate Calculatos X = 83 Y = 8 X = 51 Y = 368 Mea of X = X = 5.1875 Mea of Y = Y = 14.5 XY = 1348 = 16 Correcto factors ad Corrected values (ums of

More information

MS exam problems Fall 2012

MS exam problems Fall 2012 MS exam problems Fall 01 (From: Rya Mart) 1. (Stat 401) Cosder the followg game wth a box that cotas te balls two red, three blue, ad fve gree. A player selects two balls from the box at radom, wthout

More information

i 2 σ ) i = 1,2,...,n , and = 3.01 = 4.01

i 2 σ ) i = 1,2,...,n , and = 3.01 = 4.01 ECO 745, Homework 6 Le Cabrera. Assume that the followg data come from the lear model: ε ε ~ N, σ,,..., -6. -.5 7. 6.9 -. -. -.9. -..6.4.. -.6 -.7.7 Fd the mamum lkelhood estmates of,, ad σ ε s.6. 4. ε

More information

( ) = ( ) ( ) Chapter 13 Asymptotic Theory and Stochastic Regressors. Stochastic regressors model

( ) = ( ) ( ) Chapter 13 Asymptotic Theory and Stochastic Regressors. Stochastic regressors model Chapter 3 Asmptotc Theor ad Stochastc Regressors The ature of eplaator varable s assumed to be o-stochastc or fed repeated samples a regresso aalss Such a assumpto s approprate for those epermets whch

More information

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.?

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.? Ch 4. Statstcs 4.1 Quattatve aalyss requres : soud kowledge of chemstry : possblty of terfereces WHY do we eed to use STATISTICS Aal. Chem.? ucertaty ests. wll we accept ucertaty always? f ot, from how

More information

C. Statistics. X = n geometric the n th root of the product of numerical data ln X GM = or ln GM = X 2. X n X 1

C. Statistics. X = n geometric the n th root of the product of numerical data ln X GM = or ln GM = X 2. X n X 1 C. Statstcs a. Descrbe the stages the desg of a clcal tral, takg to accout the: research questos ad hypothess, lterature revew, statstcal advce, choce of study protocol, ethcal ssues, data collecto ad

More information

LINEAR REGRESSION ANALYSIS

LINEAR REGRESSION ANALYSIS LINEAR REGRESSION ANALYSIS MODULE V Lecture - Correctg Model Iadequaces Through Trasformato ad Weghtg Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Aalytcal methods for

More information

4. Standard Regression Model and Spatial Dependence Tests

4. Standard Regression Model and Spatial Dependence Tests 4. Stadard Regresso Model ad Spatal Depedece Tests Stadard regresso aalss fals the presece of spatal effects. I case of spatal depedeces ad/or spatal heterogeet a stadard regresso model wll be msspecfed.

More information

Linear Regression. Can height information be used to predict weight of an individual? How long should you wait till next eruption?

Linear Regression. Can height information be used to predict weight of an individual? How long should you wait till next eruption? Iter-erupto Tme Weght Correlato & Regreo 1 1 Lear Regreo 0 80 70 80 Heght 1 Ca heght formato be ued to predct weght of a dvdual? How log hould ou wat tll et erupto? Weght: Repoe varable (Outcome, Depedet)

More information

ECON 482 / WH Hong The Simple Regression Model 1. Definition of the Simple Regression Model

ECON 482 / WH Hong The Simple Regression Model 1. Definition of the Simple Regression Model ECON 48 / WH Hog The Smple Regresso Model. Defto of the Smple Regresso Model Smple Regresso Model Expla varable y terms of varable x y = β + β x+ u y : depedet varable, explaed varable, respose varable,

More information

Module 7: Probability and Statistics

Module 7: Probability and Statistics Lecture 4: Goodess of ft tests. Itroducto Module 7: Probablty ad Statstcs I the prevous two lectures, the cocepts, steps ad applcatos of Hypotheses testg were dscussed. Hypotheses testg may be used to

More information

{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:

{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution: Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed

More information

Chapter 3 Multiple Linear Regression Model

Chapter 3 Multiple Linear Regression Model Chapter 3 Multple Lear Regresso Model We cosder the problem of regresso whe study varable depeds o more tha oe explaatory or depedet varables, called as multple lear regresso model. Ths model geeralzes

More information

THE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE THE ROYAL STATISTICAL SOCIETY 00 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for the

More information

ε. Therefore, the estimate

ε. Therefore, the estimate Suggested Aswers, Problem Set 3 ECON 333 Da Hugerma. Ths s ot a very good dea. We kow from the secod FOC problem b) that ( ) SSE / = y x x = ( ) Whch ca be reduced to read y x x = ε x = ( ) The OLS model

More information

Linear and Non-Linear Regression: Powerful and Very Important Forecasting Methods

Linear and Non-Linear Regression: Powerful and Very Important Forecasting Methods Epert Joural of Busess ad Maagemet, Volume, Issue, pp. 0-8, 0 0 The Author. Publshed b Sprt Ivestf. ISSN 44-678 http://busess.epertjourals.com Lear ad No-Lear Regresso: Powerful ad Ver Importat Forecastg

More information

ECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity

ECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity ECONOMETRIC THEORY MODULE VIII Lecture - 6 Heteroskedastcty Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur . Breusch Paga test Ths test ca be appled whe the replcated data

More information

Topic 9. Regression and Correlation

Topic 9. Regression and Correlation BE54W Regresso ad Correlato Page of 43 Topc 9 Regresso ad Correlato Topc. Defto of the Lear Regresso Model... Estmato.... 3. The Aalyss of Varace Table. 4. Assumptos for the Straght Le Regresso. 5. Hypothess

More information

Chapter Statistics Background of Regression Analysis

Chapter Statistics Background of Regression Analysis Chapter 06.0 Statstcs Backgroud of Regresso Aalyss After readg ths chapter, you should be able to:. revew the statstcs backgroud eeded for learg regresso, ad. kow a bref hstory of regresso. Revew of Statstcal

More information

CHAPTER 8 REGRESSION AND CORRELATION

CHAPTER 8 REGRESSION AND CORRELATION CHAPTER 8 REGREION AND CORRELATION Determg for relatoshps ad makg predctos based from sample formato s oe of the ma dea of data aalss. Everoe wats to aswer questos lke Ca I predct how ma uts I ll sell

More information

SPECIAL CONSIDERATIONS FOR VOLUMETRIC Z-TEST FOR PROPORTIONS

SPECIAL CONSIDERATIONS FOR VOLUMETRIC Z-TEST FOR PROPORTIONS SPECIAL CONSIDERAIONS FOR VOLUMERIC Z-ES FOR PROPORIONS Oe s stctve reacto to the questo of whether two percetages are sgfcatly dfferet from each other s to treat them as f they were proportos whch the

More information

Homework Solution (#5)

Homework Solution (#5) Homework Soluto (# Chapter : #6,, 8(b, 3, 4, 44, 49, 3, 9 ad 7 Chapter. Smple Lear Regresso ad Correlato.6 (6 th edto 7, old edto Page 9 Rafall volume ( vs Ruoff volume ( : 9 8 7 6 4 3 : a. Yes, the scatter-plot

More information

ENGI 4421 Propagation of Error Page 8-01

ENGI 4421 Propagation of Error Page 8-01 ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.

More information

hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations

hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several

More information

Bias Correction in Estimation of the Population Correlation Coefficient

Bias Correction in Estimation of the Population Correlation Coefficient Kasetsart J. (Nat. Sc.) 47 : 453-459 (3) Bas Correcto Estmato of the opulato Correlato Coeffcet Juthaphor Ssomboothog ABSTRACT A estmator of the populato correlato coeffcet of two varables for a bvarate

More information

Sampling Theory MODULE V LECTURE - 14 RATIO AND PRODUCT METHODS OF ESTIMATION

Sampling Theory MODULE V LECTURE - 14 RATIO AND PRODUCT METHODS OF ESTIMATION Samplg Theor MODULE V LECTUE - 4 ATIO AND PODUCT METHODS OF ESTIMATION D. SHALABH DEPATMENT OF MATHEMATICS AND STATISTICS INDIAN INSTITUTE OF TECHNOLOG KANPU A mportat objectve a statstcal estmato procedure

More information

Handout #8. X\Y f(x) 0 1/16 1/ / /16 3/ / /16 3/16 0 3/ /16 1/16 1/8 g(y) 1/16 1/4 3/8 1/4 1/16 1

Handout #8. X\Y f(x) 0 1/16 1/ / /16 3/ / /16 3/16 0 3/ /16 1/16 1/8 g(y) 1/16 1/4 3/8 1/4 1/16 1 Hadout #8 Ttle: Foudatos of Ecoometrcs Course: Eco 367 Fall/05 Istructor: Dr. I-Mg Chu Lear Regresso Model So far we have focused mostly o the study of a sgle radom varable, ts correspodg theoretcal dstrbuto,

More information

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad

More information

Chapter 2 Supplemental Text Material

Chapter 2 Supplemental Text Material -. Models for the Data ad the t-test Chapter upplemetal Text Materal The model preseted the text, equato (-3) s more properl called a meas model. ce the mea s a locato parameter, ths tpe of model s also

More information

r y Simple Linear Regression How To Study Relation Between Two Quantitative Variables? Scatter Plot Pearson s Sample Correlation Correlation

r y Simple Linear Regression How To Study Relation Between Two Quantitative Variables? Scatter Plot Pearson s Sample Correlation Correlation Maatee Klled Correlato & Regreo How To Study Relato Betwee Two Quattatve Varable? Smple Lear Regreo 6.11 A Smple Regreo Problem 1 I there relato betwee umber of power boat the area ad umber of maatee klled?

More information

Chapter 14 Logistic Regression Models

Chapter 14 Logistic Regression Models Chapter 4 Logstc Regresso Models I the lear regresso model X β + ε, there are two types of varables explaatory varables X, X,, X k ad study varable y These varables ca be measured o a cotuous scale as

More information

Lecture 1: Introduction to Regression

Lecture 1: Introduction to Regression Lecture : Itroducto to Regresso A Eample: Eplag State Homcde Rates What kds of varables mght we use to epla/predct state homcde rates? Let s cosder just oe predctor for ow: povert Igore omtted varables,

More information

Spreadsheet Problem Solving

Spreadsheet Problem Solving 1550 1500 CO Emmssos for the US, 1989 000 Class meetg #6 Moday, Sept 14 th CO Emssos (MMT Carbo) y = 1.3x 41090.17 1450 1400 1350 1300 1989 1990 1991 199 1993 1994 1995 1996 1997 1998 1999 000 Year GEEN

More information

2SLS Estimates ECON In this case, begin with the assumption that E[ i

2SLS Estimates ECON In this case, begin with the assumption that E[ i SLS Estmates ECON 3033 Bll Evas Fall 05 Two-Stage Least Squares (SLS Cosder a stadard lear bvarate regresso model y 0 x. I ths case, beg wth the assumto that E[ x] 0 whch meas that OLS estmates of wll

More information

Statistics Review Part 3. Hypothesis Tests, Regression

Statistics Review Part 3. Hypothesis Tests, Regression Statstcs Revew Part 3 Hypothess Tests, Regresso The Importace of Samplg Dstrbutos Why all the fuss about samplg dstrbutos? Because they are fudametal to hypothess testg. Remember that our goal s to lear

More information

Logistic regression (continued)

Logistic regression (continued) STAT562 page 138 Logstc regresso (cotued) Suppose we ow cosder more complex models to descrbe the relatoshp betwee a categorcal respose varable (Y) that takes o two (2) possble outcomes ad a set of p explaatory

More information

Simple Linear Regression. How To Study Relation Between Two Quantitative Variables? Scatter Plot. Pearson s Sample Correlation.

Simple Linear Regression. How To Study Relation Between Two Quantitative Variables? Scatter Plot. Pearson s Sample Correlation. Correlato & Regreo How To Study Relato Betwee Two Quattatve Varable? Smple Lear Regreo 6. A Smple Regreo Problem I there relato betwee umber of power boat the area ad umber of maatee klled? Year NPB( )

More information

Maximum Likelihood Estimation

Maximum Likelihood Estimation Marquette Uverst Maxmum Lkelhood Estmato Dael B. Rowe, Ph.D. Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Coprght 08 b Marquette Uverst Maxmum Lkelhood Estmato We have bee sag that ~

More information