We extended the additive model in two variables to the interaction model by adding a third term to the equation.
|
|
- Polly Johnston
- 8 years ago
- Views:
Transcription
1 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 model by adding a second term to the equation: E(Y ) = β 0 + β 1 x + β 2 x 2. This a special case of the two-variable model with x 1 = x and x 2 = x 2. E(Y ) = β 0 + β 1 x 1 + β 2 x 2 1 / 16 Multiple Linear Regression Quadratic Models
2 Example: immune system and exercise x = maximal oxygen uptake (VO 2 max, ml/(kg min)); y = immunoglobulin level (IgG, mg/dl); data for 30 subjects (AEROBIC.txt). Get the data and plot them: aerobic <- read.table("text/exercises&examples/aerobic.txt", header = TRUE) plot(aerobic[, c("maxoxy", "IGG")]) Slight curvature suggests a linear model may not fit. 2 / 16 Multiple Linear Regression Quadratic Models
3 Check the linear model: plot(lm(igg ~ MAXOXY, aerobic)) Graph of residuals against fitted values shows definite curvature. Fit and summarize the quadratic model: aerobiclm <- lm(igg ~ MAXOXY + I(MAXOXY^2), aerobic) summary(aerobiclm) 3 / 16 Multiple Linear Regression Quadratic Models
4 Output Call: lm(formula = IGG ~ MAXOXY + I(MAXOXY^2), data = aerobic) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) ** MAXOXY e-05 *** I(MAXOXY^2) ** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 27 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 27 DF, p-value: < 2.2e-16 4 / 16 Multiple Linear Regression Quadratic Models
5 The quadratic term I(MAXOXY^2) is significant, so we reject the null hypothesis that the linear model is acceptable. The quadratic term is negative, which is consistent with the concavity of the curve. The other two t-ratios test irrelevant hypotheses, because the quadratic term is important. Extrapolation: the fitted curve has a maximum at MAXOXY = and declines for higher MAXOXY, which seems unlikely to represent the real relationship. 5 / 16 Multiple Linear Regression Quadratic Models
6 An alternative analysis The graph of IGG against log(maxoxy) is more linear: with(aerobic, plot(log(maxoxy), IGG)) aerobiclm2 <- lm(igg ~ log(maxoxy), aerobic) summary(aerobiclm2) with(aerobic, plot(maxoxy, IGG)) with(aerobic, lines(sort(maxoxy), fitted(aerobiclm)[order(maxoxy)], col = "blue")) with(aerobic, lines(sort(maxoxy), fitted(aerobiclm2)[order(maxoxy)], col = "red")) The fitted curve continues to increase indefinitely, but with diminishing slope. 6 / 16 Multiple Linear Regression Quadratic Models
7 Output Call: lm(formula = IGG ~ log(maxoxy), data = aerobic) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-15 *** log(maxoxy) < 2e-16 *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 28 degrees of freedom Multiple R-squared: 0.934, Adjusted R-squared: F-statistic: on 1 and 28 DF, p-value: < 2.2e-16 7 / 16 Multiple Linear Regression Quadratic Models
8 More Complex Models ST 430/514 Complete second-order model When the first-order model E(Y ) = β 0 + β 1 x 1 + β 2 x 2 is inadequate, the interaction model E(Y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 may be better, but sometimes a complete second-order model is needed: E(Y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 + β 4 x β 5 x / 16 Multiple Linear Regression More Complex Models
9 Example: cost of shipping packages Get the data and plot them: express <- read.table("text/exercises&examples/express.txt", header = TRUE) pairs(express) Fit the complete second-order model and summarize it: expresslm <- lm(cost ~ Weight * Distance + I(Weight^2) + I(Distance^2), express) summary(expresslm) plot(expresslm) 9 / 16 Multiple Linear Regression More Complex Models
10 Output ST 430/514 Call: lm(formula = Cost ~ Weight * Distance + I(Weight^2) + I(Distance^2), data = express) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 8.270e e Weight e e ** Distance 4.021e e I(Weight^2) 8.975e e *** I(Distance^2) 1.507e e Weight:Distance 7.327e e e-08 *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 14 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 5 and 14 DF, p-value: 5.371e / 16 Multiple Linear Regression More Complex Models
11 Qualitative Variables A qualitative variable (or factor) is one that indicates membership of different categories. E.g., a person s gender = male or female: a qualitative variable with two levels, indicating membership of one of two categories. E.g., package type = Fragile, Semifragile, or Durable: three levels, corresponding to three categories. 11 / 16 Multiple Linear Regression More Complex Models
12 We code a qualitative variable using indicator (dummy) variables: Choose one level to use as a base or reference level, say male or Durable. For each other level, create a variable { 1 if this item is in this category x j = 0 otherwise. For gender, there is only one other category, so the only indicator variable is { 1 for a female x = 0 for a male. 12 / 16 Multiple Linear Regression More Complex Models
13 For packages, there are two other categories, so the indicator variables are { 1 for a Fragile package x Fragile = 0 otherwise, { 1 for a Semifragile package x Semifragile = 0 otherwise, For any item, at most one of the indicator variables is non-zero, indicating a non-base category; if they are all zero, the item belongs to the base category. 13 / 16 Multiple Linear Regression More Complex Models
14 Example: shipment cost of packages, by type. Get the data and plot them: cargo <- read.table("text/exercises&examples/cargo.txt", header = TRUE) plot(cost ~ CARGO, cargo) Fit and summarize the model: cargolm <- lm(cost ~ CARGO, cargo) summary(cargolm) 14 / 16 Multiple Linear Regression More Complex Models
15 Output Call: lm(formula = COST ~ CARGO, data = cargo) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) * CARGOFragile e-05 *** CARGOSemiFrag ** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 12 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 12 DF, p-value: / 16 Multiple Linear Regression More Complex Models
16 Note that the intercept is the fitted value for CARGOFragile = 0 and CARGOSemiFrag = 0; that is, for Durable packages. The coefficients of CARGOFragile and CARGOSemiFrag measure the differences between those categories and Durable. The overall model F -test is the same as the analysis of variance test: cargoaov <- aov(cost ~ CARGO, cargo) summary(cargoaov) Output Df Sum Sq Mean Sq F value Pr(>F) CARGO *** Residuals Signif. codes: 0 *** ** 0.01 * / 16 Multiple Linear Regression More Complex Models
Comparing Nested Models
Comparing Nested Models ST 430/514 Two models are nested if one model contains all the terms of the other, and at least one additional term. The larger model is the complete (or full) model, and the smaller
More informationInteraction between quantitative predictors
Interaction between quantitative predictors In a first-order model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors
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 informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Linear Models in R Regression Regression analysis is the appropriate
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 1-propZint 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 informationUsing R for Linear Regression
Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a
More informationEDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION
EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION EDUCATION AND VOCABULARY 5-10 hours of input weekly is enough to pick up a new language (Schiff & Myers, 1988). Dutch children spend 5.5 hours/day
More informationN-Way Analysis of Variance
N-Way Analysis of Variance 1 Introduction A good example when to use a n-way ANOVA is for a factorial design. A factorial design is an efficient way to conduct an experiment. Each observation has data
More informationBasic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
More informationANOVA. February 12, 2015
ANOVA February 12, 2015 1 ANOVA models Last time, we discussed the use of categorical variables in multivariate regression. Often, these are encoded as indicator columns in the design matrix. In [1]: %%R
More informationPsychology 205: Research Methods in Psychology
Psychology 205: Research Methods in Psychology Using R to analyze the data for study 2 Department of Psychology Northwestern University Evanston, Illinois USA November, 2012 1 / 38 Outline 1 Getting ready
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a step-by-step 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 informationGeneralized Linear Models
Generalized Linear Models We have previously worked with regression models where the response variable is quantitative and normally distributed. Now we turn our attention to two types of models where the
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 informationFactors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
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 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 information5. Linear Regression
5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4
More informationMIXED MODEL ANALYSIS USING R
Research Methods Group MIXED MODEL ANALYSIS USING R Using Case Study 4 from the BIOMETRICS & RESEARCH METHODS TEACHING RESOURCE BY Stephen Mbunzi & Sonal Nagda www.ilri.org/rmg www.worldagroforestrycentre.org/rmg
More informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova
More informationDEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,
More informationTesting for Lack of Fit
Chapter 6 Testing for Lack of Fit How can we tell if a model fits the data? If the model is correct then ˆσ 2 should be an unbiased estimate of σ 2. If we have a model which is not complex enough to fit
More informationLucky vs. Unlucky Teams in Sports
Lucky vs. Unlucky Teams in Sports Introduction Assuming gambling odds give true probabilities, one can classify a team as having been lucky or unlucky so far. Do results of matches between lucky and unlucky
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationLets suppose we rolled a six-sided die 150 times and recorded the number of times each outcome (1-6) occured. The data is
In this lab we will look at how R can eliminate most of the annoying calculations involved in (a) using Chi-Squared tests to check for homogeneity in two-way tables of catagorical data and (b) computing
More informationE(y i ) = x T i β. yield of the refined product as a percentage of crude specific gravity vapour pressure ASTM 10% point ASTM end point in degrees F
Random and Mixed Effects Models (Ch. 10) Random effects models are very useful when the observations are sampled in a highly structured way. The basic idea is that the error associated with any linear,
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 informationMULTIPLE REGRESSION EXAMPLE
MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if
More informationWeek 5: Multiple Linear Regression
BUS41100 Applied Regression Analysis Week 5: Multiple Linear Regression Parameter estimation and inference, forecasting, diagnostics, dummy variables Robert B. Gramacy The University of Chicago Booth School
More informationA Handbook of Statistical Analyses Using R. Brian S. Everitt and Torsten Hothorn
A Handbook of Statistical Analyses Using R Brian S. Everitt and Torsten Hothorn CHAPTER 6 Logistic Regression and Generalised Linear Models: Blood Screening, Women s Role in Society, and Colonic Polyps
More informationModule 5: Multiple Regression Analysis
Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College
More informationStat 5303 (Oehlert): Tukey One Degree of Freedom 1
Stat 5303 (Oehlert): Tukey One Degree of Freedom 1 > catch
More informationKSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
More informationRegression step-by-step using Microsoft Excel
Step 1: Regression step-by-step using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression
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 informationPremaster Statistics Tutorial 4 Full solutions
Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for
More informationn + n log(2π) + n log(rss/n)
There is a discrepancy in R output from the functions step, AIC, and BIC over how to compute the AIC. The discrepancy is not very important, because it involves a difference of a constant factor that cancels
More informationMultivariate Logistic Regression
1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation
More informationIndependent t- Test (Comparing Two Means)
Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent
More informationTime Series Analysis
Time Series 1 April 9, 2013 Time Series Analysis This chapter presents an introduction to the branch of statistics known as time series analysis. Often the data we collect in environmental studies is collected
More informationExchange Rate Regime Analysis for the Chinese Yuan
Exchange Rate Regime Analysis for the Chinese Yuan Achim Zeileis Ajay Shah Ila Patnaik Abstract We investigate the Chinese exchange rate regime after China gave up on a fixed exchange rate to the US dollar
More information11. Analysis of Case-control Studies Logistic Regression
Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationMarginal Person. Average Person. (Average Return of College Goers) Return, Cost. (Average Return in the Population) (Marginal Return)
1 2 3 Marginal Person Average Person (Average Return of College Goers) Return, Cost (Average Return in the Population) 4 (Marginal Return) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
More informationRegression Analysis (Spring, 2000)
Regression Analysis (Spring, 2000) By Wonjae Purposes: a. Explaining the relationship between Y and X variables with a model (Explain a variable Y in terms of Xs) b. Estimating and testing the intensity
More informationWeek TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480
1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,
More information2. Regression and Correlation. Simple Linear Regression Software: R
2. Regression and Correlation Simple Linear Regression Software: R Create txt file from SAS data set data _null_; file 'C:\Documents and Settings\sphlab\Desktop\slr1.txt'; set temp; put input day:date7.
More informationLecture 11: Confidence intervals and model comparison for linear regression; analysis of variance
Lecture 11: Confidence intervals and model comparison for linear regression; analysis of variance 14 November 2007 1 Confidence intervals and hypothesis testing for linear regression Just as there was
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.
ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall
More informationMSwM examples. Jose A. Sanchez-Espigares, Alberto Lopez-Moreno Dept. of Statistics and Operations Research UPC-BarcelonaTech.
MSwM examples Jose A. Sanchez-Espigares, Alberto Lopez-Moreno Dept. of Statistics and Operations Research UPC-BarcelonaTech February 24, 2014 Abstract Two examples are described to illustrate the use of
More informationMODEL I: DRINK REGRESSED ON GPA & MALE, WITHOUT CENTERING
Interpreting Interaction Effects; Interaction Effects and Centering Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised February 20, 2015 Models with interaction effects
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
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 informationDifference of Means and ANOVA Problems
Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly
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 informationChicago Insurance Redlining - a complete example
Chapter 12 Chicago Insurance Redlining - a complete example In a study of insurance availability in Chicago, the U.S. Commission on Civil Rights attempted to examine charges by several community organizations
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 informationModule 5: Statistical Analysis
Module 5: Statistical Analysis To answer more complex questions using your data, or in statistical terms, to test your hypothesis, you need to use more advanced statistical tests. This module reviews the
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informationGetting Correct Results from PROC REG
Getting Correct Results from PROC REG Nathaniel Derby, Statis Pro Data Analytics, Seattle, WA ABSTRACT PROC REG, SAS s implementation of linear regression, is often used to fit a line without checking
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 informationStat 412/512 CASE INFLUENCE STATISTICS. Charlotte Wickham. stat512.cwick.co.nz. Feb 2 2015
Stat 412/512 CASE INFLUENCE STATISTICS Feb 2 2015 Charlotte Wickham stat512.cwick.co.nz Regression in your field See website. You may complete this assignment in pairs. Find a journal article in your field
More informationANALYSIS OF TREND CHAPTER 5
ANALYSIS OF TREND CHAPTER 5 ERSH 8310 Lecture 7 September 13, 2007 Today s Class Analysis of trends Using contrasts to do something a bit more practical. Linear trends. Quadratic trends. Trends in SPSS.
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 informationApplied Statistics. J. Blanchet and J. Wadsworth. Institute of Mathematics, Analysis, and Applications EPF Lausanne
Applied Statistics J. Blanchet and J. Wadsworth Institute of Mathematics, Analysis, and Applications EPF Lausanne An MSc Course for Applied Mathematicians, Fall 2012 Outline 1 Model Comparison 2 Model
More informationThis can dilute the significance of a departure from the null hypothesis. We can focus the test on departures of a particular form.
One-Degree-of-Freedom Tests Test for group occasion interactions has (number of groups 1) number of occasions 1) degrees of freedom. This can dilute the significance of a departure from the null hypothesis.
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 informationMGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal
MGT 267 PROJECT Forecasting the United States Retail Sales of the Pharmacies and Drug Stores Done by: Shunwei Wang & Mohammad Zainal Dec. 2002 The retail sale (Million) ABSTRACT The present study aims
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More informationA Predictive Model for NFL Rookie Quarterback Fantasy Football Points
A Predictive Model for NFL Rookie Quarterback Fantasy Football Points Steve Bronder and Alex Polinsky Duquesne University Economics Department Abstract This analysis designs a model that predicts NFL rookie
More informationLecture 8: Gamma regression
Lecture 8: Gamma regression Claudia Czado TU München c (Claudia Czado, TU Munich) ZFS/IMS Göttingen 2004 0 Overview Models with constant coefficient of variation Gamma regression: estimation and testing
More information2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or
Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.$ and Sales $: 1. Prepare a scatter plot of these data. The scatter plots for Adv.$ versus Sales, and Month versus
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationStock Price Forecasting Using Information from Yahoo Finance and Google Trend
Stock Price Forecasting Using Information from Yahoo Finance and Google Trend Selene Yue Xu (UC Berkeley) Abstract: Stock price forecasting is a popular and important topic in financial and academic studies.
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 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 E-mail: peverso1@swarthmore.edu 1. Introduction
More informationChapter 3 Quantitative Demand Analysis
Managerial Economics & Business Strategy Chapter 3 uantitative Demand Analysis McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. Overview I. The Elasticity Concept
More informationIntroduction to Multilevel Modeling Using HLM 6. By ATS Statistical Consulting Group
Introduction to Multilevel Modeling Using HLM 6 By ATS Statistical Consulting Group Multilevel data structure Students nested within schools Children nested within families Respondents nested within interviewers
More informationPOLYNOMIAL AND MULTIPLE REGRESSION. Polynomial regression used to fit nonlinear (e.g. curvilinear) data into a least squares linear regression model.
Polynomial Regression POLYNOMIAL AND MULTIPLE REGRESSION Polynomial regression used to fit nonlinear (e.g. curvilinear) data into a least squares linear regression model. It is a form of linear regression
More informationDiscussion Section 4 ECON 139/239 2010 Summer Term II
Discussion Section 4 ECON 139/239 2010 Summer Term II 1. Let s use the CollegeDistance.csv data again. (a) An education advocacy group argues that, on average, a person s educational attainment would increase
More informationExercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationAugust 2012 EXAMINATIONS Solution Part I
August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,
More informationSurvey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln. Log-Rank Test for More Than Two Groups
Survey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln Log-Rank Test for More Than Two Groups Prepared by Harlan Sayles (SRAM) Revised by Julia Soulakova (Statistics)
More informationSimple Methods and Procedures Used in Forecasting
Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria Jadamus-Hacura What Is Forecasting? Prediction of future events
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationCausal Forecasting Models
CTL.SC1x -Supply Chain & Logistics Fundamentals Causal Forecasting Models MIT Center for Transportation & Logistics Causal Models Used when demand is correlated with some known and measurable environmental
More informationWhat is R? R s Advantages R s Disadvantages Installing and Maintaining R Ways of Running R An Example Program Where to Learn More
Bob Muenchen, Author R for SAS and SPSS Users, Co-Author R for Stata Users muenchen.bob@gmail.com, http://r4stats.com What is R? R s Advantages R s Disadvantages Installing and Maintaining R Ways of Running
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationNonlinear Regression Functions. SW Ch 8 1/54/
Nonlinear Regression Functions SW Ch 8 1/54/ The TestScore STR relation looks linear (maybe) SW Ch 8 2/54/ But the TestScore Income relation looks nonlinear... SW Ch 8 3/54/ Nonlinear Regression General
More informationUse of deviance statistics for comparing models
A likelihood-ratio test can be used under full ML. The use of such a test is a quite general principle for statistical testing. In hierarchical linear models, the deviance test is mostly used for multiparameter
More informationCHAPTER 7. Exercise Solutions
CHAPTER 7 Exercise Solutions 141 Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 14 EXERCISE 7.1 (a) (b) When a GPA is increased by one unit, and other variables are held constant, average
More informationR: A Free Software Project in Statistical Computing
R: A Free Software Project in Statistical Computing Achim Zeileis Institut für Statistik & Wahrscheinlichkeitstheorie http://www.ci.tuwien.ac.at/~zeileis/ Acknowledgments Thanks: Alex Smola & Machine Learning
More informationThe Latent Variable Growth Model In Practice. Individual Development Over Time
The Latent Variable Growth Model In Practice 37 Individual Development Over Time y i = 1 i = 2 i = 3 t = 1 t = 2 t = 3 t = 4 ε 1 ε 2 ε 3 ε 4 y 1 y 2 y 3 y 4 x η 0 η 1 (1) y ti = η 0i + η 1i x t + ε ti
More informationChapter 7: Dummy variable regression
Chapter 7: Dummy variable regression Why include a qualitative independent variable?........................................ 2 Simplest model 3 Simplest case.............................................................
More informationTime-Series Regression and Generalized Least Squares in R
Time-Series Regression and Generalized Least Squares in R An Appendix to An R Companion to Applied Regression, Second Edition John Fox & Sanford Weisberg last revision: 11 November 2010 Abstract Generalized
More informationMultiple Linear Regression in Data Mining
Multiple Linear Regression in Data Mining Contents 2.1. A Review of Multiple Linear Regression 2.2. Illustration of the Regression Process 2.3. Subset Selection in Linear Regression 1 2 Chap. 2 Multiple
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 informationUnit 26: Small Sample Inference for One Mean
Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage
More information