# Design of Experiments (DOE)

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Design of Experiments (DOE) Overview The Assistant DOE includes a subset of the DOE features available in core Minitab and uses a sequential experimentation process that simplifies the process of creating and analyzing designs. The process begins with screening designs to identify the most important factors. Then, we provide higher-resolution designs to look for curvature and determine a final model that can be used to identify factor settings that optimize the response. In this paper, we outline the steps of the experimentation process. We provide information on how we determined which designs to offer in the Assistant, including the role of power. We also discuss the process of detecting and fitting curvature in the data. The paper also describes the method used for analyzing the data and identifying the best model. The paper also provides additional information about the following data checks in the Assistant Report Card: Blocks Unusual data Detection Ability

2 Method Sequential experimentation process The DOE features in the Assistant guide users through a sequential process to design and analyze one or more experiments to identify the most important factors and find the factor settings that optimize a response. A sequential experimentation approach uses a set of smaller experiments where the results at each stage guide the experimentation at the next stage. An advantage of the sequential approach is that at each stage, only a small number of experimental trials are run so that you are less likely to waste resources on unproductive trials. The Assistant provides a subset of the DOE features available in core Minitab in a structured format that simplifies the process of creating and analyzing designs. The steps in the process are: 1. Create a screening design for 6 to 15 factors. 2. Fit a screening model that includes the main effects and analyze the results to find the most important factors. 3. Create a modeling design based on the results of step 2 that includes the 25 most important factors. 4. Fit a linear model that includes main effects and 2-way interactions and analyze the results and look for evidence of curvature in the relationship between the factors and the response. 5. If curvature is not detected in step 4, use that model to identify factor settings that optimize the response. 6. If curvature is detected in step 4, the Assistant recommends that you add points for curvature to the design. 7. Fit a quadratic model that includes square terms to model the curvature and analyze the results. 8. Using the final model, identify factor settings that optimize the response. DESIGN OF EXPERIMENTS (DOE) 2

3 The following sections provide more detailed information on these aspects of Assistant DOE: Screening designs Modeling designs Fitting the model Screening designs Typically, you begin the sequential experimentation process with a large number of potential factors and then you eliminate the ones with little effect on the response. Screening designs are experimental designs that are intended to identify the few most important factors from a larger set of factors. In the Assistant, screening designs are offered for 6 to 15 factors. Type of design The Assistant screening designs are Plackett-Burman designs, a special type of Resolution III 2-level designs. There are two primary advantages of Plackett-Burman designs: They allow for the estimation of the main effects of the factors using very few experimental runs (as few as 12). Because experimental runs can be expensive to perform, this makes these designs more cost-effective. There is only partial or fractional confounding between the main effects and two-factor interactions. Effects that cannot be estimated separately from one another are said to be confounded. In Plackett-Burman designs, the confounding is considered partial because the contribution of each effect is only a fraction of the full size of the interaction effect. We determined that, for the purposes of screening, it was a reasonable approach to use the Plackett-Burman designs that estimate main effects only and do not estimate interaction terms. Screening designs are intended to include a large number of factors. Because at least one run is required for each term in the model, and the number of interaction terms increases faster than the number of main effects, for most situations it is not practical or cost-effective to fit a model with interactions. Additionally, in most cases, only a small number of factors explain most of the effects on the response. The goal of a screening design is to identify these factors, and Plackett- Burman designs enable users to identify these important main effects. Furthermore, as stated earlier, because the confounding between terms in Plackett-Burman designs is only partial, it is less likely that a significant main effect is in reality a significant 2-factor interaction. Power and folding When we created the design catalog, our goal was to only make available designs that had adequate power. We calculated the power for all the designs and eliminated certain designs due to low power, including the 12-run Plackett-Burman design for 10 or 11 factors. For designs with 10 or 11 factors, only the 20-run Plackett-Burman design is available. We also eliminated the designs for 16, 17, and 18 factors because of low power and the higher number of runs. For more information on the specific power for the designs, see the section on Detection ability. DESIGN OF EXPERIMENTS (DOE) 3

5 Fitting models using backward selection We explored several methods of fitting the models and determined that backward selection using an of 0.10 was the best approach. When you fit a model, Minitab starts by including all possible terms. Then, one by one, Minitab removes the least significant term, while maintaining the hierarchy of the model. Hierarchy means that, if an interaction term is significant, then the linear terms of both factors that form the interaction must also be included in the model. This is a form of backward selection and is intended to automate a process of model selection that is typically done by hand. In all the designs in Assistant DOE, the terms are independent or (in the case of square terms) nearly so. Therefore, multicollinearity, which indicates factors are correlated with one another, is not likely to occur. Multicollinearity can cause stepwise procedures to miss the best model. Using = 0.10 rather than the commonly used = 0.05 helps to increase the power of the tests, which increases the likelihood that important terms remain in the model. DESIGN OF EXPERIMENTS (DOE) 5

6 Data Checks Blocks Blocks are used in experimental designs to minimize bias and error due to external influences on the experiment, such as noise variables, missing variables, or differences in how the runs in each block were performed. By placing experimental runs performed together in blocks, you can determine whether differences exist between blocks and account for these differences in the model. Objective In Assistant DOE, you can include replicates of the design when creating a modeling design and can add axial points to a modeling design to fit curvature in the model. Often, replicates and axial points are performed at different times or under different conditions than runs in the base design. When runs are performed at different times or conditions, it is best practice to account for possible effects due to different conditions. Method To account for possible differences in experimental conditions for replicates or axial points and the base design, Minitab places replicates and axial points in separate blocks. Specifically, in modeling designs, Minitab places replicates of the base design in separate blocks in the model. In quadratic designs, Minitab places the axial points used to detect curvature in the design in a separate block. Results To be consistent with the treatment of other terms in the model, blocks are evaluated using the backward elimination method. The report card states whether the block term is statistically significant, indicating that there are differences across the blocks. If a difference exists between blocks, consider investigating the cause to determine if there were any inconsistencies in the experimental conditions or procedures. DESIGN OF EXPERIMENTS (DOE) 6

7 Status Condition Blocks are in the final model Blocks are significant. Because the runs in each block are typically performed at different times, the significant difference in blocks indicates that conditions may have changed over time. This difference could be due to external influences on the experiment, such as noise variables, missing variables that should have been included in the experiment, or differences in how the runs in each block were performed. Consider investigating the cause of the difference between the blocks. Blocks are not in the final model Blocks are not significant. Because the runs in each block are typically performed at different times, this result indicates that there is no evidence of differences in the experimental conditions over time. Unusual Data In the Assistant DOE procedures, we define unusual data as observations with large standardized residuals, a common measure used to identify unusual data in model-fitting procedures (Neter et al., 1996). Because unusual data can have a strong influence on the results, you may need to correct the data to make the analysis valid. Objective We wanted to determine how large the standardized residuals need to be to signal that a data point is unusual. Method We developed our guidelines for identifying unusual observations based on the standard DOE procedure in Minitab (Stat > DOE > Factorial > Analyze Factorial Design and Stat > DOE > Response Surface > Analyze Response Surface Design). Results The standardized residual equals the value of a residual,, divided by an estimate of its standard deviation. In general, an observation is considered unusual if the absolute value of the standardized residual is greater than 2. However, this guideline is somewhat conservative. You would expect approximately 5% of all observations to meet this criterion by chance with large data sets (if the errors are normally distributed). However, with small experimental data sets, few if any observations will be flagged by chance, and it is good practice to investigate the cause of unusual values. DESIGN OF EXPERIMENTS (DOE) 7

8 When checking for unusual data, the Assistant Report Card displays the following status indicators: Status Condition No standardized residuals 2 There are no unusual data points. Unusual data can have a strong influence on the results. One standardized residual 2 One data point has a large residual and is not well fit by the model. This point is marked in red on the Diagnostic Report and is in row X of the worksheet. Because unusual data can have a strong influence on the results, try to identify the cause for its unusual nature. Correct any data entry or measurement errors. Consider performing trials associated with special causes again and redoing the analysis. More than one standardized residual 2 x data points have large residuals and are not well fit by the model. These points are marked in red on the Diagnostic Report. You can hover over a point or use Minitab s brushing feature to identify the worksheet rows. Because unusual data can have a strong influence on the results, try to identify the cause for their unusual nature. Correct any data entry or measurement errors. Consider performing trials associated with special causes again and redoing the analysis. Detection ability When performing designed experiments, it is useful to know what effect size a design is likely to detect prior to collecting data. If the design isn t powerful enough to detect the desired effect size, it may be appropriate to include more runs in the design. However, because including more runs in a design can be expensive, it is important to determine whether the additional power is necessary. Objective We wanted to provide users with information about the effect size their design can detect at 60% and 80% power levels. We also wanted to provide users with information about the effect sizes for design that include additional runs when available. For screening designs with 6 to9 factors, users can choose to include 12 or 24 runs in their design. For modeling designs, users can include replicates of the base design, increasing the total number of runs in the design. Method We computed the power and the effect size that can be detected for each design in the Assistant. The power is the probability of finding a factor effect to be statistically significant. The effect sizes are in standard deviation units. DESIGN OF EXPERIMENTS (DOE) 8

9 Results The Summary report displays the effect sizes you can detect with your design with 60% power and 80% power. For screening designs where a larger (folded) design is available, the report also specifies what size effect can be detected with 80% power in the larger design. For modeling designs where more replicates are available, the report specifies what effect size can be detected with 80% power with additional replication. Then, the user can judge whether the selected design is appropriate and weigh the advantages of using a design with more runs when available. See Appendix A for specific information about the effect sizes each design can detect at 60% power and 80% power. The following image is an example of the power information provided in the Summary report. DESIGN OF EXPERIMENTS (DOE) 9

10 References Neter, J., Kutner, M.H., Nachtsheim, C.J., & Wasserman, W. (1996). Applied linear statistical models. Chicago: Irwin. DESIGN OF EXPERIMENTS (DOE) 10

11 Appendix A: Detection ability We computed the power and the effect size that can be detected for each design in the Assistant. The power is the probability of finding a factor effect to be statistically significant. The effect sizes are in standard deviation units. The effect size associated with a model term is twice the term s coefficient in the true model equation. In a screening model, the effect size has a simple interpretation: the change in the mean response when a factor changes from its low level to its high level. Table 1 The following table shows the effect sizes for the Screening designs available in the Assistant. Number of runs power 60% power 80% DESIGN OF EXPERIMENTS (DOE) 11

12 Table 2 The following table shows the effect sizes for the Modeling designs available in the Assistant. Total Categorical Replicates power 60% power 80% DESIGN OF EXPERIMENTS (DOE) 12

13 Total Categorical Replicates power 60% power 80% DESIGN OF EXPERIMENTS (DOE) 13

14 Total Categorical Replicates power 60% power 80% DESIGN OF EXPERIMENTS (DOE) 14

15 Total Categorical Replicates power 60% power 80% DESIGN OF EXPERIMENTS (DOE) 15

### The DOE features in the Assistant guide users through a sequential process to design and analyze one or more experiments to identify the most

This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. The Assistant DOE includes a subset

### Regression analysis in the Assistant fits a model with one continuous predictor and one continuous response and can fit two types of models:

This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. The simple regression procedure in the

: 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

### KEYS TO SUCCESSFUL DESIGNED EXPERIMENTS

KEYS TO SUCCESSFUL DESIGNED EXPERIMENTS Mark J. Anderson and Shari L. Kraber Consultants, Stat-Ease, Inc., Minneapolis, MN (e-mail: Mark@StatEase.com) ABSTRACT This paper identifies eight keys to success

### JMP Design of Experiments (DOE) Fit the design to the problem, not the problem to the design

JMP Design of Experiments (DOE) Fit the design to the problem, not the problem to the design The JMP DOE Difference: Tailor-Made Designs Don't be forced to fit your problem to the available desgins For

### Chapter 4 and 5 solutions

Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,

### Attribute Agreement Analysis

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Attribute

### HOW TO USE MINITAB: DESIGN OF EXPERIMENTS. Noelle M. Richard 08/27/14

HOW TO USE MINITAB: DESIGN OF EXPERIMENTS 1 Noelle M. Richard 08/27/14 CONTENTS 1. Terminology 2. Factorial Designs When to Use? (preliminary experiments) Full Factorial Design General Full Factorial Design

### Analytical Method Validation

Analytical Method Validation A. Es-haghi Ph.D. Dept. of Physico chemistry vaccine and serum research institute a.eshaghi@rvsri.ir http://www.rvsri.ir/ Introduction Test procedures for assessment of the

Table of Contents Introduction to Minitab...2 Example 1 One-Way ANOVA...3 Determining Sample Size in One-way ANOVA...8 Example 2 Two-factor Factorial Design...9 Example 3: Randomized Complete Block Design...14

### 4. Multiple Regression in Practice

30 Multiple Regression in Practice 4. Multiple Regression in Practice The preceding chapters have helped define the broad principles on which regression analysis is based. What features one should look

### Joseph M. Juran Center for Research in Supply Chain, Operations, and Quality

Joseph M. Juran Center for Research in Supply Chain, Operations, and Quality Professor Kevin Linderman Academic Co-Director of Joseph M. Juran Center for Research in Supply Chain, Operations, and Quality

### South Carolina College- and Career-Ready (SCCCR) Probability and Statistics

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way

### 12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand when to use multiple Understand the multiple equation and what the coefficients represent Understand different methods

### Robust Test Designs for Dynamic Marketing, Retail, and Advertising Programs

Robust Test Designs for Dynamic Marketing, Retail, and Advertising Programs Bell, Gordon LucidView 80 Rolling Links Blvd. Oak Ridge, TN 37830 USA E-mail: gbell@lucidview.com Introduction Marketing and

### Factorial Analysis of Variance

Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

### Chapter 13 Introduction to Nonlinear Regression( 非 線 性 迴 歸 )

Chapter 13 Introduction to Nonlinear Regression( 非 線 性 迴 歸 ) and Neural Networks( 類 神 經 網 路 ) 許 湘 伶 Applied Linear Regression Models (Kutner, Nachtsheim, Neter, Li) hsuhl (NUK) LR Chap 10 1 / 35 13 Examples

### MAT Solving Linear Systems Using Matrices and Row Operations

MAT 171 8.5 Solving Linear Systems Using Matrices and Row Operations A. Introduction to Matrices Identifying the Size and Entries of a Matrix B. The Augmented Matrix of a System of Equations Forming Augmented

### Full Factorial Design of Experiments

Full Factorial Design of Experiments 0 Module Objectives Module Objectives By the end of this module, the participant will: Generate a full factorial design Look for factor interactions Develop coded orthogonal

### This paper describes an interactive spreadsheet-based tool that can be used to generate data representative

Vol. 8, No. 2, January 2008, pp. 55 64 issn 1532-0545 08 0802 0055 informs I N F O R M S Transactions on Education An Interactive Spreadsheet-Based Tool to Support Teaching Design of Experiments S. T.

### Didacticiel - Études de cas

1 Topic Regression analysis with LazStats (OpenStat). LazStat 1 is a statistical software which is developed by Bill Miller, the father of OpenStat, a wellknow tool by statisticians since many years. These

### Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS

Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple

### SPSS Explore procedure

SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,

### DEPARTMENT 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,

### GLOSSARY FOR DESIGN OF EXPERIMENTS

GLOSSARY FOR DESIGN OF EXPERIMENTS Adaptation provenant du site Internet http://www.mathoptions.com ANOVA -- An acronym for "ANalysis Of VAriance," a statistical technique that separates the variation

### RARITAN VALLEY COMMUNITY COLLEGE ACADEMIC COURSE OUTLINE MATH 111H STATISTICS II HONORS

RARITAN VALLEY COMMUNITY COLLEGE ACADEMIC COURSE OUTLINE MATH 111H STATISTICS II HONORS I. Basic Course Information A. Course Number and Title: MATH 111H Statistics II Honors B. New or Modified Course:

### [ABOUT THE AUTHOR. First Steps in Experimental Design The Screening Experiment. John A. Wass

First Steps in Experimental Design The Screening Experiment John A. Wass Statistical Viewpoint addresses principles of statistics useful to practitioners in compliance and validation. We intend to present

### 5. Fit the models to each phenotypic dataset using ouch and record the AICc and parameter estimates.

25 629 630 631 632 633 634 635 636 APPENDIX A. SUPPLEMENTARY FIGURES Fig. A1 is a schematic diagram of the simulation study design. Fig. A2 shows the distribution of selection opportunity, discriminability

### Premaster 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

### How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

### Multiple Comparison Tests for Balanced, One-Factor Designs

Multiple Comparison Tests for Balanced, One-Factor Designs Term Paper FRST 533 Dec. 15, 2005 Craig Farnden 1.0 Introduction Frequently after completing an analysis of variance test in a single factor experimental

### Multiple 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

### Multiple Regression YX1 YX2 X1X2 YX1.X2

Multiple Regression Simple or total correlation: relationship between one dependent and one independent variable, Y versus X Coefficient of simple determination: r (or r, r ) YX YX XX Partial correlation:

### Multiple 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.

### Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0.

Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged

### 5.6 2 k p Fractional Factorial Designs

5.6 2 k p Fractional Factorial Designs There are k factors of interest each having 2 levels. There are only enough resources to run 1/2 p of the full factorial 2 k design. Thus, we say we want to run a

### Multiple Regression in SPSS STAT 314

Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan

### Scatter Plot, Correlation, and Regression on the TI-83/84

Scatter Plot, Correlation, and Regression on the TI-83/84 Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. This page

### ESTIMATING THE DISTRIBUTION OF DEMAND USING BOUNDED SALES DATA

ESTIMATING THE DISTRIBUTION OF DEMAND USING BOUNDED SALES DATA Michael R. Middleton, McLaren School of Business, University of San Francisco 0 Fulton Street, San Francisco, CA -00 -- middleton@usfca.edu

Name: Date: PC1144 Physics IV Radioactivity 5 Laboratory Worksheet Part A: Simulated Radioactive Decay Group Data Session Data Throw Removed (A) Remaining (N) Removed (A) Remaining (N) 0 0 200 0 1 2 3

### SELECTING THE BEST MODEL FOR MULTIPLE LINEAR REGRESSION

SELECTING THE BEST MODEL FOR MULTIPLE LINEAR REGRESSION Introduction In multiple regression a common goal is to determine which independent variables contribute significantly to explaining the variability

### PASS Sample Size Software. Linear Regression

Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes

### 11. 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:

### ABSORBENCY OF PAPER TOWELS

ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?

### 2. 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

### Designing a Better Paper Helicopter

Designing a Better Paper Helicopter USING RESPONSE SURFACE METHODOLOGY Webinar: Designing a Better Paper Helicopter: Using Response Surface Methodology Author Erik Barry Erhardt discusses the article in

### Credit Risk Analysis Using Logistic Regression Modeling

Credit Risk Analysis Using Logistic Regression Modeling Introduction A loan officer at a bank wants to be able to identify characteristics that are indicative of people who are likely to default on loans,

### Analysis of Variance. MINITAB User s Guide 2 3-1

3 Analysis of Variance Analysis of Variance Overview, 3-2 One-Way Analysis of Variance, 3-5 Two-Way Analysis of Variance, 3-11 Analysis of Means, 3-13 Overview of Balanced ANOVA and GLM, 3-18 Balanced

### Simple 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

### Empirical Model-Building and Response Surfaces

Empirical Model-Building and Response Surfaces GEORGE E. P. BOX NORMAN R. DRAPER Technische Universitat Darmstadt FACHBEREICH INFORMATIK BIBLIOTHEK Invortar-Nf.-. Sachgsbiete: Standort: New York John Wiley

### Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step

Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different

### " Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

Regression analysis Advanced Financial Accounting II Åbo Akademi School of Business Regression analysis A statistical process for estimating the relationships among variables Includes many techniques for

### Partial Fractions. Combining fractions over a common denominator is a familiar operation from algebra:

Partial Fractions Combining fractions over a common denominator is a familiar operation from algebra: From the standpoint of integration, the left side of Equation 1 would be much easier to work with than

### Florida Math for College Readiness

Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

### How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power

STRUCTURAL EQUATION MODELING, 9(4), 599 620 Copyright 2002, Lawrence Erlbaum Associates, Inc. TEACHER S CORNER How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power Linda K. Muthén

### Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

### MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL. by Michael L. Orlov Chemistry Department, Oregon State University (1996)

MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL by Michael L. Orlov Chemistry Department, Oregon State University (1996) INTRODUCTION In modern science, regression analysis is a necessary part

### Quality Engineering & Management. Session 7.1: Design of Experiments

Quality Engineering & Management Session 7.1: Design of Experiments Dr. Holly Ott Chair: Prof. Martin Grunow TUM School of Management Holly Ott Quality Engineering & Management Module 7 1 Learning Objectives

### Stepwise Regression. Chapter 311. Introduction. Variable Selection Procedures. Forward (Step-Up) Selection

Chapter 311 Introduction Often, theory and experience give only general direction as to which of a pool of candidate variables (including transformed variables) should be included in the regression model.

### How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power

How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power Linda K. Muthén Muthén & Muthén 11965 Venice Blvd., Suite 407 Los Angeles, CA 90066 Telephone: (310) 391-9971 Fax: (310) 391-8971

### 1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

### SOME NOTES ON STATISTICAL INTERPRETATION. Below I provide some basic notes on statistical interpretation for some selected procedures.

1 SOME NOTES ON STATISTICAL INTERPRETATION Below I provide some basic notes on statistical interpretation for some selected procedures. The information provided here is not exhaustive. There is more to

### Supporting Online Material for

www.sciencemag.org/cgi/content/full/319/5862/414/dc1 Supporting Online Material for Application of Bloom s Taxonomy Debunks the MCAT Myth Alex Y. Zheng, Janessa K. Lawhorn, Thomas Lumley, Scott Freeman*

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

### ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section

ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 5-3.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 6-4.2 Solving Equations by

### Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association

Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association This information is adapted from and draws heavily on: Sheskin, David J. 2000. Handbook of Parametric and

### Traditional Conjoint Analysis with Excel

hapter 8 Traditional onjoint nalysis with Excel traditional conjoint analysis may be thought of as a multiple regression problem. The respondent s ratings for the product concepts are observations on the

### 5. 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

### Using Excel for Statistics Tips and Warnings

Using Excel for Statistics Tips and Warnings November 2000 University of Reading Statistical Services Centre Biometrics Advisory and Support Service to DFID Contents 1. Introduction 3 1.1 Data Entry and

### Penalized regression: Introduction

Penalized regression: Introduction Patrick Breheny August 30 Patrick Breheny BST 764: Applied Statistical Modeling 1/19 Maximum likelihood Much of 20th-century statistics dealt with maximum likelihood

### MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

### EDUCATION AND PRODUCTION. A Model for Persistency of Egg Production 1

EDUCATION AND PRODUCTION A Model for Persistency of Egg Production 1 M. Grossman,*,,2 T. N. Gossman,* and W. J. Koops*, *Department of Animal Sciences, University of Illinois, Urbana, Illinois 61801; Department

### 1.1 Solving a Linear Equation ax + b = 0

1.1 Solving a Linear Equation ax + b = 0 To solve an equation ax + b = 0 : (i) move b to the other side (subtract b from both sides) (ii) divide both sides by a Example: Solve x = 0 (i) x- = 0 x = (ii)

### Validating Methods using Waters Empower TM 2 Method. Validation. Manager

Validating Methods using Waters Empower TM 2 Method Validation Manager (MVM) Anders Janesten Nordic Informatics Sales Specialist 2008 Waters Corporation Decision-centric centric method development information

### What is the purpose of this document? What is in the document? How do I send Feedback?

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Statistics

### Multiple Linear Regression

Multiple Linear Regression by Lin Naing @ Mohd. Ayub Sadiq School of Dental Sciences Universiti Sains Malaysia 1 Contents Simple Linear Regression (Revision) Basic Theory of Multiple Linear Regression

### A Correlation of. to the. South Carolina Data Analysis and Probability Standards

A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards

### Correlation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down)

Two-Variable Statistics Correlation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down) Positive Correlation As one variable

### Lasso on Categorical Data

Lasso on Categorical Data Yunjin Choi, Rina Park, Michael Seo December 14, 2012 1 Introduction In social science studies, the variables of interest are often categorical, such as race, gender, and nationality.

### Least Squares Estimation

Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

### Using JMP with a Specific

1 Using JMP with a Specific Example of Regression Ying Liu 10/21/ 2009 Objectives 2 Exploratory data analysis Simple liner regression Polynomial regression How to fit a multiple regression model How to

### Correlational Research

Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.

### Fairfield Public Schools

Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity

### Design of Experiments and Experimental Data Processing

Design of Experiments and Experimental Data Processing Course plan October 9, 2008 Fall 2008 Prof. Ivan Kalaykov Room: T-1224, Tel. 019-303625, ivan.kalaykov@oru.se 1 Course objectives In order to discover

### Residuals. Residuals = ª Department of ISM, University of Alabama, ST 260, M23 Residuals & Minitab. ^ e i = y i - y i

A continuation of regression analysis Lesson Objectives Continue to build on regression analysis. Learn how residual plots help identify problems with the analysis. M23-1 M23-2 Example 1: continued Case

### Lecture - 32 Regression Modelling Using SPSS

Applied Multivariate Statistical Modelling Prof. J. Maiti Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur Lecture - 32 Regression Modelling Using SPSS (Refer

### Equations and Inequalities

Rational Equations Overview of Objectives, students should be able to: 1. Solve rational equations with variables in the denominators.. Recognize identities, conditional equations, and inconsistent equations.

### Using SPSS for Multiple Regression. UDP 520 Lab 7 Lin Lin December 4 th, 2007

Using SPSS for Multiple Regression UDP 520 Lab 7 Lin Lin December 4 th, 2007 Step 1 Define Research Question What factors are associated with BMI? Predict BMI. Step 2 Conceptualizing Problem (Theory) Individual

### 2. Linear regression with multiple regressors

2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions

### UNDERSTANDING MULTIPLE REGRESSION

UNDERSTANDING Multiple regression analysis (MRA) is any of several related statistical methods for evaluating the effects of more than one independent (or predictor) variable on a dependent (or outcome)

### Studying Material Inventory Management for Sock Production Factory

Studying Inventory Management for Sock Production Factory Pattanapong Ariyasit*, Nattaphon Supawatcharaphorn** Industrial Engineering Department, Faculty of Engineering, Sripatum University E-mail: pattanapong.ar@spu.ac.th*,

### By Hui Bian Office for Faculty Excellence

By Hui Bian Office for Faculty Excellence 1 Email: bianh@ecu.edu Phone: 328-5428 Location: 2307 Old Cafeteria Complex 2 When want to predict one variable from a combination of several variables. When want

### Figure 1. Figure 2. Figure 3. Figure 4. normality such as non-parametric procedures.

Introduction to Building a Linear Regression Model Leslie A. Christensen The Goodyear Tire & Rubber Company, Akron Ohio Abstract This paper will explain the steps necessary to build a linear regression

### Graduate Certificate in Systems Engineering

Graduate Certificate in Systems Engineering Systems Engineering is a multi-disciplinary field that aims at integrating the engineering and management functions in the development and creation of a product,

### UBS Global Asset Management has

IIJ-130-STAUB.qxp 4/17/08 4:45 PM Page 1 RENATO STAUB is a senior assest allocation and risk analyst at UBS Global Asset Management in Zurich. renato.staub@ubs.com Deploying Alpha: A Strategy to Capture