Using JMP with a Specific


 Alexia Anthony
 2 years ago
 Views:
Transcription
1 1 Using JMP with a Specific Example of Regression Ying Liu 10/21/ 2009 Objectives 2 Exploratory data analysis Simple liner regression Polynomial regression How to fit a multiple regression model How to fit a multiple regression model with interactions How to generate and compare candidate models Regression diagnostics Evaluating the assumptions of regression Recommendations 1
2 Brief Information about JMP October was the 20th anniversary of JMP's first release. A product of SAS. JMP grows fast because of its interactive, comprehensive, highly visual. 3 JMP discovery statistical software and JMP Genomics The functionality of JMP is built around four datadriven tasks: Data Access Data Management Data Analysis Data Presentation JMP files (.jmp.jsl,.jrn,.jrp,.jmpprj, jmpmenu) 4 JMP data .jmp, (data file : open all kinds of formats) JMP script.jsl (can be saved with.txt) JMP journal.jrn JMP report.jrp JMP project.jmpprj JMP menu archives.jmpmenu 2
3 JMP 5 JMP 6 3
4 Exploratory Data Analysis 7 Correlation analysis is used to examine and describe the linear relationship between two continuous variables. Pearson correlation coefficient, r STRONG WEAK STRONG Exploratory Data Analysis 8 r=0 r=
5 Exploratory Data Analysis
6 Misundersatnding the Correlation Coefficient 11 A common error is that using correlation between two variables to conclude a causeand effect relationship. An example: Crime rate # of policeman City A 2 20 City B 5 25 Q: Is it true that the more policemen cause high crime rate? Correlation does not necessarily imply causation. Exploring data with Scatterplots and Correlations Look for relationship using scatterplots. Add correlation coefficients to further explore the possible relationships. Data: Fitness.JMP 12 The Variables of interest are listed below: Name Name of runner Gender gender of the runner Oxy oxygen consumption (higher Oxy is associated with better aerobic fitness) Runtime time to run 1.5 miles in mins Age age of runner Weight weight of the runner (kg) RunPulse pulse rate at the end of the run RstPulse resting pulse rate MaxPulse max. pulse rate during the run. 6
7 Exploring data with Scatterplots and Correlations 13 Exploring data with Scatterplots and Correlations 14 Note: These calculations omit observations that are missing data for any variable; when this occurs, JMP indicates the number of omitted observations at the bottom of the table. 7
8 Exploring data with Scatterplots and Correlations 15 Exploring data with Scatterplots and Correlations 16 8
9 Exploring data with Scatterplots and Correlations 17 Simple Linear Regression 18 Objectives Distinguish between one_way ANOVA and simple linear regression. Understand the principles of simple linear regression. Fit a simple linear regression model. Interpret simple linear regression result from JMP. 9
10 ANOVA versus Regression 19 Continuous response Categorical Predictor Continuous Predictor Oneway ANOVA Simple Linear Regression Simple Linear Regression Model The equation: Y= β 0 + β 1 X+ ε 20 Where Y is the response variable. X is the predictor variable. β 0 is the intercept parameter, which corresponding to the value of the response variable when the predictor is 0. β 1 is the slope parameter, which corresponding to the change in the response variable given oneunit change in the predictor variable. ε is an error term representing deviation of Y about the line defined by β 0 + β 1 X. 10
11 Simple Linear Regression ModeVariability 21 The estimates of the unknown population parameters β 0 and β 1, are obtained by the method of least squares Unexplained variability: the error sum of squares SSE ( Y ˆ i Yi ) Explained variability: The model sum of squares SSM 2 ( ˆ Y ) Y i Total variability : The corrected total sum of squares 2 ( Y ) Y i 2 The Baseline Model 22 The baseline model: Yˆ = ˆ β 0 The intercept is the sample mean of the response. To determine whether the predictor variable explains a significant amount of variability in the response variable, the simple linear model is compared to the baseline model. 11
12 Model Hypothesis Test Null hypothesis 23 H 0 : β 1 =0 Alternative hypothesis H a : β 1 0 Fitting a Simple Linear Regression 24 12
13 Fitting a Simple Linear Regression 25 Fitting a Simple Linear Regression Linear Fit Oxy = *Runtime 26 13
14 Fitting a Simple Linear Regression 27 Polynomial Regression A simple linear regression model might inadequately characterize the relationship between predictor and response variables if the association between these variables does not follow a straight. 28 Consider a polynomial regression when the residuals from a simple linear regression model exhibit curvature. In general, building higherorder polynomials is not recommended e except as it might be suggested ed by the pattern of the residuals. 14
15 Hierarchical Models In polynomial regression, if a higherorder term is statistically significant, all lowerorder terms must be included in the final model. This structure maintains model hierarchy. 29 The predictor x has a calculated pvalue< The pvalue for x 2 is The pvalue for x 3 is The pvalue for x 4 is If alpha=0.05, which parameters should be included in your model? A. y=x 2, x 3, x 4 B. y=x, x 3 C. y= x, x 2, x 3 D. y= x, x 2, x 3, x 4 Fitting a Polynomial Regression Model Data set: Cars.jmp Response: MidPrice Average price of a base model and model with all the extra options. 30 Predictor: HwyMPG Average highway miles per gallon (EPA rating). 15
16 Fitting a Polynomial Regression Model 31 Steps to obtain the scatterplots
17 Fitting a Polynomial Regression Model 33 Fitting a Polynomial Regression Model 34 Can we claim the model as below? MidPrice = *HwyMPG 17
18 Res Residual Plot 35 HwyMPG Lack of Fit Test 36 H 0 : The model is adequate (no lack of fit). H a : The model is not adequate (lack of fit). Reject null hypothesis 18
19 Fitting HigherOrder Model 37 Fitting HigherOrder Model quadratic 38 19
20 Fitting HigherOrder Model without vans 39 Fitting HigherOrder Model without vans 40 20
21 Fitting HigherOrder Model without vans 41 The adjusted Rsquare has a value of about 56%, which is a bit larger than that for the quadratic model fit the entire data set (31%) Multiple Regression Model Model: Y=β 0 + β 1 X 1 + β k X k +ε 42 Model Hypothesis Test H 0 : β 0 = β 1 =β k H a : Not all βs equal zero. 21
22 Multiple Linear Regression vs. Simple Linear Regression Main Advantage Enables an investigation of the relationship between Y and several independent variables simultaneously. 43 Main Disadvantages Increased complexity makes it more difficult to. Ascertain which model is best Interpret epe the models. odes Model Comparison Statistics JMP software provides several ways to compare competing regression models including 44 Mean square Error (MSE) Smaller is better. AdjustedR bigger is better Akaike s Information Criterionsmaller is better. Mallow s C p look for models with C p <p, where equals Mallow s C p look for models with C p p, where equals the # of parameters in the model, including the intercept. 22
23 Fitting HigherOrder Model without vans 45 Backward Stepwise Regression 46 23
24 Backward Stepwise Regression 47 Backward Stepwise Regression 48 24
25 Backward Stepwise Regression 49 Backward Stepwise Regression 50 25
26 Forward Stepwise Regression 51 Backward Stepwise Regression 52 26
27 Backward and Froward Stepwise Regression 53 SSE DF MSE R 2 Adj R 2 Cp AICc Backward Forward Assumptions for Linear Rgression 54 The variables are related linearly. The errors are normally distributed with a mean zero. The errors have a constant variance. The errors are independent. 27
28 Two Types of Plots Are Useful to VerifyAassumptions 55 A scatterplot of the residuals versus the predicted values is useful for identifying problematic patterns in the residuals. A histogram and normal quantile plot are useful for identifying potential problems with nonnormality. For multiple regression, leverage plots are recommended. Two Types of Plots Are Useful to VerifyAassumptions 56 A scatterplot of the residuals versus the predicted values is useful for identifying problematic patterns in the residuals. A histogram and normal quantile plot are useful for identifying potential problems with nonnormality. For multiple regression, leverage plots are recommended. 28
29 A recommendation when Assumptions Have Not Been Met Data : Cars.jmp Response: MidPrice Predictor: CityMPG 57 Two Types of Plots Are Useful to VerifyAassumptions 58 29
30 Two Types of Plots Are Useful to VerifyAassumptions 59 Residual vs. City MPG Two Types of Plots Are Useful to Verify Assumptions 60 30
31 Transforming Variables 61 Variable transformations can be useful when one or more of the assumptions of linear regression are violated. They are typically used to Linearize the relationship between X and Y. Stablize the variance of the residuals Normalize the residuals. Transforming Variables 62 Common transformation include, but not limited to, the square, square root, log, and reciprocal of the response. Not all transformation will correct a given situation. The analysis is performed on the transformed variable, and the result must be interpreted t accordingly. 31
32 Transforming Variables Questions? 32
Yiming Peng, Department of Statistics. February 12, 2013
Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop
More informationSimple 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 Statistical model for linear regression Estimating
More informationSimple Linear Regression Chapter 11
Simple Linear Regression Chapter 11 Rationale Frequently decisionmaking situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related
More informationwhere b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.
Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes
More informationThe scatterplot indicates a positive linear relationship between waist size and body fat percentage:
STAT E150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the
More informationData and Regression Analysis. Lecturer: Prof. Duane S. Boning. Rev 10
Data and Regression Analysis Lecturer: Prof. Duane S. Boning Rev 10 1 Agenda 1. Comparison of Treatments (One Variable) Analysis of Variance (ANOVA) 2. Multivariate Analysis of Variance Model forms 3.
More informationCORRELATION AND SIMPLE REGRESSION ANALYSIS USING SAS IN DAIRY SCIENCE
CORRELATION AND SIMPLE REGRESSION ANALYSIS USING SAS IN DAIRY SCIENCE A. K. Gupta, Vipul Sharma and M. Manoj NDRI, Karnal132001 When analyzing farm records, simple descriptive statistics can reveal a
More informationA. Karpinski
Chapter 3 Multiple Linear Regression Page 1. Overview of multiple regression 32 2. Considering relationships among variables 33 3. Extending the simple regression model to multiple predictors 34 4.
More informationSELFTEST: SIMPLE REGRESSION
ECO 22000 McRAE SELFTEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an inclass examination, but you should be able to describe the procedures
More informationPractice 3 SPSS. Partially based on Notes from the University of Reading:
Practice 3 SPSS Partially based on Notes from the University of Reading: http://www.reading.ac.uk Simple Linear Regression A simple linear regression model is fitted when you want to investigate whether
More information1. ε is normally distributed with a mean of 0 2. the variance, σ 2, is constant 3. All pairs of error terms are uncorrelated
STAT E150 Statistical Methods Residual Analysis; Data Transformations The validity of the inference methods (hypothesis testing, confidence intervals, and prediction intervals) depends on the error term,
More informationMultiple Regression in SPSS STAT 314
Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan
More informatione = random error, assumed to be normally distributed with mean 0 and standard deviation σ
1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.
More informationData Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression
Data Mining and Data Warehousing Henryk Maciejewski Data Mining Predictive modelling: regression Algorithms for Predictive Modelling Contents Regression Classification Auxiliary topics: Estimation of prediction
More information5. Multiple regression
5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationRegression in SPSS. Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology
Regression in SPSS Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology John P. Bentley Department of Pharmacy Administration University of
More informationMultiple Regression YX1 YX2 X1X2 YX1.X2
Multiple Regression Simple or total correlation: relationship between one dependent and one independent variable, Y versus X Coefficient of simple determination: r (or r, r ) YX YX XX Partial correlation:
More informationCollinearity of independent variables. Collinearity is a condition in which some of the independent variables are highly correlated.
Collinearity of independent variables Collinearity is a condition in which some of the independent variables are highly correlated. Why is this a problem? Collinearity tends to inflate the variance of
More informationInternational Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA Email: peverso1@swarthmore.edu 1. Introduction
More informationOutline. Topic 4  Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4  Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test  Fall 2013 R 2 and the coefficient of correlation
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a stepbystep guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
More informationUNDERSTANDING MULTIPLE REGRESSION
UNDERSTANDING Multiple regression analysis (MRA) is any of several related statistical methods for evaluating the effects of more than one independent (or predictor) variable on a dependent (or outcome)
More information0.1 Multiple Regression Models
0.1 Multiple Regression Models We will introduce the multiple Regression model as a mean of relating one numerical response variable y to two or more independent (or predictor variables. We will see different
More informationWe extended the additive model in two variables to the interaction model by adding a third term to the equation.
Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic
More informationResiduals. Residuals = ª Department of ISM, University of Alabama, ST 260, M23 Residuals & Minitab. ^ e i = y i  y i
A continuation of regression analysis Lesson Objectives Continue to build on regression analysis. Learn how residual plots help identify problems with the analysis. M231 M232 Example 1: continued Case
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationCHAPTER 2 AND 10: Least Squares Regression
CHAPTER 2 AND 0: Least Squares Regression In chapter 2 and 0 we will be looking at the relationship between two quantitative variables measured on the same individual. General Procedure:. Make a scatterplot
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationThe general form of the PROC GLM statement is
Linear Regression Analysis using PROC GLM Regression analysis is a statistical method of obtaining an equation that represents a linear relationship between two variables (simple linear regression), or
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More informationRegression, least squares
Regression, least squares Joe Felsenstein Department of Genome Sciences and Department of Biology Regression, least squares p.1/24 Fitting a straight line X Two distinct cases: The X values are chosen
More informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationRNR / ENTO Assumptions for Simple Linear Regression
74 RNR / ENTO 63 Assumptions for Simple Linear Regression Statistical statements (hypothesis tests and CI estimation) with least squares estimates depends on 4 assumptions:. Linearity of the mean responses
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationPrediction and Confidence Intervals in Regression
Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SHDH. Hours are detailed in the syllabus.
More informationStatistical Modelling in Stata 5: Linear Models
Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 08/11/2016 Structure This Week What is a linear model? How
More informationMultiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear. In the main dialog box, input the dependent variable and several predictors.
More informationˆ Y i = X 1i
For the Parameter Model Y i = β 0 + β 1 X 1i + ε i It is assumed that the error vector is: ε i ~ NID(0,σ ) The errors Normally and Independently Distributed with a constant variance (σ ) throughout the
More informationThe aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree
PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and
More informationChapter 11: Linear Regression  Inference in Regression Analysis  Part 2
Chapter 11: Linear Regression  Inference in Regression Analysis  Part 2 Note: Whether we calculate confidence intervals or perform hypothesis tests we need the distribution of the statistic we will use.
More informationSoci708 Statistics for Sociologists
Soci708 Statistics for Sociologists Module 11 Multiple Regression 1 François Nielsen University of North Carolina Chapel Hill Fall 2009 1 Adapted from slides for the course Quantitative Methods in Sociology
More informationChapter 11: Two Variable Regression Analysis
Department of Mathematics Izmir University of Economics Week 1415 20142015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions
More informationNotes on Applied Linear Regression
Notes on Applied Linear Regression Jamie DeCoster Department of Social Psychology Free University Amsterdam Van der Boechorststraat 1 1081 BT Amsterdam The Netherlands phone: +31 (0)20 4448935 email:
More informationLecture 5: Correlation and Linear Regression
Lecture 5: Correlation and Linear Regression 3.5. (Pearson) correlation coefficient The correlation coefficient measures the strength of the linear relationship between two variables. The correlation is
More informationInference for Regression
Simple Linear Regression Inference for Regression The simple linear regression model Estimating regression parameters; Confidence intervals and significance tests for regression parameters Inference about
More informationRegression analysis in the Assistant fits a model with one continuous predictor and one continuous response and can fit two types of models:
This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. The simple regression procedure in the
More informationStatistics for Management IISTAT 362Final Review
Statistics for Management IISTAT 362Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to
More informationLectures 4&5 Program. 1. Residuals and diagnostics. 2. Variable selection
Lectures 4&5 Program 1. Residuals and diagnostics 2. Variable selection 1 Assumptions for linear regression y i = η i + ε i i = 1, 2,..., n 1. Linearity: η i = β 0 + β 1 x i1 + + β p x ip 2. Constant variance
More informationName: Student ID#: Serial #:
STAT 22 Business Statistics II Term3 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Department Of Mathematics & Statistics DHAHRAN, SAUDI ARABIA STAT 22: BUSINESS STATISTICS II Third Exam July, 202 9:20
More informationAP * Statistics Review. Linear Regression
AP * Statistics Review Linear Regression Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production
More informationLecture 18 Linear Regression
Lecture 18 Statistics Unit Andrew Nunekpeku / Charles Jackson Fall 2011 Outline 1 1 Situation  used to model quantitative dependent variable using linear function of quantitative predictor(s). Situation
More informationAn Intermediate Course in SPSS. Mr. Liberato Camilleri
An Intermediate Course in SPSS by Mr. Liberato Camilleri 3. Simple linear regression 3. Regression Analysis The model that is applicable in the simplest regression structure is the simple linear regression
More information12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2
PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand linear regression with a single predictor Understand how we assess the fit of a regression model Total Sum of Squares
More informationCorrelation Regression
Correlation Regression Διατμηματικό ΠΜΣ Επαγγελματική και Περιβαλλοντική ΥγείαΔιαχείριση και Οικονομική Αποτίμηση Δημήτρης Φουσκάκης Correlation To assess whether two variables are linearly associated,,
More informationStatistics II Final Exam  January Use the University stationery to give your answers to the following questions.
Statistics II Final Exam  January 2012 Use the University stationery to give your answers to the following questions. Do not forget to write down your name and class group in each page. Indicate clearly
More informationUsing Minitab for Regression Analysis: An extended example
Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to
More information12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2
PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand when to use multiple Understand the multiple equation and what the coefficients represent Understand different methods
More information5. Linear Regression
5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4
More informationAP Statistics Solutions to Packet 14
AP Statistics Solutions to Packet 4 Inference for Regression Inference about the Model Predictions and Conditions HW #,, 6, 7 4. AN ETINCT BEAST, I Archaeopteryx is an extinct beast having feathers like
More informationChapter 9. Section Correlation
Chapter 9 Section 9.1  Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation
More informationBy Hui Bian Office for Faculty Excellence
By Hui Bian Office for Faculty Excellence 1 Email: bianh@ecu.edu Phone: 3285428 Location: 2307 Old Cafeteria Complex 2 When want to predict one variable from a combination of several variables. When want
More informationIntroduction to proc glm
Lab 7: Proc GLM and oneway ANOVA STT 422: Summer, 2004 Vince Melfi SAS has several procedures for analysis of variance models, including proc anova, proc glm, proc varcomp, and proc mixed. We mainly will
More informationRegression in ANOVA. James H. Steiger. Department of Psychology and Human Development Vanderbilt University
Regression in ANOVA James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) 1 / 30 Regression in ANOVA 1 Introduction 2 Basic Linear
More informationE205 Final: Version B
Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random
More informationSTAT 350 Practice Final Exam Solution (Spring 2015)
PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects
More information2. Simple Linear Regression
Research methods  II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationSTAT 503 class: July 27, 2012 due: July 30, Lab 5: ANOVA, Linear Regression (10 pts. + 3 pts. Bonus)
STAT 503 class: July 27, 2012 due: July 30, 2012 Lab 5: ANOVA, Linear Regression (10 pts. + 3 pts. Bonus) Objectives Part 1: ANOVA 1.1) Oneway ANOVA 1.2) Residual Plot 1.3) TwoWay ANOVA (BONUS) Part
More informationChapter 8. Linear Regression. Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 8 Linear Regression Copyright 2012, 2008, 2005 Pearson Education, Inc. Fat Versus Protein: An Example The following is a scatterplot of total fat versus protein for 30 items on the Burger King
More informationInterpreting Multiple Regression: A Short Overview
Interpreting Multiple Regression: A Short Overview AbdelSalam G. AbdelSalam Laboratory for Interdisciplinary Statistical Analysis (LISA) Department of Statistics Virginia Polytechnic Institute and State
More informationPerform hypothesis testing
Multivariate hypothesis tests for fixed effects Testing homogeneity of level1 variances In the following sections, we use the model displayed in the figure below to illustrate the hypothesis tests. Partial
More informationInterpreting Multiple Regression
Fall Semester, 2001 Statistics 621 Lecture 5 Robert Stine 1 Preliminaries Interpreting Multiple Regression Project and assignments Hope to have some further information on project soon. Due date for Assignment
More informationPASS Sample Size Software. Linear Regression
Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes
More informationAMS7: WEEK 8. CLASS 1. Correlation Monday May 18th, 2015
AMS7: WEEK 8. CLASS 1 Correlation Monday May 18th, 2015 Type of Data and objectives of the analysis Paired sample data (Bivariate data) Determine whether there is an association between two variables This
More information1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ
STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More informationAssumptions in the Normal Linear Regression Model. A2: The error terms (and thus the Y s at each X) have constant variance.
Assumptions in the Normal Linear Regression Model A1: There is a linear relationship between X and Y. A2: The error terms (and thus the Y s at each X) have constant variance. A3: The error terms are independent.
More informationSection 14 Simple Linear Regression: Introduction to Least Squares Regression
Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship
More informationThis chapter will demonstrate how to perform multiple linear regression with IBM SPSS
CHAPTER 7B Multiple Regression: Statistical Methods Using IBM SPSS This chapter will demonstrate how to perform multiple linear regression with IBM SPSS first using the standard method and then using the
More informationSIMPLE REGRESSION ANALYSIS
SIMPLE REGRESSION ANALYSIS Introduction. Regression analysis is used when two or more variables are thought to be systematically connected by a linear relationship. In simple regression, we have only two
More informationMultiple Regression  Selecting the Best Equation An Example Techniques for Selecting the "Best" Regression Equation
Multiple Regression  Selecting the Best Equation When fitting a multiple linear regression model, a researcher will likely include independent variables that are not important in predicting the dependent
More informationInference in Regression Analysis. Dr. Frank Wood
Inference in Regression Analysis Dr. Frank Wood Inference in the Normal Error 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
More informationThe Simple Linear Regression Model: Specification and Estimation
Chapter 3 The Simple Linear Regression Model: Specification and Estimation 3.1 An Economic Model Suppose that we are interested in studying the relationship between household income and expenditure on
More information11/20/2014. Correlational research is used to describe the relationship between two or more naturally occurring variables.
Correlational research is used to describe the relationship between two or more naturally occurring variables. Is age related to political conservativism? Are highly extraverted people less afraid of rejection
More informationYou have data! What s next?
You have data! What s next? Data Analysis, Your Research Questions, and Proposal Writing Zoo 511 Spring 2014 Part 1:! Research Questions Part 1:! Research Questions Write down > 2 things you thought were
More informationpsyc3010 lecture 8 standard and hierarchical multiple regression last week: correlation and regression Next week: moderated regression
psyc3010 lecture 8 standard and hierarchical multiple regression last week: correlation and regression Next week: moderated regression 1 last week this week last week we revised correlation & regression
More informationSTA 4163 Lecture 10: Practice Problems
STA 463 Lecture 0: Practice Problems Problem.0: A study was conducted to determine whether a student's final grade in STA406 is linearly related to his or her performance on the MATH ability test before
More information7. Tests of association and Linear Regression
7. Tests of association and Linear Regression In this chapter we consider 1. Tests of Association for 2 qualitative variables. 2. Measures of the strength of linear association between 2 quantitative variables.
More informationMulticollinearity in Regression Models
00 Jeeshim and KUCC65. (0030509) Multicollinearity.doc Introduction Multicollinearity in Regression Models Multicollinearity is a high degree of correlation (linear dependency) among several independent
More informationRegression Analysis. Data Calculations Output
Regression Analysis In an attempt to find answers to questions such as those posed above, empirical labour economists use a useful tool called regression analysis. Regression analysis is essentially a
More informationLecture 7 Linear Regression Diagnostics
Lecture 7 Linear Regression Diagnostics BIOST 515 January 27, 2004 BIOST 515, Lecture 6 Major assumptions 1. The relationship between the outcomes and the predictors is (approximately) linear. 2. The error
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationSydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.
Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under
More informationRegression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between
More informationCHAPTER 9: SERIAL CORRELATION
Serial correlation (or autocorrelation) is the violation of Assumption 4 (observations of the error term are uncorrelated with each other). Pure Serial Correlation This type of correlation tends to be
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationMS&E 226: Small Data. Lecture 17: Additional topics in inference (v1) Ramesh Johari
MS&E 226: Small Data Lecture 17: Additional topics in inference (v1) Ramesh Johari ramesh.johari@stanford.edu 1 / 34 Warnings 2 / 34 Modeling assumptions: Regression Remember that most of the inference
More informationA short primer on residual plots
Chapter 24 A short primer on residual plots Contents 24.1 Linear Regression................................... 1598 24.2 ANOVA residual plots................................. 1599 24.3 Logistic Regression
More information