Simple Linear Regression the model, estimation and testing

Size: px
Start display at page:

Download "Simple Linear Regression the model, estimation and testing"

Transcription

1 Simple Linear Regression the model, estimation and testing Lecture No. 05

2 Example 1 A production manager has compared the dexterity test scores of five assembly-line employees with their hourly productivity.

3 Example 1 dependent variable random error (residual) intercept independent variable slope

4 Simple Linear Regression the model The goal of a regression analysis is to obtain predictions of one variable using the known values of another

5 Simple Linear Regression Three assumptions: The ε term is assumed to be random variable that: 1. Has a mean of 0 2. Is normally distributed 3. Has constant variance at every value of X (Homoscedastic)

6 Simple Linear Regression Three assumptions: For any given value of x, the y values are assumed to be normally distributed about the population regression line and to have the same standard deviation σ The regression line based on sample data is an estimate of this true line.

7 Example 1 Sample regression line

8 The Least-Squares Criterion The least-squares criterion requires that the sum of the squared deviations between y values in the scatter diagram and y values predicted by the equation be minimized. In symbolic terms:

9 Determining the Least-Squares Regression Line

10 Example 1

11 Example 1

12 Example 1 - Point Estimates Using the Regression Line If a job applicant were to score x = 15 on the manual dexterity test, we would predict this person would be capable of producing 64.2 units per hour on the assembly line.

13 Estimation of standard error To develop interval estimates for the dependent variable, we must first determine the standard error of estimate. This is a standard deviation describing the dispersion of data points above and below the regression line. The formula for the standard error of estimate is shown below and is very similar to that for determining a sample standard deviation s:

14 Example 1 A production manager has compared the dexterity test scores of five assembly-line employees with their hourly productivity.

15 Example 1 Now calculate the standard error of estimate as

16 Confidence and prediction Interval for the mean of y given a specific x value Given a specific value of x, we can make two kinds of interval estimates regarding y: (1) a confidence interval for the (unknown) true mean of y, and (2) a prediction interval for an individual y observation.

17 Confidence interval for the mean of y given a specific x value

18 Example 1 Confidence Interval For persons scoring x = 15 on the dexterity test, what is the 95% confidence interval for their mean productivity? For the 95% level of confidence and df=n-2=3, t =3.182 and the 95% confidence interval can now be calculated as Based on these calculations, we have 95% confidence that the mean productivity for persons scoring x = 15 on the dexterity test will be between and units per hour.

19 Prediction Interval for an Individual y Observation For a given value of x, the estimation interval for an individual y observation is called the prediction interval. Prediction interval for an individual y, given a specific value of x: additional 1

20 Example 1 Prediction Interval A prospective employee has scored x = 15 on the dexterity test. What is the 95% prediction interval for his productivity? For this applicant, we have 95% confidence that his productivity as an employee would be between and units per hour.

21 Example 1 Prediction Interval The 95% prediction interval for individual y values becomes slightly wider whenever the interval is based on x values that are farther away from the mean of x.

22 Testing and Estimation for the Slope

23 Testing and Estimation for the Slope

24 Example 1 Testing and Estimation for the Slope An equivalent method of testing the significance of the linear relationship is to examine whether the slope β 1 of the population regression line could be zero. For the dexterity test data, the slope of the sample regression line was b 1 = Using the 0.05 level of significance, examine whether the slope of the population regression line could be zero. 2. Construct the 95% confidence interval for the slope of the population regression line.

25 Example 1 Testing and Estimation for the Slope

26 Example 1 Testing and Estimation for the Slope p value We reject the null hypothesis

27 Confidence interval for the Slope

28 Example 1 Testing and Estimation for the Slope 95% Confidence Interval for the Slope of the Population Regression Line

29 Example 2 50 randomly selected students took a math aptitude test before they began their statistics course. The Statistics Department has three questions. What linear regression equation best predicts statistics performance, based on math aptitude scores? If a student made an 80 on the aptitude test, what grade would we expect him to make in statistics? Make a confidence prediction interval for x=80 using 0.05 level of significance

30 Example 2 Solution in Excel

31 Example 2

32 Example 2

33 Example 2

34 Example 2 Solution in STATISTICA

35 Example

36 Example

37 Example 2

38 Example 2 another way to plot the graphs

39 Example 2 another way to plot the graphs

40 Example 2 another way to plot the graphs Regression bands Prediction intervals Confidence intervals

41 Example

42 Example 2 If a student made an 80 on the aptitude test, what grade would we expect him to make in statistics? Make a confidence prediction interval for x=80 using 0.05 level of significance.

43 Example 2

CRITERIA FOR USE. A GRAPHICAL EXPLANATION OF BI-VARIATE (2 VARIABLE) REGRESSION ANALYSISSys

CRITERIA FOR USE. A GRAPHICAL EXPLANATION OF BI-VARIATE (2 VARIABLE) REGRESSION ANALYSISSys Multiple Regression Analysis 1 CRITERIA FOR USE Multiple regression analysis is used to test the effects of n independent (predictor) variables on a single dependent (criterion) variable. Regression tests

More information

STATISTICS INFORMED DECISIONS USING DATA

STATISTICS INFORMED DECISIONS USING DATA STATISTICS INFORMED DECISIONS USING DATA Fifth Edition Chapter 4 Describing the Relation between Two Variables 4.1 Scatter Diagrams and Correlation Learning Objectives 1. Draw and interpret scatter diagrams

More information

MMI 409 Spring 2009 Final Examination Gordon Bleil. 1. Is there a difference in depression as a function of group and drug?

MMI 409 Spring 2009 Final Examination Gordon Bleil. 1. Is there a difference in depression as a function of group and drug? MMI 409 Spring 2009 Final Examination Gordon Bleil Table of Contents Research Scenario and General Assumptions Questions for Dataset (Questions are hyperlinked to detailed answers) 1. Is there a difference

More information

Statistics for Psychology

Statistics for Psychology Statistics for Psychology SIXTH EDITION CHAPTER 12 Prediction Prediction a major practical application of statistical methods: making predictions make informed (and precise) guesses about such things as

More information

Dr. Kelly Bradley Final Exam Summer {2 points} Name

Dr. Kelly Bradley Final Exam Summer {2 points} Name {2 points} Name You MUST work alone no tutors; no help from classmates. Email me or see me with questions. You will receive a score of 0 if this rule is violated. This exam is being scored out of 00 points.

More information

Business Statistics Probability

Business Statistics Probability Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment

More information

Pitfalls in Linear Regression Analysis

Pitfalls in Linear Regression Analysis Pitfalls in Linear Regression Analysis Due to the widespread availability of spreadsheet and statistical software for disposal, many of us do not really have a good understanding of how to use regression

More information

bivariate analysis: The statistical analysis of the relationship between two variables.

bivariate analysis: The statistical analysis of the relationship between two variables. bivariate analysis: The statistical analysis of the relationship between two variables. cell frequency: The number of cases in a cell of a cross-tabulation (contingency table). chi-square (χ 2 ) test for

More information

Chapter 3 CORRELATION AND REGRESSION

Chapter 3 CORRELATION AND REGRESSION CORRELATION AND REGRESSION TOPIC SLIDE Linear Regression Defined 2 Regression Equation 3 The Slope or b 4 The Y-Intercept or a 5 What Value of the Y-Variable Should be Predicted When r = 0? 7 The Regression

More information

Linear Regression in SAS

Linear Regression in SAS 1 Suppose we wish to examine factors that predict patient s hemoglobin levels. Simulated data for six patients is used throughout this tutorial. data hgb_data; input id age race $ bmi hgb; cards; 21 25

More information

Midterm STAT-UB.0003 Regression and Forecasting Models. I will not lie, cheat or steal to gain an academic advantage, or tolerate those who do.

Midterm STAT-UB.0003 Regression and Forecasting Models. I will not lie, cheat or steal to gain an academic advantage, or tolerate those who do. Midterm STAT-UB.0003 Regression and Forecasting Models The exam is closed book and notes, with the following exception: you are allowed to bring one letter-sized page of notes into the exam (front and

More information

IAPT: Regression. Regression analyses

IAPT: Regression. Regression analyses Regression analyses IAPT: Regression Regression is the rather strange name given to a set of methods for predicting one variable from another. The data shown in Table 1 and come from a student project

More information

The Pretest! Pretest! Pretest! Assignment (Example 2)

The Pretest! Pretest! Pretest! Assignment (Example 2) The Pretest! Pretest! Pretest! Assignment (Example 2) May 19, 2003 1 Statement of Purpose and Description of Pretest Procedure When one designs a Math 10 exam one hopes to measure whether a student s ability

More information

NORTH SOUTH UNIVERSITY TUTORIAL 2

NORTH SOUTH UNIVERSITY TUTORIAL 2 NORTH SOUTH UNIVERSITY TUTORIAL 2 AHMED HOSSAIN,PhD Data Management and Analysis AHMED HOSSAIN,PhD - Data Management and Analysis 1 Correlation Analysis INTRODUCTION In correlation analysis, we estimate

More information

Multiple Linear Regression (Dummy Variable Treatment) CIVL 7012/8012

Multiple Linear Regression (Dummy Variable Treatment) CIVL 7012/8012 Multiple Linear Regression (Dummy Variable Treatment) CIVL 7012/8012 2 In Today s Class Recap Single dummy variable Multiple dummy variables Ordinal dummy variables Dummy-dummy interaction Dummy-continuous/discrete

More information

12.1 Inference for Linear Regression. Introduction

12.1 Inference for Linear Regression. Introduction 12.1 Inference for Linear Regression vocab examples Introduction Many people believe that students learn better if they sit closer to the front of the classroom. Does sitting closer cause higher achievement,

More information

Simple Linear Regression

Simple Linear Regression Simple Linear Regression Assoc. Prof Dr Sarimah Abdullah Unit of Biostatistics & Research Methodology School of Medical Sciences, Health Campus Universiti Sains Malaysia Regression Regression analysis

More information

Research Methods in Forest Sciences: Learning Diary. Yoko Lu December Research process

Research Methods in Forest Sciences: Learning Diary. Yoko Lu December Research process Research Methods in Forest Sciences: Learning Diary Yoko Lu 285122 9 December 2016 1. Research process It is important to pursue and apply knowledge and understand the world under both natural and social

More information

10. LINEAR REGRESSION AND CORRELATION

10. LINEAR REGRESSION AND CORRELATION 1 10. LINEAR REGRESSION AND CORRELATION The contingency table describes an association between two nominal (categorical) variables (e.g., use of supplemental oxygen and mountaineer survival ). We have

More information

Final Exam Version A

Final Exam Version A Final Exam Version A Open Book and Notes your 4-digit code: Staple the question sheets to your answers Write your name only once on the back of this sheet. Problem 1: (10 points) A popular method to isolate

More information

Class 7 Everything is Related

Class 7 Everything is Related Class 7 Everything is Related Correlational Designs l 1 Topics Types of Correlational Designs Understanding Correlation Reporting Correlational Statistics Quantitative Designs l 2 Types of Correlational

More information

1.4 - Linear Regression and MS Excel

1.4 - Linear Regression and MS Excel 1.4 - Linear Regression and MS Excel Regression is an analytic technique for determining the relationship between a dependent variable and an independent variable. When the two variables have a linear

More information

MEA DISCUSSION PAPERS

MEA DISCUSSION PAPERS Inference Problems under a Special Form of Heteroskedasticity Helmut Farbmacher, Heinrich Kögel 03-2015 MEA DISCUSSION PAPERS mea Amalienstr. 33_D-80799 Munich_Phone+49 89 38602-355_Fax +49 89 38602-390_www.mea.mpisoc.mpg.de

More information

3.2 Least- Squares Regression

3.2 Least- Squares Regression 3.2 Least- Squares Regression Linear (straight- line) relationships between two quantitative variables are pretty common and easy to understand. Correlation measures the direction and strength of these

More information

Correlation and regression

Correlation and regression PG Dip in High Intensity Psychological Interventions Correlation and regression Martin Bland Professor of Health Statistics University of York http://martinbland.co.uk/ Correlation Example: Muscle strength

More information

Unit 1 Exploring and Understanding Data

Unit 1 Exploring and Understanding Data Unit 1 Exploring and Understanding Data Area Principle Bar Chart Boxplot Conditional Distribution Dotplot Empirical Rule Five Number Summary Frequency Distribution Frequency Polygon Histogram Interquartile

More information

Multiple Regression Analysis

Multiple Regression Analysis Multiple Regression Analysis Basic Concept: Extend the simple regression model to include additional explanatory variables: Y = β 0 + β1x1 + β2x2 +... + βp-1xp + ε p = (number of independent variables

More information

Chapter 3: Describing Relationships

Chapter 3: Describing Relationships Chapter 3: Describing Relationships Objectives: Students will: Construct and interpret a scatterplot for a set of bivariate data. Compute and interpret the correlation, r, between two variables. Demonstrate

More information

Regression Including the Interaction Between Quantitative Variables

Regression Including the Interaction Between Quantitative Variables Regression Including the Interaction Between Quantitative Variables The purpose of the study was to examine the inter-relationships among social skills, the complexity of the social situation, and performance

More information

Psychology Research Process

Psychology Research Process Psychology Research Process Logical Processes Induction Observation/Association/Using Correlation Trying to assess, through observation of a large group/sample, what is associated with what? Examples:

More information

Conditional Distributions and the Bivariate Normal Distribution. James H. Steiger

Conditional Distributions and the Bivariate Normal Distribution. James H. Steiger Conditional Distributions and the Bivariate Normal Distribution James H. Steiger Overview In this module, we have several goals: Introduce several technical terms Bivariate frequency distribution Marginal

More information

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment

More information

11/18/2013. Correlational Research. Correlational Designs. Why Use a Correlational Design? CORRELATIONAL RESEARCH STUDIES

11/18/2013. Correlational Research. Correlational Designs. Why Use a Correlational Design? CORRELATIONAL RESEARCH STUDIES Correlational Research Correlational Designs Correlational research is used to describe the relationship between two or more naturally occurring variables. Is age related to political conservativism? Are

More information

HW 3.2: page 193 #35-51 odd, 55, odd, 69, 71-78

HW 3.2: page 193 #35-51 odd, 55, odd, 69, 71-78 35. What s My Line? You use the same bar of soap to shower each morning. The bar weighs 80 grams when it is new. Its weight goes down by 6 grams per day on average. What is the equation of the regression

More information

Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol.

Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol. Ho (null hypothesis) Ha (alternative hypothesis) Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol. Hypothesis: Ho:

More information

Section 3.2 Least-Squares Regression

Section 3.2 Least-Squares Regression Section 3.2 Least-Squares Regression Linear relationships between two quantitative variables are pretty common and easy to understand. Correlation measures the direction and strength of these relationships.

More information

2.75: 84% 2.5: 80% 2.25: 78% 2: 74% 1.75: 70% 1.5: 66% 1.25: 64% 1.0: 60% 0.5: 50% 0.25: 25% 0: 0%

2.75: 84% 2.5: 80% 2.25: 78% 2: 74% 1.75: 70% 1.5: 66% 1.25: 64% 1.0: 60% 0.5: 50% 0.25: 25% 0: 0% Capstone Test (will consist of FOUR quizzes and the FINAL test grade will be an average of the four quizzes). Capstone #1: Review of Chapters 1-3 Capstone #2: Review of Chapter 4 Capstone #3: Review of

More information

BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT QUADRATIC (U-SHAPED) REGRESSION MODELS

BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT QUADRATIC (U-SHAPED) REGRESSION MODELS BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT QUADRATIC (U-SHAPED) REGRESSION MODELS 12 June 2012 Michael Wood University of Portsmouth Business School SBS Department, Richmond Building Portland

More information

REGRESSION MODELLING IN PREDICTING MILK PRODUCTION DEPENDING ON DAIRY BOVINE LIVESTOCK

REGRESSION MODELLING IN PREDICTING MILK PRODUCTION DEPENDING ON DAIRY BOVINE LIVESTOCK REGRESSION MODELLING IN PREDICTING MILK PRODUCTION DEPENDING ON DAIRY BOVINE LIVESTOCK Agatha POPESCU University of Agricultural Sciences and Veterinary Medicine Bucharest, 59 Marasti, District 1, 11464,

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Key Vocabulary:! individual! variable! frequency table! relative frequency table! distribution! pie chart! bar graph! two-way table! marginal distributions! conditional distributions!

More information

Chapter 3: Examining Relationships

Chapter 3: Examining Relationships Name Date Per Key Vocabulary: response variable explanatory variable independent variable dependent variable scatterplot positive association negative association linear correlation r-value regression

More information

Sample Math 71B Final Exam #1. Answer Key

Sample Math 71B Final Exam #1. Answer Key Sample Math 71B Final Exam #1 Answer Key 1. (2 points) Graph the equation. Be sure to plot the points on the graph at. 2. Solve for. 3. Given that, find and simplify. 4. Suppose and a. (1 point) Find.

More information

Find the slope of the line that goes through the given points. 1) (-9, -68) and (8, 51) 1)

Find the slope of the line that goes through the given points. 1) (-9, -68) and (8, 51) 1) Math 125 Semester Review Problems Name Find the slope of the line that goes through the given points. 1) (-9, -68) and (8, 51) 1) Solve the inequality. Graph the solution set, and state the solution set

More information

CHAPTER TWO REGRESSION

CHAPTER TWO REGRESSION CHAPTER TWO REGRESSION 2.0 Introduction The second chapter, Regression analysis is an extension of correlation. The aim of the discussion of exercises is to enhance students capability to assess the effect

More information

Understandable Statistics

Understandable Statistics Understandable Statistics correlated to the Advanced Placement Program Course Description for Statistics Prepared for Alabama CC2 6/2003 2003 Understandable Statistics 2003 correlated to the Advanced Placement

More information

UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test February 2016

UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test February 2016 UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test February 2016 STAB22H3 Statistics I, LEC 01 and LEC 02 Duration: 1 hour and 45 minutes Last Name: First Name:

More information

Still important ideas

Still important ideas Readings: OpenStax - Chapters 1 13 & Appendix D & E (online) Plous Chapters 17 & 18 - Chapter 17: Social Influences - Chapter 18: Group Judgments and Decisions Still important ideas Contrast the measurement

More information

SCATTER PLOTS AND TREND LINES

SCATTER PLOTS AND TREND LINES 1 SCATTER PLOTS AND TREND LINES LEARNING MAP INFORMATION STANDARDS 8.SP.1 Construct and interpret scatter s for measurement to investigate patterns of between two quantities. Describe patterns such as

More information

SPRING GROVE AREA SCHOOL DISTRICT. Course Description. Instructional Strategies, Learning Practices, Activities, and Experiences.

SPRING GROVE AREA SCHOOL DISTRICT. Course Description. Instructional Strategies, Learning Practices, Activities, and Experiences. SPRING GROVE AREA SCHOOL DISTRICT PLANNED COURSE OVERVIEW Course Title: Basic Introductory Statistics Grade Level(s): 11-12 Units of Credit: 1 Classification: Elective Length of Course: 30 cycles Periods

More information

MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES OBJECTIVES

MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES OBJECTIVES 24 MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES In the previous chapter, simple linear regression was used when you have one independent variable and one dependent variable. This chapter

More information

Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F

Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F Plous Chapters 17 & 18 Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

More information

TEACHING REGRESSION WITH SIMULATION. John H. Walker. Statistics Department California Polytechnic State University San Luis Obispo, CA 93407, U.S.A.

TEACHING REGRESSION WITH SIMULATION. John H. Walker. Statistics Department California Polytechnic State University San Luis Obispo, CA 93407, U.S.A. Proceedings of the 004 Winter Simulation Conference R G Ingalls, M D Rossetti, J S Smith, and B A Peters, eds TEACHING REGRESSION WITH SIMULATION John H Walker Statistics Department California Polytechnic

More information

Chapter 11 Multiple Regression

Chapter 11 Multiple Regression Chapter 11 Multiple Regression PSY 295 Oswald Outline The problem An example Compensatory and Noncompensatory Models More examples Multiple correlation Chapter 11 Multiple Regression 2 Cont. Outline--cont.

More information

Multiple Regression. James H. Steiger. Department of Psychology and Human Development Vanderbilt University

Multiple Regression. James H. Steiger. Department of Psychology and Human Development Vanderbilt University Multiple Regression James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) Multiple Regression 1 / 19 Multiple Regression 1 The Multiple

More information

Biology 345: Biometry Fall 2005 SONOMA STATE UNIVERSITY Lab Exercise 5 Residuals and multiple regression Introduction

Biology 345: Biometry Fall 2005 SONOMA STATE UNIVERSITY Lab Exercise 5 Residuals and multiple regression Introduction Biology 345: Biometry Fall 2005 SONOMA STATE UNIVERSITY Lab Exercise 5 Residuals and multiple regression Introduction In this exercise, we will gain experience assessing scatterplots in regression and

More information

South Australian Research and Development Institute. Positive lot sampling for E. coli O157

South Australian Research and Development Institute. Positive lot sampling for E. coli O157 final report Project code: Prepared by: A.MFS.0158 Andreas Kiermeier Date submitted: June 2009 South Australian Research and Development Institute PUBLISHED BY Meat & Livestock Australia Limited Locked

More information

Regression CHAPTER SIXTEEN NOTE TO INSTRUCTORS OUTLINE OF RESOURCES

Regression CHAPTER SIXTEEN NOTE TO INSTRUCTORS OUTLINE OF RESOURCES CHAPTER SIXTEEN Regression NOTE TO INSTRUCTORS This chapter includes a number of complex concepts that may seem intimidating to students. Encourage students to focus on the big picture through some of

More information

CHILD HEALTH AND DEVELOPMENT STUDY

CHILD HEALTH AND DEVELOPMENT STUDY CHILD HEALTH AND DEVELOPMENT STUDY 9. Diagnostics In this section various diagnostic tools will be used to evaluate the adequacy of the regression model with the five independent variables developed in

More information

Midterm Exam MMI 409 Spring 2009 Gordon Bleil

Midterm Exam MMI 409 Spring 2009 Gordon Bleil Midterm Exam MMI 409 Spring 2009 Gordon Bleil Table of contents: (Hyperlinked to problem sections) Problem 1 Hypothesis Tests Results Inferences Problem 2 Hypothesis Tests Results Inferences Problem 3

More information

Study Guide for the Final Exam

Study Guide for the Final Exam Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

More information

STATISTICS AND RESEARCH DESIGN

STATISTICS AND RESEARCH DESIGN Statistics 1 STATISTICS AND RESEARCH DESIGN These are subjects that are frequently confused. Both subjects often evoke student anxiety and avoidance. To further complicate matters, both areas appear have

More information

Results. Example 1: Table 2.1 The Effect of Additives on Daphnia Heart Rate. Time (min)

Results. Example 1: Table 2.1 The Effect of Additives on Daphnia Heart Rate. Time (min) Notes for Alphas Line graphs provide a way to map independent and dependent variables that are both quantitative. When both variables are quantitative, the segment that connects every two points on the

More information

Psychology Research Process

Psychology Research Process Psychology Research Process Logical Processes Induction Observation/Association/Using Correlation Trying to assess, through observation of a large group/sample, what is associated with what? Examples:

More information

WDHS Curriculum Map Probability and Statistics. What is Statistics and how does it relate to you?

WDHS Curriculum Map Probability and Statistics. What is Statistics and how does it relate to you? WDHS Curriculum Map Probability and Statistics Time Interval/ Unit 1: Introduction to Statistics 1.1-1.3 2 weeks S-IC-1: Understand statistics as a process for making inferences about population parameters

More information

Content. Basic Statistics and Data Analysis for Health Researchers from Foreign Countries. Research question. Example Newly diagnosed Type 2 Diabetes

Content. Basic Statistics and Data Analysis for Health Researchers from Foreign Countries. Research question. Example Newly diagnosed Type 2 Diabetes Content Quantifying association between continuous variables. Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General

More information

Table of Contents. Plots. Essential Statistics for Nursing Research 1/12/2017

Table of Contents. Plots. Essential Statistics for Nursing Research 1/12/2017 Essential Statistics for Nursing Research Kristen Carlin, MPH Seattle Nursing Research Workshop January 30, 2017 Table of Contents Plots Descriptive statistics Sample size/power Correlations Hypothesis

More information

Simple Linear Regression: Prediction. Instructor: G. William Schwert

Simple Linear Regression: Prediction. Instructor: G. William Schwert APS 425 Fall 2015 Simple Linear Regression: Prediction Instructor: G. William Schwert 585-275-2470 schwert@schwert.ssb.rochester.edu Ciba-Geigy Ritalin Experiment Ritalin is tested to see if it helps with

More information

Results & Statistics: Description and Correlation. I. Scales of Measurement A Review

Results & Statistics: Description and Correlation. I. Scales of Measurement A Review Results & Statistics: Description and Correlation The description and presentation of results involves a number of topics. These include scales of measurement, descriptive statistics used to summarize

More information

Problem Set 3 ECN Econometrics Professor Oscar Jorda. Name. ESSAY. Write your answer in the space provided.

Problem Set 3 ECN Econometrics Professor Oscar Jorda. Name. ESSAY. Write your answer in the space provided. Problem Set 3 ECN 140 - Econometrics Professor Oscar Jorda Name ESSAY. Write your answer in the space provided. 1) Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height

More information

FORM C Dr. Sanocki, PSY 3204 EXAM 1 NAME

FORM C Dr. Sanocki, PSY 3204 EXAM 1 NAME PSYCH STATS OLD EXAMS, provided for self-learning. LEARN HOW TO ANSWER the QUESTIONS; memorization of answers won t help. All answers are in the textbook or lecture. Instructors can provide some clarification

More information

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo Please note the page numbers listed for the Lind book may vary by a page or two depending on which version of the textbook you have. Readings: Lind 1 11 (with emphasis on chapters 10, 11) Please note chapter

More information

Choosing a Significance Test. Student Resource Sheet

Choosing a Significance Test. Student Resource Sheet Choosing a Significance Test Student Resource Sheet Choosing Your Test Choosing an appropriate type of significance test is a very important consideration in analyzing data. If an inappropriate test is

More information

Lecture 6B: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression

Lecture 6B: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression Lecture 6B: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression! Equation of Regression Line; Residuals! Effect of Explanatory/Response Roles! Unusual Observations! Sample

More information

AP Stats Chap 27 Inferences for Regression

AP Stats Chap 27 Inferences for Regression AP Stats Chap 27 Inferences for Regression Finally, we re interested in examining how slopes of regression lines vary from sample to sample. Each sample will have it s own slope, b 1. These are all estimates

More information

Chapter 2 Organizing and Summarizing Data. Chapter 3 Numerically Summarizing Data. Chapter 4 Describing the Relation between Two Variables

Chapter 2 Organizing and Summarizing Data. Chapter 3 Numerically Summarizing Data. Chapter 4 Describing the Relation between Two Variables Tables and Formulas for Sullivan, Fundamentals of Statistics, 4e 014 Pearson Education, Inc. Chapter Organizing and Summarizing Data Relative frequency = frequency sum of all frequencies Class midpoint:

More information

BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT REGRESSION MODELS

BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT REGRESSION MODELS BOOTSTRAPPING CONFIDENCE LEVELS FOR HYPOTHESES ABOUT REGRESSION MODELS 17 December 2009 Michael Wood University of Portsmouth Business School SBS Department, Richmond Building Portland Street, Portsmouth

More information

11/24/2017. Do not imply a cause-and-effect relationship

11/24/2017. Do not imply a cause-and-effect relationship 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 information

Clincial Biostatistics. Regression

Clincial Biostatistics. Regression Regression analyses Clincial Biostatistics Regression Regression is the rather strange name given to a set of methods for predicting one variable from another. The data shown in Table 1 and come from a

More information

Online Supplementary Appendix

Online Supplementary Appendix Online Supplementary Appendix This appendix has been provided by the authors to give readers additional information about their work. Supplement to: Lehman * LH, Saeed * M, Talmor D, Mark RG, and Malhotra

More information

SPSS output for 420 midterm study

SPSS output for 420 midterm study Ψ Psy Midterm Part In lab (5 points total) Your professor decides that he wants to find out how much impact amount of study time has on the first midterm. He randomly assigns students to study for hours,

More information

SUMMER 2011 RE-EXAM PSYF11STAT - STATISTIK

SUMMER 2011 RE-EXAM PSYF11STAT - STATISTIK SUMMER 011 RE-EXAM PSYF11STAT - STATISTIK Full Name: Årskortnummer: Date: This exam is made up of three parts: Part 1 includes 30 multiple choice questions; Part includes 10 matching questions; and Part

More information

111, section 8.6 Applications of the Normal Distribution

111, section 8.6 Applications of the Normal Distribution 111, section 8.6 Applications of the Normal Distribution notes by Tim Pilachowski A probability density function f(x) for a continuous random variable has two necessary characteristics. 1. f(x) 0 for all

More information

EXECUTIVE SUMMARY DATA AND PROBLEM

EXECUTIVE SUMMARY DATA AND PROBLEM EXECUTIVE SUMMARY Every morning, almost half of Americans start the day with a bowl of cereal, but choosing the right healthy breakfast is not always easy. Consumer Reports is therefore calculated by an

More information

MODULE S1 DESCRIPTIVE STATISTICS

MODULE S1 DESCRIPTIVE STATISTICS MODULE S1 DESCRIPTIVE STATISTICS All educators are involved in research and statistics to a degree. For this reason all educators should have a practical understanding of research design. Even if an educator

More information

Multiple Linear Regression Analysis

Multiple Linear Regression Analysis Revised July 2018 Multiple Linear Regression Analysis This set of notes shows how to use Stata in multiple regression analysis. It assumes that you have set Stata up on your computer (see the Getting Started

More information

Research paper. Split-plot ANOVA. Split-plot design. Split-plot design. SPSS output: between effects. SPSS output: within effects

Research paper. Split-plot ANOVA. Split-plot design. Split-plot design. SPSS output: between effects. SPSS output: within effects Research paper Effects of alcohol and caffeine on driving ability Split-plot ANOVA conditions: No alcohol; no caffeine alcohol; no caffeine No alcohol; caffeine Alcohol; caffeine Driving in simulator Error

More information

12/30/2017. PSY 5102: Advanced Statistics for Psychological and Behavioral Research 2

12/30/2017. PSY 5102: Advanced Statistics for Psychological and Behavioral Research 2 PSY 5102: Advanced Statistics for Psychological and Behavioral Research 2 Selecting a statistical test Relationships among major statistical methods General Linear Model and multiple regression Special

More information

Week 17 and 21 Comparing two assays and Measurement of Uncertainty Explain tools used to compare the performance of two assays, including

Week 17 and 21 Comparing two assays and Measurement of Uncertainty Explain tools used to compare the performance of two assays, including Week 17 and 21 Comparing two assays and Measurement of Uncertainty 2.4.1.4. Explain tools used to compare the performance of two assays, including 2.4.1.4.1. Linear regression 2.4.1.4.2. Bland-Altman plots

More information

Effect of Sample Size on Correlation and Regression Coefficients

Effect of Sample Size on Correlation and Regression Coefficients Effect of Sample Size on Correlation and Regression Coefficients Swati Gupta 1 Research Scholar, Department of Education, Aligarh Muslim University, India Dr. Mamun Ali Naji Qasem 2 Faculty of Education,

More information

Decomposition of the Genotypic Value

Decomposition of the Genotypic Value Decomposition of the Genotypic Value 1 / 17 Partitioning of Phenotypic Values We introduced the general model of Y = G + E in the first lecture, where Y is the phenotypic value, G is the genotypic value,

More information

5 To Invest or not to Invest? That is the Question.

5 To Invest or not to Invest? That is the Question. 5 To Invest or not to Invest? That is the Question. Before starting this lab, you should be familiar with these terms: response y (or dependent) and explanatory x (or independent) variables; slope and

More information

Regression Equation. November 29, S10.3_3 Regression. Key Concept. Chapter 10 Correlation and Regression. Definitions

Regression Equation. November 29, S10.3_3 Regression. Key Concept. Chapter 10 Correlation and Regression. Definitions MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 10 Correlation and Regression 10 1 Review and Preview 10 2 Correlation 10 3 Regression 10 4 Variation and Prediction Intervals

More information

Chapter 23. Inference About Means. Copyright 2010 Pearson Education, Inc.

Chapter 23. Inference About Means. Copyright 2010 Pearson Education, Inc. Chapter 23 Inference About Means Copyright 2010 Pearson Education, Inc. Getting Started Now that we know how to create confidence intervals and test hypotheses about proportions, it d be nice to be able

More information

CHAPTER III RESEARCH METHODOLOGY

CHAPTER III RESEARCH METHODOLOGY CHAPTER III RESEARCH METHODOLOGY In this chapter, the researcher will elaborate the methodology of the measurements. This chapter emphasize about the research methodology, data source, population and sampling,

More information

Differential Item Functioning

Differential Item Functioning Differential Item Functioning Lecture #11 ICPSR Item Response Theory Workshop Lecture #11: 1of 62 Lecture Overview Detection of Differential Item Functioning (DIF) Distinguish Bias from DIF Test vs. Item

More information

PSYCHOLOGY 300B (A01) One-sample t test. n = d = ρ 1 ρ 0 δ = d (n 1) d

PSYCHOLOGY 300B (A01) One-sample t test. n = d = ρ 1 ρ 0 δ = d (n 1) d PSYCHOLOGY 300B (A01) Assignment 3 January 4, 019 σ M = σ N z = M µ σ M d = M 1 M s p d = µ 1 µ 0 σ M = µ +σ M (z) Independent-samples t test One-sample t test n = δ δ = d n d d = µ 1 µ σ δ = d n n = δ

More information

CHAPTER 3 RESEARCH METHODOLOGY

CHAPTER 3 RESEARCH METHODOLOGY CHAPTER 3 RESEARCH METHODOLOGY 3.1 Introduction 3.1 Methodology 3.1.1 Research Design 3.1. Research Framework Design 3.1.3 Research Instrument 3.1.4 Validity of Questionnaire 3.1.5 Statistical Measurement

More information

Lecture 12: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression

Lecture 12: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression Lecture 12: more Chapter 5, Section 3 Relationships between Two Quantitative Variables; Regression Equation of Regression Line; Residuals Effect of Explanatory/Response Roles Unusual Observations Sample

More information

Daniel Boduszek University of Huddersfield

Daniel Boduszek University of Huddersfield Daniel Boduszek University of Huddersfield d.boduszek@hud.ac.uk Introduction to Multiple Regression (MR) Types of MR Assumptions of MR SPSS procedure of MR Example based on prison data Interpretation of

More information