Statistics and Quantitative Analysis U4320
|
|
- Osborn McBride
- 5 years ago
- Views:
Transcription
1 Statistics and Quantitative Analysis U3 Lecture 13: Explaining Variation Prof. Sharyn O Halloran Explaining Variation: Adjusted R (cont) Definition of Adjusted R So we'd like a measure like R, but one that takes into account the fact that adding extra variables always increases your explanatory power. The statistic we use for this is call the Adjusted R, and its formula is: n 1 R = 1 ( 1 R ); n = number of observations, Includes constant k = number of independent variables. The Adjusted R can actually fall if the variable you add doesn't explain much of the variance. Explaining Variation: Adjusted R (cont) Back to the Example Comparing Adjusted R Model 1:.9 Model :.31 Model 3:.33 Model :.3 Interpretation You can see that the adjusted R rises from equation 1 to equation, and from equation to equation 3. But then it falls from equation 3 to, when we add in the variables for national parks and the zodiac. Explaining Variation: Adjusted R (cont) Example: Equation Analysis of Variance Sum DFof Squares Mean Square Regression Residual F=.13 Signif F =. We calculate: Multiple R.15 R Square.3555 Adjusted R Square.31 Standard Error.5 Variable B SE B Beta T T Sig T SKOOL TUBETIME (Constant) R n 1 = 1 ( 1 R ) 7 1 = 1 ( ) =. 31 Copyright Sharyn O'Halloran 1 1
2 Explaining Variation: Adjusted R (cont) Stepwise Regression One strategy for model building is to add variables only if they increase your adjusted R. This technique is called stepwise regression. However, I don't want to emphasize this approach to strongly. Just as people can fixate on R they can fixate on adjusted R. If you have a theory that suggests that certain variables are important for your analysis then include them whether or not they increase the adjusted R. Negative findings can be important! Comparing Models: F-Tests When to use an F-Test? Say you add a number of variables into a regression model and you want to see if, as a group, they are significant in explaining variation in your dependent variable Y. The F-test tells you whether a group of variables, or even an entire model, is jointly significant. This is in contrast to a t-test, which tells whether an individual coefficient is significantly different from zero. In short, does the specified model explain a significant proportion of the total variation. Equations To be precise, say our original equation is: Model 1: Y = b + b 1 X 1 + b X, We add two more variables, so the new equation is: Model : Y = b + b 1 X 1 + b X + b 3 X 3 + b X. We want to test the hypothesis that Η : β 3 = β =. We want to test the joint hypothesis that X 3 and X together are not significant factors in determining Y. Using Adjusted R First There's an easy way to tell if these two variables are not significant. First, run the regression without X 3 and X in it, then run the regression with X 3 and X. Now look at the adjusted R 's for the two regressions. If the adjusted R went down, then X 3 and X are not jointly significant. So the adjusted R can serve as a quick test for insignificance. Copyright Sharyn O'Halloran 1
3 Calculating an F-Test If the adjusted R goes up, then you need to do a more complicated test, F-Test. Ratio Let regression 1 be the model without X 3 and X, and let regression include X 3 and X. The basic idea of the F statistic, then, is to compute the ratio: SSE SSE SSE 1 Correction We have to correct for the number of independent we add. So the complete statistic is: SSE1 SSE m is the number of F = m ; SSE additional variables added to the model m = number of restrictions; k = number of independent variables. Remember: k is the total number of independent variables, including the ones that you are testing and the constant. Correction (cont.) This equation defines an F-statistic with m and n-k degrees of freedom. We write it like this: m F To get critical values for the F statistic, we use a set of tables, just like for the normal and t- statistics. Example Adding Extra Variables: Are a group of variables jointly significant? Are the variables YELOWSTN and MYSIGN jointly significant? Model1: TRUSTTV = b + blikejpan + b SKOOL + b TUBETIME 1 3 Model : TRUSTTV = b + blikejpan+ b SKOOL + b TUBETIME + b MYSIGN+ b YELOWSTN Copyright Sharyn O'Halloran 1 3
4 Adding Extra Variables (cont.) State the null hypothesis H : B = B = 5 Calculate the F-statistic Our formula for the F-statistic is: SSE1 SSE F = m, SSE What is SSE 1? the sum of squared errors in the first regression. What is SSE? the sum of squared errors in the second regression m = N = 7 k = The formula is: F = =.319 Reject or fail to reject the null hypothesis? The critical value at the 5 % level F 7 from the table, is 3.. Is the F-statistic > F 7? If yes, then we reject the null hypothesis that the variables are not significantly different from zero; otherwise we fail to reject. We can reject the null hypothesis because.319 < 3.. β= Testing All Variables: Is the Model Significant? Equation : Impact of school and TV watched DF Sum of SquaresMean Square Regression Residual F Statistic =.1 Signif F =.E- Multiple R.15 R Square.35 Adjusted R Square.31 Standard Error.5 Dependent Variable: Trust TV Variable B SE B Beta T Sig T SKOOL TUBETIME (Constant) Copyright Sharyn O'Halloran 1
5 Hypothesis Testing: State Hypothesis H : β = β = 1 Calculate test statistic Again, we start with our formula: SSE1 SSE F = m, SSE Calculate F-statistic SSE = 1.7 This is the number reported in your printout under the F statistic. SSE 1 is the sum of squared errors when there are no explanatory variables at all. If there are no explanatory variables, then SSR must be. In this case, SSE=SST. So we can substitute SST for SSE1 in our formula. SST = SSR + SSE = = F = =.1. Reject or fail to reject the null hypothesis? The critical value at the 5% level, F 7 from 3 your table, is 3.. So this time we can reject the null hypothesis that β 1 = β =. Interpretation? The model explains a significant amount of the total variation in how much people trust what is said on TV. Comparing Models: Example Study of 7 Seventh Grade students in a mid-western school. Path Diagram Gender + + Copyright Sharyn O'Halloran 1 5
6 1 1 1 Average of Average of Gender Data Average of Average of Variables = student s score on a standard test = student s grade point average Gender= students gender (1 for male; for female) Descriptive Statistics Gender Mean 7.5 Mean 1.9 Mean. Standard Error. Standard Error 1.9 Standard Error. Mode 9.17 Mode 111. Mode 1. Sample Variance.1 Sample Variance Sample Variance. Kurtosis 1.1 Kurtosis. Kurtosis -1.7 Minimum.53 Minimum 7. Minimum. Sum 5.3 Sum 9. Sum 7. Relation between and Gender Average of Average of Grand Total Graphs Relation between and For Women Only Relation between and For Men Only Hypothesis Testing: Hypothesizes concerning coefficients H : β = 1 H : β a 1 We want to know if and Gender explain a significant amount of the variation in. Hypothesizes Concerning Models H H a : β = β = 1 : β = β 1 Estimation Model I Relation between and 1 1 y =.11x = b + b 1 SUMMARY OUTPUT Dependent Variable: Regression Statistics Multiple R.3 R Square. Adjusted R Square.39 Standard Error 1.3 Observations 7. ANOVA df SS MS F Significance F Regression E-1 Residual Total Coefficients Standard Error t Stat P-value Intercept E-1 = Copyright Sharyn O'Halloran 1
7 Model II: Relation between and 1 1 = Gender = = b + b + b Gender 1 SUMMARY OUTPUT Dependent Variable: Regression Statistics Multiple R.7 R Square.5 Adjusted R Square. Standard Error 1.5 Observations 7. ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept Gender Is Model I better than Model II? F = F-test Statistics SSE SSE m SSE , = = F =. <.1 7 = Gender β=..1 Yes it is. Interactive Terms Regression Statistics Multiple R.75 R Square.5 Adjusted R Square.33 Standard Error 1.55 Observations 77. ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept Gender *Gender The interactive term is not statistically significant. A high or low has the same effect on independent of gender. Interpretation Coefficients Both and Gender matter. increases by.11 points holding Gender constant. Gender Decreases by.97 points holding constant. Models F-statistic shows that the model that includes Gender performs significantly better in explaining variation then does the model with only. We are therefore able to reject the null hypothesis that model 1=model at the 5% significance level. Copyright Sharyn O'Halloran 1 7
8 Final Paper Clearly state your hypothesis. Use a path diagram to present the causal relation. Use the correlations to help you determine what causes what. State the alternative hypothesis. Present descriptive statistics. This includes a correlation matrix and histogram or scatter plot. Estimate your model. You can do simple regression, include interactive terms, do path analysis, use dummy variables; whatever is appropriate to your hypothesis. Present your results. Interpret your results. Draw out the policy implications of your analysis. The paper should begin with a brief which states the basic project and your main findings. Copyright Sharyn O'Halloran 1
Statistics and Quantitative Analysis U4320. Lecture 13: Explaining Variation Prof. Sharyn O Halloran
Statistics and Quantitative Analysis U4320 Lecture 13: Eplaining Variation Prof. Sharyn O Halloran I. Eplaining Variation: R 2 A. Breaking Down the Distances Let's go back to the basics of regression analysis.
More informationLECTURE 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
More informationCorrelation 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
More informationInferences 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
More informationSociology 593 Exam 2 Answer Key March 28, 2002
Sociology 59 Exam Answer Key March 8, 00 I. True-False. (0 points) Indicate whether the following statements are true or false. If false, briefly explain why.. A variable is called CATHOLIC. This probably
More informationStatistics and Quantitative Analysis U4320. Segment 10 Prof. Sharyn O Halloran
Statistics and Quantitative Analysis U4320 Segment 10 Prof. Sharyn O Halloran Key Points 1. Review Univariate Regression Model 2. Introduce Multivariate Regression Model Assumptions Estimation Hypothesis
More informationInference 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
More informationReview of Multiple Regression
Ronald H. Heck 1 Let s begin with a little review of multiple regression this week. Linear models [e.g., correlation, t-tests, analysis of variance (ANOVA), multiple regression, path analysis, multivariate
More informationChapter 3 Multiple Regression Complete Example
Department of Quantitative Methods & Information Systems ECON 504 Chapter 3 Multiple Regression Complete Example Spring 2013 Dr. Mohammad Zainal Review Goals After completing this lecture, you should be
More informationBusiness 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
More informationCan you tell the relationship between students SAT scores and their college grades?
Correlation One Challenge Can you tell the relationship between students SAT scores and their college grades? A: The higher SAT scores are, the better GPA may be. B: The higher SAT scores are, the lower
More informationChapter 14 Student Lecture Notes 14-1
Chapter 14 Student Lecture Notes 14-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 14 Multiple Regression Analysis and Model Building Chap 14-1 Chapter Goals After completing this
More informationLecture 28 Chi-Square Analysis
Lecture 28 STAT 225 Introduction to Probability Models April 23, 2014 Whitney Huang Purdue University 28.1 χ 2 test for For a given contingency table, we want to test if two have a relationship or not
More informationSociology 593 Exam 2 March 28, 2002
Sociology 59 Exam March 8, 00 I. True-False. (0 points) Indicate whether the following statements are true or false. If false, briefly explain why.. A variable is called CATHOLIC. This probably means that
More informationWELCOME! Lecture 13 Thommy Perlinger
Quantitative Methods II WELCOME! Lecture 13 Thommy Perlinger Parametrical tests (tests for the mean) Nature and number of variables One-way vs. two-way ANOVA One-way ANOVA Y X 1 1 One dependent variable
More informationBasic 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
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Eplained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationRegression 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
More informationSTA441: Spring Multiple Regression. This slide show is a free open source document. See the last slide for copyright information.
STA441: Spring 2018 Multiple Regression This slide show is a free open source document. See the last slide for copyright information. 1 Least Squares Plane 2 Statistical MODEL There are p-1 explanatory
More informationChapter 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
More informationSociology Research Statistics I Final Exam Answer Key December 15, 1993
Sociology 592 - Research Statistics I Final Exam Answer Key December 15, 1993 Where appropriate, show your work - partial credit may be given. (On the other hand, don't waste a lot of time on excess verbiage.)
More informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationA discussion on multiple regression models
A discussion on multiple regression models In our previous discussion of simple linear regression, we focused on a model in which one independent or explanatory variable X was used to predict the value
More informationChapter 8 Student Lecture Notes 8-1. Department of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance
Chapter 8 Student Lecture Notes 8-1 Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing
More informationECON 497 Midterm Spring
ECON 497 Midterm Spring 2009 1 ECON 497: Economic Research and Forecasting Name: Spring 2009 Bellas Midterm You have three hours and twenty minutes to complete this exam. Answer all questions and explain
More informationMultiple Regression. Peerapat Wongchaiwat, Ph.D.
Peerapat Wongchaiwat, Ph.D. wongchaiwat@hotmail.com The Multiple Regression Model Examine the linear relationship between 1 dependent (Y) & 2 or more independent variables (X i ) Multiple Regression Model
More informationChapter 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
More informationMathematics 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
More informationComputer Exercise 3 Answers Hypothesis Testing
Computer Exercise 3 Answers Hypothesis Testing. reg lnhpay xper yearsed tenure ---------+------------------------------ F( 3, 6221) = 512.58 Model 457.732594 3 152.577531 Residual 1851.79026 6221.297667619
More informationStatistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 13 Simple Linear Regression 13-1 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of
More informationCHAPTER 4 Analysis of Variance. One-way ANOVA Two-way ANOVA i) Two way ANOVA without replication ii) Two way ANOVA with replication
CHAPTER 4 Analysis of Variance One-way ANOVA Two-way ANOVA i) Two way ANOVA without replication ii) Two way ANOVA with replication 1 Introduction In this chapter, expand the idea of hypothesis tests. We
More information1.) Fit the full model, i.e., allow for separate regression lines (different slopes and intercepts) for each species
Lecture notes 2/22/2000 Dummy variables and extra SS F-test Page 1 Crab claw size and closing force. Problem 7.25, 10.9, and 10.10 Regression for all species at once, i.e., include dummy variables for
More informationDepartment of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance ECON 509. Dr.
Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should be able
More informationInference 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
More informationChapter 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
More informationChapter 7 Student Lecture Notes 7-1
Chapter 7 Student Lecture Notes 7- Chapter Goals QM353: Business Statistics Chapter 7 Multiple Regression Analysis and Model Building After completing this chapter, you should be able to: Explain model
More informationLecture 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
More informationRegression 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
More informationt-test for b Copyright 2000 Tom Malloy. All rights reserved. Regression
t-test for b Copyright 2000 Tom Malloy. All rights reserved. Regression Recall, back some time ago, we used a descriptive statistic which allowed us to draw the best fit line through a scatter plot. We
More informationDifference in two or more average scores in different groups
ANOVAs Analysis of Variance (ANOVA) Difference in two or more average scores in different groups Each participant tested once Same outcome tested in each group Simplest is one-way ANOVA (one variable as
More informationSimple Linear Regression: One Qualitative IV
Simple Linear Regression: One Qualitative IV 1. Purpose As noted before regression is used both to explain and predict variation in DVs, and adding to the equation categorical variables extends regression
More informationInteractions. Interactions. Lectures 1 & 2. Linear Relationships. y = a + bx. Slope. Intercept
Interactions Lectures 1 & Regression Sometimes two variables appear related: > smoking and lung cancers > height and weight > years of education and income > engine size and gas mileage > GMAT scores and
More informationNotes 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
More informationChapter Fifteen. Frequency Distribution, Cross-Tabulation, and Hypothesis Testing
Chapter Fifteen Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Copyright 2010 Pearson Education, Inc. publishing as Prentice Hall 15-1 Internet Usage Data Table 15.1 Respondent Sex Familiarity
More informationTwo-Way ANOVA. Chapter 15
Two-Way ANOVA Chapter 15 Interaction Defined An interaction is present when the effects of one IV depend upon a second IV Interaction effect : The effect of each IV across the levels of the other IV When
More informationLecture 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
More informationCorrelation. A statistics method to measure the relationship between two variables. Three characteristics
Correlation Correlation A statistics method to measure the relationship between two variables Three characteristics Direction of the relationship Form of the relationship Strength/Consistency Direction
More informationInference. ME104: Linear Regression Analysis Kenneth Benoit. August 15, August 15, 2012 Lecture 3 Multiple linear regression 1 1 / 58
Inference ME104: Linear Regression Analysis Kenneth Benoit August 15, 2012 August 15, 2012 Lecture 3 Multiple linear regression 1 1 / 58 Stata output resvisited. reg votes1st spend_total incumb minister
More informationSTAT 350 Final (new Material) Review Problems Key Spring 2016
1. The editor of a statistics textbook would like to plan for the next edition. A key variable is the number of pages that will be in the final version. Text files are prepared by the authors using LaTeX,
More informationChapter 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
More informationChapter Learning Objectives. Regression Analysis. Correlation. Simple Linear Regression. Chapter 12. Simple Linear Regression
Chapter 12 12-1 North Seattle Community College BUS21 Business Statistics Chapter 12 Learning Objectives In this chapter, you learn:! How to use regression analysis to predict the value of a dependent
More informationSTAT 512 MidTerm I (2/21/2013) Spring 2013 INSTRUCTIONS
STAT 512 MidTerm I (2/21/2013) Spring 2013 Name: Key INSTRUCTIONS 1. This exam is open book/open notes. All papers (but no electronic devices except for calculators) are allowed. 2. There are 5 pages in
More informationSchool of Mathematical Sciences. Question 1
School of Mathematical Sciences MTH5120 Statistical Modelling I Practical 8 and Assignment 7 Solutions Question 1 Figure 1: The residual plots do not contradict the model assumptions of normality, constant
More informationAMS 7 Correlation and Regression Lecture 8
AMS 7 Correlation and Regression Lecture 8 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Suumer 2014 1 / 18 Correlation pairs of continuous observations. Correlation
More informationEconometrics. 4) Statistical inference
30C00200 Econometrics 4) Statistical inference Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Confidence intervals of parameter estimates Student s t-distribution
More informationVariance 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
More informationAnswers to Problem Set #4
Answers to Problem Set #4 Problems. Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated variance covariance matrix are given by: bβ bβ 2 bβ 3 = 2
More informationCh 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
More informationChapter 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
More informationData Analysis 1 LINEAR REGRESSION. Chapter 03
Data Analysis 1 LINEAR REGRESSION Chapter 03 Data Analysis 2 Outline The Linear Regression Model Least Squares Fit Measures of Fit Inference in Regression Other Considerations in Regression Model Qualitative
More informationMultiple Regression Analysis
Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 +... β k x k + u 2. Inference 0 Assumptions of the Classical Linear Model (CLM)! So far, we know: 1. The mean and variance of the OLS estimators
More informationTests of Linear Restrictions
Tests of Linear Restrictions 1. Linear Restricted in Regression Models In this tutorial, we consider tests on general linear restrictions on regression coefficients. In other tutorials, we examine some
More informationChapter 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,
More informationInference 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
More informationLab 10 - Binary Variables
Lab 10 - Binary Variables Spring 2017 Contents 1 Introduction 1 2 SLR on a Dummy 2 3 MLR with binary independent variables 3 3.1 MLR with a Dummy: different intercepts, same slope................. 4 3.2
More informationBNAD 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
More information(ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box.
FINAL EXAM ** Two different ways to submit your answer sheet (i) Use MS-Word and place it in a drop-box. (ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box. Deadline: December
More informationEconomics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama
Economics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama Course Packet The purpose of this packet is to show you one particular dataset and how it is used in
More informationThis document contains 3 sets of practice problems.
P RACTICE PROBLEMS This document contains 3 sets of practice problems. Correlation: 3 problems Regression: 4 problems ANOVA: 8 problems You should print a copy of these practice problems and bring them
More informationTable of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z).
Table of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z). For example P(X.04) =.8508. For z < 0 subtract the value from,
More informationSTAT Chapter 10: Analysis of Variance
STAT 515 -- Chapter 10: Analysis of Variance Designed Experiment A study in which the researcher controls the levels of one or more variables to determine their effect on the variable of interest (called
More informationwhere Female = 0 for males, = 1 for females Age is measured in years (22, 23, ) GPA is measured in units on a four-point scale (0, 1.22, 3.45, etc.
Notes on regression analysis 1. Basics in regression analysis key concepts (actual implementation is more complicated) A. Collect data B. Plot data on graph, draw a line through the middle of the scatter
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Explained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationAnalysis of Variance: Part 1
Analysis of Variance: Part 1 Oneway ANOVA When there are more than two means Each time two means are compared the probability (Type I error) =α. When there are more than two means Each time two means are
More information16.400/453J Human Factors Engineering. Design of Experiments II
J Human Factors Engineering Design of Experiments II Review Experiment Design and Descriptive Statistics Research question, independent and dependent variables, histograms, box plots, etc. Inferential
More informationCIVL 7012/8012. Simple Linear Regression. Lecture 3
CIVL 7012/8012 Simple Linear Regression Lecture 3 OLS assumptions - 1 Model of population Sample estimation (best-fit line) y = β 0 + β 1 x + ε y = b 0 + b 1 x We want E b 1 = β 1 ---> (1) Meaning we want
More informationAn Analysis of College Algebra Exam Scores December 14, James D Jones Math Section 01
An Analysis of College Algebra Exam s December, 000 James D Jones Math - Section 0 An Analysis of College Algebra Exam s Introduction Students often complain about a test being too difficult. Are there
More informationCh 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
More informationPsych 230. Psychological Measurement and Statistics
Psych 230 Psychological Measurement and Statistics Pedro Wolf December 9, 2009 This Time. Non-Parametric statistics Chi-Square test One-way Two-way Statistical Testing 1. Decide which test to use 2. State
More informationCh. 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
More informationChapter 10-Regression
Chapter 10-Regression 10.1 Regression equation predicting infant mortality from income Y = Infant mortality X = Income Y = 6.70 s Y = 0.698 s 2 Y = 0.487 X = 46.00 s X = 6.289 s 2 X = 39.553 cov XY = 2.7245
More informationFREC 608 Guided Exercise 9
FREC 608 Guided Eercise 9 Problem. Model of Average Annual Precipitation An article in Geography (July 980) used regression to predict average annual rainfall levels in California. Data on the following
More informationPredictive 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
More informationMultiple linear regression
Multiple linear regression Course MF 930: Introduction to statistics June 0 Tron Anders Moger Department of biostatistics, IMB University of Oslo Aims for this lecture: Continue where we left off. Repeat
More informationThe 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:
More informationPubH 7405: REGRESSION ANALYSIS. MLR: INFERENCES, Part I
PubH 7405: REGRESSION ANALYSIS MLR: INFERENCES, Part I TESTING HYPOTHESES Once we have fitted a multiple linear regression model and obtained estimates for the various parameters of interest, we want to
More informationArea1 Scaled Score (NAPLEX) .535 ** **.000 N. Sig. (2-tailed)
Institutional Assessment Report Texas Southern University College of Pharmacy and Health Sciences "An Analysis of 2013 NAPLEX, P4-Comp. Exams and P3 courses The following analysis illustrates relationships
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 19, 2010 Instructor: John Parman Final Exam - Solutions You have until 5:30pm to complete this exam. Please remember to put your
More informationCh 13 & 14 - Regression Analysis
Ch 3 & 4 - Regression Analysis Simple Regression Model I. Multiple Choice:. A simple regression is a regression model that contains a. only one independent variable b. only one dependent variable c. more
More informationBasic 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:
More informationUnit 27 One-Way Analysis of Variance
Unit 27 One-Way Analysis of Variance Objectives: To perform the hypothesis test in a one-way analysis of variance for comparing more than two population means Recall that a two sample t test is applied
More informationMultiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company
Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple
More informationMATH ASSIGNMENT 2: SOLUTIONS
MATH 204 - ASSIGNMENT 2: SOLUTIONS (a) Fitting the simple linear regression model to each of the variables in turn yields the following results: we look at t-tests for the individual coefficients, and
More informationOne-Way ANOVA. Some examples of when ANOVA would be appropriate include:
One-Way ANOVA 1. Purpose Analysis of variance (ANOVA) is used when one wishes to determine whether two or more groups (e.g., classes A, B, and C) differ on some outcome of interest (e.g., an achievement
More informationReview of Statistics
Review of Statistics Topics Descriptive Statistics Mean, Variance Probability Union event, joint event Random Variables Discrete and Continuous Distributions, Moments Two Random Variables Covariance and
More informationVariance 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
More informationRegression Analysis and Forecasting Prof. Shalabh Department of Mathematics and Statistics Indian Institute of Technology-Kanpur
Regression Analysis and Forecasting Prof. Shalabh Department of Mathematics and Statistics Indian Institute of Technology-Kanpur Lecture 10 Software Implementation in Simple Linear Regression Model using
More informationSTA 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.
More informationFactorial designs. Experiments
Chapter 5: Factorial designs Petter Mostad mostad@chalmers.se Experiments Actively making changes and observing the result, to find causal relationships. Many types of experimental plans Measuring response
More informationSTAT 135 Lab 11 Tests for Categorical Data (Fisher s Exact test, χ 2 tests for Homogeneity and Independence) and Linear Regression
STAT 135 Lab 11 Tests for Categorical Data (Fisher s Exact test, χ 2 tests for Homogeneity and Independence) and Linear Regression Rebecca Barter April 20, 2015 Fisher s Exact Test Fisher s Exact Test
More information