Lecture 5: Linear Regression
|
|
|
- Kristopher Wade
- 5 years ago
- Views:
Transcription
1 EAS31136/B9036: Statistics in Earth & Atmospheric Sciences Lecture 5: Linear Regression Instructor: Prof. Johnny Luo
2 Dates Topic Reading (Based on the 2 nd Edition of Wilks book) Other Activity Aug 31 Introduction; Review of probability Wilks, Chap 2 Pre-test Sep 7 Matlab tutorial (optional) Sep 14 Review of probability; Probability Distribution 1 Wilks, Chap 2, 3 Sep 21 Probability Distribution 2 Wilks, Chap 3, 4 Sep 28 Hypothesis testing Wilks, Chap 5 Oct 5 Linear regression I Wilks Chap 6; von Storch 8-9 Oct 12 Linear regression II Wilks Chap 6; von Storch 8-9 Oct 19 Time series analysis I Wilks 8; von Storch Oct 26 Midterm; discussion of final project Project 1-page abstract due Nov 2 Time series analysis II Wilks 8; von Storch Nov 9 Principal Component Analysis & Empirical orthogonal functions I Wilks 11; von Storch 13 Nov 16 Principal Component Analysis & Empirical orthogonal functions II Wilks 11; von Storch 13 Project progress report due Nov 30 Cluster analysis Wilks 14 Dec 7 Final project presentation
3 Outline 1. Simple linear regression 2. Distribution of residuals & ANOVA 3. Sampling distribution of the regression coefficients 4. Multiple linear regression
4 x: predictor y: predictand hat ^: predicted value of the predictand In a practical sense, the simple linear regression problem boils down to determining a & b Usually, we do so by minimize error or residual:
5 Least square method:
6 Outline 1. Simple linear regression 2. Distribution of residuals & ANOVA 3. Sampling distribution of the regression coefficients 4. Multiple linear regression
7 We want to know how to evaluate our fit Unbiased (Guaranteed b/c the least square approach) Spread n-2 because two parameters (a and b) were estimated
8 Quantify regression and error SSR (Sum of squares, regression) SSE (Sum of squared error) SST (Sum of squares, total)
9 Analysis of Variance (ANOVA) Table
10 Goodness-of-Fit Measures Measure #1: MSE = SSE/(n-2) Measure #2: Measure #3: F ratio = MSR/MSE
11 Outline 1. Simple linear regression 2. Distribution of residuals & ANOVA 3. Sampling distribution of the regression coefficients 4. Multiple linear regression
12 We don t know the true values for a and b. All we have are just estimates and these estimates following sampling distribution.
13 Information on sampling distributions of the regression coefficients can be used to test if the linear regression is meaningful (or worth doing). Take the slope b for example, usually we use one-sample t test Ø Statistic: Ø Null hypothesis: b = 0 (i.e., flat line) Ø Usually we set the test value at 5%. Ø Check the calculated t against t-table to find the corresponding p value; if the p value is < 5%, then we reject the null hypothesis and conclude b 0.
14
15
16 Analysis Concept We focused on the Atlantic ITCZ Ocean
17
18 Example 1. Go to class website ( and download the following two files: temp_precip_ithaca.txt temp_precip_canandaigua.txt Each file contains the following four columns: day (of Jan 1987), precipitation (inches), Max. temperature ( 0 F), and Min. temperature ( 0 F). First, use Min. Temp. at Ithaca as the predictor (x) and Min. Temp. at Canandaigua as the predictand (y). Solve the coefficients for y = a + b*x. Plot the data points and the fitted line. Use matlab if possible. Second, fill in the ANOVA table. Calculate SST, SSR, SSE, etc.
19 When you set n = 1, it becomes y = p 1 x + p 2 LM = fitlm(x,y) fits a simple linear regression model ANOVA(LM, summary ) will give the whole ANOVA Table A sample code for Matlab can be found at:
20
Lecture 4: Statistical Hypothesis Testing
EAS31136/B9036: Statistics in Earth & Atmospheric Sciences Lecture 4: Statistical Hypothesis Testing Instructor: Prof. Johnny Luo www.sci.ccny.cuny.edu/~luo Dates Topic Reading (Based on the 2 nd Edition
Lecture 1: Review of Probability
EAS31136/B9036: Statistics in Earth & Atmospheric Sciences Lecture 1: Review of Probability Instructor: Prof. Johnny Luo www.sci.ccny.cuny.edu/~luo Dates Topic Reading (Based on the 2 nd Edition of Wilks
Lecture 2: Probability Distributions
EAS31136/B9036: Statistics in Earth & Atmospheric Sciences Lecture 2: Probability Distributions Instructor: Prof. Johnny Luo www.sci.ccny.cuny.edu/~luo Dates Topic Reading (Based on the 2 nd Edition of
Chapter 14 Student Lecture Notes Department of Quantitative Methods & Information Systems. Business Statistics. Chapter 14 Multiple Regression
Chapter 14 Student Lecture Notes 14-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 14 Multiple Regression QMIS 0 Dr. Mohammad Zainal Chapter Goals After completing
Chapter 4. Regression Models. Learning Objectives
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
Linear regression. We have that the estimated mean in linear regression is. ˆµ Y X=x = ˆβ 0 + ˆβ 1 x. The standard error of ˆµ Y X=x is.
Linear regression We have that the estimated mean in linear regression is The standard error of ˆµ Y X=x is where x = 1 n s.e.(ˆµ Y X=x ) = σ ˆµ Y X=x = ˆβ 0 + ˆβ 1 x. 1 n + (x x)2 i (x i x) 2 i x i. The
Chapter 12 - Lecture 2 Inferences about regression coefficient
Chapter 12 - Lecture 2 Inferences about regression coefficient April 19th, 2010 Facts about slope Test Statistic Confidence interval Hypothesis testing Test using ANOVA Table Facts about slope In previous
Regression Analysis. Regression: Methodology for studying the relationship among two or more variables
Regression Analysis Regression: Methodology for studying the relationship among two or more variables Two major aims: Determine an appropriate model for the relationship between the variables Predict the
Lecture 15 Multiple regression I Chapter 6 Set 2 Least Square Estimation The quadratic form to be minimized is
Lecture 15 Multiple regression I Chapter 6 Set 2 Least Square Estimation The quadratic form to be minimized is Q = (Y i β 0 β 1 X i1 β 2 X i2 β p 1 X i.p 1 ) 2, which in matrix notation is Q = (Y Xβ) (Y
Inferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
The Multiple Regression Model
Multiple Regression The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & or more independent variables (X i ) Multiple Regression Model with k Independent Variables:
Simple Linear Regression
9-1 l Chapter 9 l Simple Linear Regression 9.1 Simple Linear Regression 9.2 Scatter Diagram 9.3 Graphical Method for Determining Regression 9.4 Least Square Method 9.5 Correlation Coefficient and Coefficient
Concordia University (5+5)Q 1.
(5+5)Q 1. Concordia University Department of Mathematics and Statistics Course Number Section Statistics 360/1 40 Examination Date Time Pages Mid Term Test May 26, 2004 Two Hours 3 Instructor Course Examiner
Ch 2: Simple Linear Regression
Ch 2: Simple Linear Regression 1. Simple Linear Regression Model A simple regression model with a single regressor x is y = β 0 + β 1 x + ɛ, where we assume that the error ɛ is independent random component
Mathematics for Economics MA course
Mathematics for Economics MA course Simple Linear Regression Dr. Seetha Bandara Simple Regression Simple linear regression is a statistical method that allows us to summarize and study relationships between
Econ 3790: Business and Economics Statistics. Instructor: Yogesh Uppal
Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal yuppal@ysu.edu Sampling Distribution of b 1 Expected value of b 1 : Variance of b 1 : E(b 1 ) = 1 Var(b 1 ) = σ 2 /SS x Estimate of
SIMPLE REGRESSION ANALYSIS. Business Statistics
SIMPLE REGRESSION ANALYSIS Business Statistics CONTENTS Ordinary least squares (recap for some) Statistical formulation of the regression model Assessing the regression model Testing the regression coefficients
Regression Models. Chapter 4. Introduction. Introduction. Introduction
Chapter 4 Regression Models Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna 008 Prentice-Hall, Inc. Introduction Regression analysis is a very valuable tool for a manager
We like to capture and represent the relationship between a set of possible causes and their response, by using a statistical predictive model.
Statistical Methods in Business Lecture 5. Linear Regression We like to capture and represent the relationship between a set of possible causes and their response, by using a statistical predictive model.
Variance Decomposition and Goodness of Fit
Variance Decomposition and Goodness of Fit 1. Example: Monthly Earnings and Years of Education In this tutorial, we will focus on an example that explores the relationship between total monthly earnings
Variance Decomposition in Regression James M. Murray, Ph.D. University of Wisconsin - La Crosse Updated: October 04, 2017
Variance Decomposition in Regression James M. Murray, Ph.D. University of Wisconsin - La Crosse Updated: October 04, 2017 PDF file location: http://www.murraylax.org/rtutorials/regression_anovatable.pdf
Correlation and the Analysis of Variance Approach to Simple Linear Regression
Correlation and the Analysis of Variance Approach to Simple Linear Regression Biometry 755 Spring 2009 Correlation and the Analysis of Variance Approach to Simple Linear Regression p. 1/35 Correlation
STAT420 Midterm Exam. University of Illinois Urbana-Champaign October 19 (Friday), :00 4:15p. SOLUTIONS (Yellow)
STAT40 Midterm Exam University of Illinois Urbana-Champaign October 19 (Friday), 018 3:00 4:15p SOLUTIONS (Yellow) Question 1 (15 points) (10 points) 3 (50 points) extra ( points) Total (77 points) Points
16.3 One-Way ANOVA: The Procedure
16.3 One-Way ANOVA: The Procedure Tom Lewis Fall Term 2009 Tom Lewis () 16.3 One-Way ANOVA: The Procedure Fall Term 2009 1 / 10 Outline 1 The background 2 Computing formulas 3 The ANOVA Identity 4 Tom
Simple Linear Regression
Simple Linear Regression MATH 282A Introduction to Computational Statistics University of California, San Diego Instructor: Ery Arias-Castro http://math.ucsd.edu/ eariasca/math282a.html MATH 282A University
Ch. 1: Data and Distributions
Ch. 1: Data and Distributions Populations vs. Samples How to graphically display data Histograms, dot plots, stem plots, etc Helps to show how samples are distributed Distributions of both continuous and
Inference for Regression
Inference for Regression Section 9.4 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 13b - 3339 Cathy Poliak, Ph.D. cathy@math.uh.edu
Business Statistics. Chapter 14 Introduction to Linear Regression and Correlation Analysis QMIS 220. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 14 Introduction to Linear Regression and Correlation Analysis QMIS 220 Dr. Mohammad Zainal Chapter Goals After completing
Review of the General Linear Model
Review of the General Linear Model EPSY 905: Multivariate Analysis Online Lecture #2 Learning Objectives Types of distributions: Ø Conditional distributions The General Linear Model Ø Regression Ø Analysis
One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups
One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups In analysis of variance, the main research question is whether the sample means are from different populations. The
F-tests and Nested Models
F-tests and Nested Models Nested Models: A core concept in statistics is comparing nested s. Consider the Y = β 0 + β 1 x 1 + β 2 x 2 + ǫ. (1) The following reduced s are special cases (nested within)
Simple Linear Regression Using Ordinary Least Squares
Simple Linear Regression Using Ordinary Least Squares Purpose: To approximate a linear relationship with a line. Reason: We want to be able to predict Y using X. Definition: The Least Squares Regression
Lecture 9: Linear Regression
Lecture 9: Linear Regression Goals Develop basic concepts of linear regression from a probabilistic framework Estimating parameters and hypothesis testing with linear models Linear regression in R Regression
Stats Review Chapter 14. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter 14 Revised 8/16 Note: This review is meant to highlight basic concepts from the course. It does not cover all concepts presented by your instructor. Refer back to your notes, unit
Estimating σ 2. We can do simple prediction of Y and estimation of the mean of Y at any value of X.
Estimating σ 2 We can do simple prediction of Y and estimation of the mean of Y at any value of X. To perform inferences about our regression line, we must estimate σ 2, the variance of the error term.
Inference in Normal Regression Model. Dr. Frank Wood
Inference in Normal Regression Model Dr. Frank Wood Remember We know that the point estimator of b 1 is b 1 = (Xi X )(Y i Ȳ ) (Xi X ) 2 Last class we derived the sampling distribution of b 1, it being
Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
What is Multiple Linear Regression Several independent variables may influence the change in response variable we are trying to study. When several independent variables are included in the equation, the
Chapter 14 Simple Linear Regression (A)
Chapter 14 Simple Linear Regression (A) 1. Characteristics Managerial decisions often are based on the relationship between two or more variables. can be used to develop an equation showing how the variables
Basic Business Statistics 6 th Edition
Basic Business Statistics 6 th Edition Chapter 12 Simple Linear Regression Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of a dependent variable based
Inference for the Regression Coefficient
Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression line. We can shows that b 0 and b 1 are the unbiased estimates
Chapter 2. Continued. Proofs For ANOVA Proof of ANOVA Identity. the product term in the above equation can be simplified as n
Chapter 2. Continued Proofs For ANOVA Proof of ANOVA Identity We are going to prove that Writing SST SSR + SSE. Y i Ȳ (Y i Ŷ i ) + (Ŷ i Ȳ ) Squaring both sides summing over all i 1,...n, we get (Y i Ȳ
Multiple Linear Regression
Multiple Linear Regression Simple linear regression tries to fit a simple line between two variables Y and X. If X is linearly related to Y this explains some of the variability in Y. In most cases, there
CS 5014: Research Methods in Computer Science
Computer Science Clifford A. Shaffer Department of Computer Science Virginia Tech Blacksburg, Virginia Fall 2010 Copyright c 2010 by Clifford A. Shaffer Computer Science Fall 2010 1 / 207 Correlation and
LECTURE 6. Introduction to Econometrics. Hypothesis testing & Goodness of fit
LECTURE 6 Introduction to Econometrics Hypothesis testing & Goodness of fit October 25, 2016 1 / 23 ON TODAY S LECTURE We will explain how multiple hypotheses are tested in a regression model We will define
Regression Analysis II
Regression Analysis II Measures of Goodness of fit Two measures of Goodness of fit Measure of the absolute fit of the sample points to the sample regression line Standard error of the estimate An index
Lecture 3: Inference in SLR
Lecture 3: Inference in SLR STAT 51 Spring 011 Background Reading KNNL:.1.6 3-1 Topic Overview This topic will cover: Review of hypothesis testing Inference about 1 Inference about 0 Confidence Intervals
TMA4255 Applied Statistics V2016 (5)
TMA4255 Applied Statistics V2016 (5) Part 2: Regression Simple linear regression [11.1-11.4] Sum of squares [11.5] Anna Marie Holand To be lectured: January 26, 2016 wiki.math.ntnu.no/tma4255/2016v/start
Regression Models. Chapter 4
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Introduction Regression analysis
Biostatistics 380 Multiple Regression 1. Multiple Regression
Biostatistics 0 Multiple Regression ORIGIN 0 Multiple Regression Multiple Regression is an extension of the technique of linear regression to describe the relationship between a single dependent (response)
Regression: Main Ideas Setting: Quantitative outcome with a quantitative explanatory variable. Example, cont.
TCELL 9/4/205 36-309/749 Experimental Design for Behavioral and Social Sciences Simple Regression Example Male black wheatear birds carry stones to the nest as a form of sexual display. Soler et al. wanted
Multivariate Regression
Multivariate Regression The so-called supervised learning problem is the following: we want to approximate the random variable Y with an appropriate function of the random variables X 1,..., X p with the
Linear models and their mathematical foundations: Simple linear regression
Linear models and their mathematical foundations: Simple linear regression Steffen Unkel Department of Medical Statistics University Medical Center Göttingen, Germany Winter term 2018/19 1/21 Introduction
STAT 540: Data Analysis and Regression
STAT 540: Data Analysis and Regression Wen Zhou http://www.stat.colostate.edu/~riczw/ Email: riczw@stat.colostate.edu Department of Statistics Colorado State University Fall 205 W. Zhou (Colorado State
Lecture 30. DATA 8 Summer Regression Inference
DATA 8 Summer 2018 Lecture 30 Regression Inference Slides created by John DeNero (denero@berkeley.edu) and Ani Adhikari (adhikari@berkeley.edu) Contributions by Fahad Kamran (fhdkmrn@berkeley.edu) and
Econ 3790: Statistics Business and Economics. Instructor: Yogesh Uppal
Econ 3790: Statistics Business and Economics Instructor: Yogesh Uppal Email: yuppal@ysu.edu Chapter 14 Covariance and Simple Correlation Coefficient Simple Linear Regression Covariance Covariance between
Lecture 1 Linear Regression with One Predictor Variable.p2
Lecture Linear Regression with One Predictor Variablep - Basics - Meaning of regression parameters p - β - the slope of the regression line -it indicates the change in mean of the probability distn of
Summary of Chapter 7 (Sections ) and Chapter 8 (Section 8.1)
Summary of Chapter 7 (Sections 7.2-7.5) and Chapter 8 (Section 8.1) Chapter 7. Tests of Statistical Hypotheses 7.2. Tests about One Mean (1) Test about One Mean Case 1: σ is known. Assume that X N(µ, σ
Finding Relationships Among Variables
Finding Relationships Among Variables BUS 230: Business and Economic Research and Communication 1 Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions, hypothesis
36-309/749 Experimental Design for Behavioral and Social Sciences. Sep. 22, 2015 Lecture 4: Linear Regression
36-309/749 Experimental Design for Behavioral and Social Sciences Sep. 22, 2015 Lecture 4: Linear Regression TCELL Simple Regression Example Male black wheatear birds carry stones to the nest as a form
BNAD 276 Lecture 10 Simple Linear Regression Model
1 / 27 BNAD 276 Lecture 10 Simple Linear Regression Model Phuong Ho May 30, 2017 2 / 27 Outline 1 Introduction 2 3 / 27 Outline 1 Introduction 2 4 / 27 Simple Linear Regression Model Managerial decisions
Formal Statement of Simple Linear Regression Model
Formal Statement of Simple Linear Regression Model Y i = β 0 + β 1 X i + ɛ i Y i value of the response variable in the i th trial β 0 and β 1 are parameters X i is a known constant, the value of the predictor
STA 2101/442 Assignment Four 1
STA 2101/442 Assignment Four 1 One version of the general linear model with fixed effects is y = Xβ + ɛ, where X is an n p matrix of known constants with n > p and the columns of X linearly independent.
ST Correlation and Regression
Chapter 5 ST 370 - Correlation and Regression Readings: Chapter 11.1-11.4, 11.7.2-11.8, Chapter 12.1-12.2 Recap: So far we ve learned: Why we want a random sample and how to achieve it (Sampling Scheme)
Econ 3790: Business and Economic Statistics. Instructor: Yogesh Uppal
Econ 3790: Business and Economic Statistics Instructor: Yogesh Uppal Email: yuppal@ysu.edu Chapter 13, Part A: Analysis of Variance and Experimental Design Introduction to Analysis of Variance Analysis
GAMINGRE 8/1/ of 7
FYE 09/30/92 JULY 92 0.00 254,550.00 0.00 0 0 0 0 0 0 0 0 0 254,550.00 0.00 0.00 0.00 0.00 254,550.00 AUG 10,616,710.31 5,299.95 845,656.83 84,565.68 61,084.86 23,480.82 339,734.73 135,893.89 67,946.95
STA 6167 Exam 1 Spring 2016 PRINT Name
STA 6167 Exam 1 Spring 2016 PRINT Name Unless stated otherwise, for all significance tests, use = 0.05 significance level. Q.1. A regression model was fit, relating estimated cost of de-commissioning oil
Sociology 6Z03 Review II
Sociology 6Z03 Review II John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review II Fall 2016 1 / 35 Outline: Review II Probability Part I Sampling Distributions Probability
Correlation Analysis
Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the
Figure 1: The fitted line using the shipment route-number of ampules data. STAT5044: Regression and ANOVA The Solution of Homework #2 Inyoung Kim
0.0 1.0 1.5 2.0 2.5 3.0 8 10 12 14 16 18 20 22 y x Figure 1: The fitted line using the shipment route-number of ampules data STAT5044: Regression and ANOVA The Solution of Homework #2 Inyoung Kim Problem#
Measuring the fit of the model - SSR
Measuring the fit of the model - SSR Once we ve determined our estimated regression line, we d like to know how well the model fits. How far/close are the observations to the fitted line? One way to do
Linear Regression. In this problem sheet, we consider the problem of linear regression with p predictors and one intercept,
Linear Regression In this problem sheet, we consider the problem of linear regression with p predictors and one intercept, y = Xβ + ɛ, where y t = (y 1,..., y n ) is the column vector of target values,
Power Analysis using GPower 3.1
Power Analysis using GPower 3.1 a one-day hands-on practice workshop (session 1) Dr. John Xie Statistics Support Officer, Quantitative Consulting Unit, Research Office, Charles Sturt University, NSW, Australia
Chapter 13 Student Lecture Notes Department of Quantitative Methods & Information Systems. Business Statistics
Chapter 13 Student Lecture Notes 13-1 Department of Quantitative Methods & Information Sstems Business Statistics Chapter 14 Introduction to Linear Regression and Correlation Analsis QMIS 0 Dr. Mohammad
Lecture 6 Multiple Linear Regression, cont.
Lecture 6 Multiple Linear Regression, cont. BIOST 515 January 22, 2004 BIOST 515, Lecture 6 Testing general linear hypotheses Suppose we are interested in testing linear combinations of the regression
Business Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
Ma 3/103: Lecture 25 Linear Regression II: Hypothesis Testing and ANOVA
Ma 3/103: Lecture 25 Linear Regression II: Hypothesis Testing and ANOVA March 6, 2017 KC Border Linear Regression II March 6, 2017 1 / 44 1 OLS estimator 2 Restricted regression 3 Errors in variables 4
Lecture 10 Multiple Linear Regression
Lecture 10 Multiple Linear Regression STAT 512 Spring 2011 Background Reading KNNL: 6.1-6.5 10-1 Topic Overview Multiple Linear Regression Model 10-2 Data for Multiple Regression Y i is the response variable
Multivariate Regression (Chapter 10)
Multivariate Regression (Chapter 10) This week we ll cover multivariate regression and maybe a bit of canonical correlation. Today we ll mostly review univariate multivariate regression. With multivariate
STA121: Applied Regression Analysis
STA121: Applied Regression Analysis Linear Regression Analysis - Chapters 3 and 4 in Dielman Artin Department of Statistical Science September 15, 2009 Outline 1 Simple Linear Regression Analysis 2 Using
Regression used to predict or estimate the value of one variable corresponding to a given value of another variable.
CHAPTER 9 Simple Linear Regression and Correlation Regression used to predict or estimate the value of one variable corresponding to a given value of another variable. X = independent variable. Y = dependent
Applied Regression Analysis
Applied Regression Analysis Chapter 3 Multiple Linear Regression Hongcheng Li April, 6, 2013 Recall simple linear regression 1 Recall simple linear regression 2 Parameter Estimation 3 Interpretations of
MULTIPLE REGRESSION ANALYSIS AND OTHER ISSUES. Business Statistics
MULTIPLE REGRESSION ANALYSIS AND OTHER ISSUES Business Statistics CONTENTS Multiple regression Dummy regressors Assumptions of regression analysis Predicting with regression analysis Old exam question
Lecture 2 Simple Linear Regression STAT 512 Spring 2011 Background Reading KNNL: Chapter 1
Lecture Simple Linear Regression STAT 51 Spring 011 Background Reading KNNL: Chapter 1-1 Topic Overview This topic we will cover: Regression Terminology Simple Linear Regression with a single predictor
Outline. Remedial Measures) Extra Sums of Squares Standardized Version of the Multiple Regression Model
Outline 1 Multiple Linear Regression (Estimation, Inference, Diagnostics and Remedial Measures) 2 Special Topics for Multiple Regression Extra Sums of Squares Standardized Version of the Multiple Regression
Simple and Multiple Linear Regression
Sta. 113 Chapter 12 and 13 of Devore March 12, 2010 Table of contents 1 Simple Linear Regression 2 Model Simple Linear Regression A simple linear regression model is given by Y = β 0 + β 1 x + ɛ where
Ch 3: Multiple Linear Regression
Ch 3: Multiple Linear Regression 1. Multiple Linear Regression Model Multiple regression model has more than one regressor. For example, we have one response variable and two regressor variables: 1. delivery
Hypothesis Testing for Var-Cov Components
Hypothesis Testing for Var-Cov Components When the specification of coefficients as fixed, random or non-randomly varying is considered, a null hypothesis of the form is considered, where Additional output
Regression. Estimation of the linear function (straight line) describing the linear component of the joint relationship between two variables X and Y.
Regression Bivariate i linear regression: Estimation of the linear function (straight line) describing the linear component of the joint relationship between two variables and. Generally describe as a
Analysis of Variance. ภาว น ศ ร ประภาน ก ล คณะเศรษฐศาสตร มหาว ทยาล ยธรรมศาสตร
Analysis of Variance ภาว น ศ ร ประภาน ก ล คณะเศรษฐศาสตร มหาว ทยาล ยธรรมศาสตร pawin@econ.tu.ac.th Outline Introduction One Factor Analysis of Variance Two Factor Analysis of Variance ANCOVA MANOVA Introduction
Chapter 4: Regression Models
Sales volume of company 1 Textbook: pp. 129-164 Chapter 4: Regression Models Money spent on advertising 2 Learning Objectives After completing this chapter, students will be able to: Identify variables,
Bayesian Analysis LEARNING OBJECTIVES. Calculating Revised Probabilities. Calculating Revised Probabilities. Calculating Revised Probabilities
Valua%on and pricing (November 5, 2013) LEARNING OBJECTIVES Lecture 7 Decision making (part 3) Regression theory Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com 1. List the steps
Simple Linear Regression
Simple Linear Regression In simple linear regression we are concerned about the relationship between two variables, X and Y. There are two components to such a relationship. 1. The strength of the relationship.
Applied Regression. Applied Regression. Chapter 2 Simple Linear Regression. Hongcheng Li. April, 6, 2013
Applied Regression Chapter 2 Simple Linear Regression Hongcheng Li April, 6, 2013 Outline 1 Introduction of simple linear regression 2 Scatter plot 3 Simple linear regression model 4 Test of Hypothesis
LI EAR REGRESSIO A D CORRELATIO
CHAPTER 6 LI EAR REGRESSIO A D CORRELATIO Page Contents 6.1 Introduction 10 6. Curve Fitting 10 6.3 Fitting a Simple Linear Regression Line 103 6.4 Linear Correlation Analysis 107 6.5 Spearman s Rank Correlation
Inference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
Data Science for Engineers Department of Computer Science and Engineering Indian Institute of Technology, Madras
Data Science for Engineers Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture 36 Simple Linear Regression Model Assessment So, welcome to the second lecture on
A Statistical-Dynamical Seasonal Forecast of US Landfalling TC Activity
A Statistical-Dynamical Seasonal Forecast of US Landfalling TC Activity Johnny Chan and Samson K S Chiu Guy Carpenter Asia-Pacific Climate Impact Centre City University of Hong Kong Research sponsored
Notes for Week 13 Analysis of Variance (ANOVA) continued WEEK 13 page 1
Notes for Wee 13 Analysis of Variance (ANOVA) continued WEEK 13 page 1 Exam 3 is on Friday May 1. A part of one of the exam problems is on Predictiontervals : When randomly sampling from a normal population
MS&E 226: Small Data
MS&E 226: Small Data Lecture 15: Examples of hypothesis tests (v5) Ramesh Johari ramesh.johari@stanford.edu 1 / 32 The recipe 2 / 32 The hypothesis testing recipe In this lecture we repeatedly apply the
Basic Business Statistics, 10/e
Chapter 4 4- Basic Business Statistics th Edition Chapter 4 Introduction to Multiple Regression Basic Business Statistics, e 9 Prentice-Hall, Inc. Chap 4- Learning Objectives In this chapter, you learn: