+ a a m. y = a 1. x 1. x m. x 2. Basics

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

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

Correlation and Regression Analysis

Chapter V Correlato ad Regresso Aalss R. 5.. So far we have cosdered ol uvarate dstrbutos. Ma a tme, however, we come across problems whch volve two or more varables. Ths wll be the subject matter of the

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

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

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

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,

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

Functions of Random Variables

Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,

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

Generative classification models

CS 75 Mache Learg Lecture Geeratve classfcato models Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Data: D { d, d,.., d} d, Classfcato represets a dscrete class value Goal: lear f : X Y Bar classfcato

Kernel-based Methods and Support Vector Machines

Kerel-based Methods ad Support Vector Maches Larr Holder CptS 570 Mache Learg School of Electrcal Egeerg ad Computer Scece Washgto State Uverst Refereces Muller et al. A Itroducto to Kerel-Based Learg

X X X E[ ] E X E X. is the ()m n where the ( i,)th. j element is the mean of the ( i,)th., then

Secto 5 Vectors of Radom Varables Whe workg wth several radom varables,,..., to arrage them vector form x, t s ofte coveet We ca the make use of matrx algebra to help us orgaze ad mapulate large umbers

Rademacher Complexity. Examples

Algorthmc Foudatos of Learg Lecture 3 Rademacher Complexty. Examples Lecturer: Patrck Rebesch Verso: October 16th 018 3.1 Itroducto I the last lecture we troduced the oto of Rademacher complexty ad showed

Study of Correlation using Bayes Approach under bivariate Distributions

Iteratoal Joural of Scece Egeerg ad Techolog Research IJSETR Volume Issue Februar 4 Stud of Correlato usg Baes Approach uder bvarate Dstrbutos N.S.Padharkar* ad. M.N.Deshpade** *Govt.Vdarbha Isttute of

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.

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

Principal Components. Analysis. Basic Intuition. A Method of Self Organized Learning

Prcpal Compoets Aalss A Method of Self Orgazed Learg Prcpal Compoets Aalss Stadard techque for data reducto statstcal patter matchg ad sgal processg Usupervsed learg: lear from examples wthout a teacher

Model Fitting, RANSAC. Jana Kosecka

Model Fttg, RANSAC Jaa Kosecka Fttg: Issues Prevous strateges Le detecto Hough trasform Smple parametrc model, two parameters m, b m + b Votg strateg Hard to geeralze to hgher dmesos a o + a + a 2 2 +

Econ 388 R. Butler 2016 rev Lecture 5 Multivariate 2 I. Partitioned Regression and Partial Regression Table 1: Projections everywhere

Eco 388 R. Butler 06 rev Lecture 5 Multvarate I. Parttoed Regresso ad Partal Regresso Table : Projectos everywhere P = ( ) ad M = I ( ) ad s a vector of oes assocated wth the costat term Sample Model Regresso

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ

Line Fitting and Regression

Marquette Uverst MSCS6 Le Fttg ad Regresso Dael B. Rowe, Ph.D. Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Coprght 8 b Marquette Uverst Least Squares Regresso MSCS6 For LSR we have pots

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

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

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

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

Section 2 Notes. Elizabeth Stone and Charles Wang. January 15, Expectation and Conditional Expectation of a Random Variable.

Secto Notes Elzabeth Stoe ad Charles Wag Jauar 5, 9 Jot, Margal, ad Codtoal Probablt Useful Rules/Propertes. P ( x) P P ( x; ) or R f (x; ) d. P ( xj ) P (x; ) P ( ) 3. P ( x; ) P ( xj ) P ( ) 4. Baes

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

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

3. Basic Concepts: Consequences and Properties

: 3. Basc Cocepts: Cosequeces ad Propertes Markku Jutt Overvew More advaced cosequeces ad propertes of the basc cocepts troduced the prevous lecture are derved. Source The materal s maly based o Sectos.6.8

Supervised learning: Linear regression Logistic regression

CS 57 Itroducto to AI Lecture 4 Supervsed learg: Lear regresso Logstc regresso Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 57 Itro to AI Data: D { D D.. D D Supervsed learg d a set of eamples s

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-

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

( ) = ( ) ( ) 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

Machine Learning. Introduction to Regression. Le Song. CSE6740/CS7641/ISYE6740, Fall 2012

Mache Learg CSE6740/CS764/ISYE6740, Fall 0 Itroducto to Regresso Le Sog Lecture 4, August 30, 0 Based o sldes from Erc g, CMU Readg: Chap. 3, CB Mache learg for apartmet hutg Suppose ou are to move to

Lecture Notes Forecasting the process of estimating or predicting unknown situations

Lecture Notes. Ecoomc Forecastg. Forecastg the process of estmatg or predctg ukow stuatos Eample usuall ecoomsts predct future ecoomc varables Forecastg apples to a varet of data () tme seres data predctg

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

Introduction to local (nonparametric) density estimation. methods

Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest

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,

Lecture 3. Least Squares Fitting. Optimization Trinity 2014 P.H.S.Torr. Classic least squares. Total least squares.

Lecture 3 Optmzato Trt 04 P.H.S.Torr Least Squares Fttg Classc least squares Total least squares Robust Estmato Fttg: Cocepts ad recpes Least squares le fttg Data:,,,, Le equato: = m + b Fd m, b to mmze

Bayesian Classification. CS690L Data Mining: Classification(2) Bayesian Theorem: Basics. Bayesian Theorem. Training dataset. Naïve Bayes Classifier

Baa Classfcato CS6L Data Mg: Classfcato() Referece: J. Ha ad M. Kamber, Data Mg: Cocepts ad Techques robablstc learg: Calculate explct probabltes for hypothess, amog the most practcal approaches to certa

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

Lecture Notes 2. The ability to manipulate matrices is critical in economics.

Lecture Notes. Revew of Matrces he ablt to mapulate matrces s crtcal ecoomcs.. Matr a rectagular arra of umbers, parameters, or varables placed rows ad colums. Matrces are assocated wth lear equatos. lemets

Power Flow S + Buses with either or both Generator Load S G1 S G2 S G3 S D3 S D1 S D4 S D5. S Dk. Injection S G1

ower Flow uses wth ether or both Geerator Load G G G D D 4 5 D4 D5 ecto G Net Comple ower ecto - D D ecto s egatve sg at load bus = _ G D mlarl Curret ecto = G _ D At each bus coservato of comple power

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:

Linear Regression. Hsiao-Lung Chan Dept Electrical Engineering Chang Gung University, Taiwan

Lear Regresso Hsao-Lug Cha Dept Electrcal Egeerg Chag Gug Uverst, Tawa chahl@mal.cgu.edu.tw Curve fttg Least-squares regresso Data ehbt a sgfcat degree of error or scatter A curve for the tred of the data

Transforms that are commonly used are separable

Trasforms s Trasforms that are commoly used are separable Eamples: Two-dmesoal DFT DCT DST adamard We ca the use -D trasforms computg the D separable trasforms: Take -D trasform of the rows > rows ( )

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 ~

Lecture 3 Probability review (cont d)

STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto

Source-Channel Prediction in Error Resilient Video Coding

Source-Chael Predcto Error Reslet Vdeo Codg Hua Yag ad Keeth Rose Sgal Compresso Laboratory ECE Departmet Uversty of Calfora, Sata Barbara Outle Itroducto Source-chael predcto Smulato results Coclusos

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses

Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s

Regression and the LMS Algorithm

CSE 556: Itroducto to Neural Netorks Regresso ad the LMS Algorthm CSE 556: Regresso 1 Problem statemet CSE 556: Regresso Lear regresso th oe varable Gve a set of N pars of data {, d }, appromate d b a

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses

Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s

Generalized Linear Models. Statistical Models. Classical Linear Regression Why easy formulation if complicated formulation exists?

Statstcal Models Geeralzed Lear Models Classcal lear regresso complcated formlato of smple model, strctral ad radom compoet of the model Lectre 5 Geeralzed Lear Models Geeralzed lear models geeral descrpto

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

Dimensionality reduction Feature selection

CS 750 Mache Learg Lecture 3 Dmesoalty reducto Feature selecto Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 750 Mache Learg Dmesoalty reducto. Motvato. Classfcato problem eample: We have a put data

: At least two means differ SST

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

Linear Regression. Hsiao-Lung Chan Dept Electrical Engineering Chang Gung University, Taiwan

Lear Regresso Hsao-Lug Cha Dept Electrcal Egeerg Chag Gug Uverst, Tawa chahl@mal.cgu.edu.tw Curve fttg Least-squares regresso Data ehbt a sgfcat degree of error or scatter A curve for the tred of the data

Evaluation of uncertainty in measurements

Evaluato of ucertaty measuremets Laboratory of Physcs I Faculty of Physcs Warsaw Uversty of Techology Warszawa, 05 Itroducto The am of the measuremet s to determe the measured value. Thus, the measuremet

Chapter 4 Multiple Random Variables

Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:

Recall MLR 5 Homskedasticity error u has the same variance given any values of the explanatory variables Var(u x1,...,xk) = 2 or E(UU ) = 2 I

Chapter 8 Heterosedastcty Recall MLR 5 Homsedastcty error u has the same varace gve ay values of the eplaatory varables Varu,..., = or EUU = I Suppose other GM assumptos hold but have heterosedastcty.

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

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

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..

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

EECE 301 Signals & Systems

EECE 01 Sgals & Systems Prof. Mark Fowler Note Set #9 Computg D-T Covoluto Readg Assgmet: Secto. of Kame ad Heck 1/ Course Flow Dagram The arrows here show coceptual flow betwee deas. Note the parallel

An Introduction to. Support Vector Machine

A Itroducto to Support Vector Mache Support Vector Mache (SVM) A classfer derved from statstcal learg theory by Vapk, et al. 99 SVM became famous whe, usg mages as put, t gave accuracy comparable to eural-etwork

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

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

ρ < 1 be five real numbers. The

Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace

Multivariate Transformation of Variables and Maximum Likelihood Estimation

Marquette Uversty Multvarate Trasformato of Varables ad Maxmum Lkelhood Estmato Dael B. Rowe, Ph.D. Assocate Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Copyrght 03 by Marquette Uversty

Matrix Algebra Tutorial With Examples in Matlab

Matr Algebra Tutoral Wth Eamples Matlab by Klaus Moelter Departmet of Agrcultural ad Appled Ecoomcs Vrga Tech emal: moelter@vt.edu web: http://faculty.ageco.vt.edu/moelter/ Specfcally desged as a / day

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

Overview. Basic concepts of Bayesian learning. Most probable model given data Coin tosses Linear regression Logistic regression

Overvew Basc cocepts of Bayesa learg Most probable model gve data Co tosses Lear regresso Logstc regresso Bayesa predctos Co tosses Lear regresso 30 Recap: regresso problems Iput to learg problem: trag

DISTURBANCE TERMS. is a scalar and x i

DISTURBANCE TERMS I a feld of research desg, we ofte have the qesto abot whether there s a relatoshp betwee a observed varable (sa, ) ad the other observed varables (sa, x ). To aswer the qesto, we ma

Bayes (Naïve or not) Classifiers: Generative Approach

Logstc regresso Bayes (Naïve or ot) Classfers: Geeratve Approach What do we mea by Geeratve approach: Lear p(y), p(x y) ad the apply bayes rule to compute p(y x) for makg predctos Ths s essetally makg

Analysis of Variance with Weibull Data

Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad

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.

9.1 Introduction to the probit and logit models

EC3000 Ecoometrcs Lecture 9 Probt & Logt Aalss 9. Itroducto to the probt ad logt models 9. The logt model 9.3 The probt model Appedx 9. Itroducto to the probt ad logt models These models are used regressos

Lecture 12: Multilayer perceptrons II

Lecture : Multlayer perceptros II Bayes dscrmats ad MLPs he role of hdde uts A eample Itroducto to Patter Recoto Rcardo Guterrez-Osua Wrht State Uversty Bayes dscrmats ad MLPs ( As we have see throuhout

Bayes Estimator for Exponential Distribution with Extension of Jeffery Prior Information

Malaysa Joural of Mathematcal Sceces (): 97- (9) Bayes Estmator for Expoetal Dstrbuto wth Exteso of Jeffery Pror Iformato Hadeel Salm Al-Kutub ad Noor Akma Ibrahm Isttute for Mathematcal Research, Uverst

Uncertainty, Data, and Judgment

Ucertaty, Data, ad Judgmet Sesso 06 Structure of the Course Topc Sesso Probablty -5 Estmato 6-8 Hypothess Testg 9-10 Regresso 11-16 1 Mcrosoft AND Itel (50-50) You vest $,500 MSFT ad $,500 INTC X = Aual

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

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]

CS 2750 Machine Learning. Lecture 8. Linear regression. CS 2750 Machine Learning. Linear regression. is a linear combination of input components x

CS 75 Mache Learg Lecture 8 Lear regresso Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 75 Mache Learg Lear regresso Fucto f : X Y s a lear combato of put compoets f + + + K d d K k - parameters

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,

13. Parametric and Non-Parametric Uncertainties, Radial Basis Functions and Neural Network Approximations

Lecture 7 3. Parametrc ad No-Parametrc Ucertates, Radal Bass Fuctos ad Neural Network Approxmatos he parameter estmato algorthms descrbed prevous sectos were based o the assumpto that the system ucertates

COV. Violation of constant variance of ε i s but they are still independent. The error term (ε) is said to be heteroscedastic.

c Pogsa Porchawseskul, Faculty of Ecoomcs, Chulalogkor Uversty olato of costat varace of s but they are stll depedet. C,, he error term s sad to be heteroscedastc. c Pogsa Porchawseskul, Faculty of Ecoomcs,

Chapter 5 Properties of a Random Sample

Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample

Random Variate Generation ENM 307 SIMULATION. Anadolu Üniversitesi, Endüstri Mühendisliği Bölümü. Yrd. Doç. Dr. Gürkan ÖZTÜRK.

adom Varate Geerato ENM 307 SIMULATION Aadolu Üverstes, Edüstr Mühedslğ Bölümü Yrd. Doç. Dr. Gürka ÖZTÜK 0 adom Varate Geerato adom varate geerato s about procedures for samplg from a varety of wdely-used

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

Wu-Hausman Test: But if X and ε are independent, βˆ. ECON 324 Page 1

Wu-Hausma Test: Detectg Falure of E( ε X ) Caot drectly test ths assumpto because lack ubased estmator of ε ad the OLS resduals wll be orthogoal to X, by costructo as ca be see from the momet codto X'

Systematic Selection of Parameters in the development of Feedforward Artificial Neural Network Models through Conventional and Intelligent Algorithms

THALES Project No. 65/3 Systematc Selecto of Parameters the developmet of Feedforward Artfcal Neural Network Models through Covetoal ad Itellget Algorthms Research Team G.-C. Vosakos, T. Gaakaks, A. Krmpes,

CS 2750 Machine Learning Lecture 5. Density estimation. Density estimation

CS 750 Mache Learg Lecture 5 esty estmato Mlos Hausrecht mlos@tt.edu 539 Seott Square esty estmato esty estmato: s a usuervsed learg roblem Goal: Lear a model that rereset the relatos amog attrbutes the

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

Binary Response Nonparametric Regression Model And Its Application in University Graduation

Proceedgs of IICMA 9 Topc, pp.. Bary Respose Noparametrc Regresso Model Ad Its Applcato Uversty Graduato Jerry Dw Troyo Puromo Statstcs Departmet Isttut Tekolog Sepuluh Nopember Emal: errypuromo@yahoo.com

best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best

Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg

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

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

Descriptive Statistics

Page Techcal Math II Descrptve Statstcs Descrptve Statstcs Descrptve statstcs s the body of methods used to represet ad summarze sets of data. A descrpto of how a set of measuremets (for eample, people