# UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. PROBLEM SET No. 5 Official Solutions

Size: px
Start display at page:

Download "UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. PROBLEM SET No. 5 Official Solutions"

Transcription

1 1 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences C. SPANOS Special Issues in Semiconductor Manufacturing EECS 290H Fall 0 PROBLEM SET No. Official Solutions 1. A process engineer is about to begin a comprehensive study to determine the effects of five variables on the etch rate of polysilicon. a) If a 2 factorial design were used, how many runs would be made? 2 = 32 b) If σ 2 is the experimental error variance of an individual observation, what is the variance of the main effect? Assuming 32 runs, then the variance of the main effect will be 2σ 2 /16 = σ 2 /8. c) What is the simple formula for a 99% confidence interval for the main effect of variable 1? (Simple here means that you can assume that the σ of the process is known.) Assuming that we know sigma, then the 99% interval is given as: Effx 1 ± 2.67σ/2.83 d) On the basis of some previous work it is believed that σ = nm/min. If the experimenter wants 9% confidence intervals for the main effect and interactions whose lengths are equal to nm/min, (i.e. the upper limit minus the lower limit is equal to nm/min), how many replications of the 2 factorial design will be required? The width of the 9% intervals will be = 2 x 1.96 * * Sqrt(4/N), where N=32, 64, 96,... In order to get as close as possible to satisfying this equation when N is a multiple of 32, I choose N=992, or 31 replications of the 32 run experiment. 2. Consider the following data representing non-uniformity (in %) of Films Grown by CVD, where A, B, C and D represent different chambers and (1), (2) and (3) represent different recipes. (1) A B C D

2 2 (2) (3) Carry out analysis of variance first using the data as is and then using the transformation Y = y -1. Plot the residuals, and consider whether in the new response metric there is evidence of model inadequacy. Compare the treatment averages for the two different representations of the response. The basic ANOVA shown below reveals that the interaction term is insignificant for either the straight or the transformed data. The transformed data analysis however, does give me stronger significance and much more reasonably distributed residuals. In both cases the treatment averages are significantly impacted by the treatment choice. In the next pages I repeat the analysis in greater detail and by exluding the inisgnificant interaction term Response Non-Uniformity Model Error Prob > F C. Total <.0001 Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Recipe <.0001 Chamber <.0001 Recipe*Chamber Response Y^-1 Model Error Prob > F C. Total <.0001 Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Recipe <.0001 Chamber <.0001 Recipe*Chamber

3 3 Response Non-Uniformity, excluding interaction term Non-Uniformity Predicted P<.0001 RSq=0.6 RMSE=0.182 Non-Uniformity Actual Model Error Prob > F C. Total <.0001 Lack Of Fit Lack Of Fit Pure Error Prob > F Total Error Max RSq Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Recipe <.0001 Chamber <.0001 Non-Uniformity Residual Non-Uniformity Predicted Residuals do NOT appear to be IIND. A transformation is NEEDED here

4 4 Response Y^-1, excluding interaction term 6 4 Y^-1 Actual Y^-1 Predicted P<.0001 RSq=0.84 RMSE= Model Error Prob > F C. Total <.0001 Lack Of Fit Lack Of Fit Pure Error Prob > F Total Error Max RSq Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Recipe <.0001 Chamber <.0001 Y^-1 Residual Y^-1 Predicted

5 3. Consider a fractional factorial design. (a) How many variables does the design have? This design has 8 variables. (b) How many runs are involved in the design? = 2 4 = 16 runs. (c) How many levels are used for each of the variables? This is a 2-level factorial, so two levels are used. (d) How many independent generators are there? Since this is a 16 th fraction (the -4 in the exponent), we will need four independent generators. (e) Write the required generators that give you the maximum resolution. Here I cheated by looking them up at Box Hunter an Hunter: I=1248, I=138, I=2368, I=1237 (f) What is the resolution of your design? This is a resolution IV design: no main effects are confounded with two parameter interactions or with other main effects. 4. Construct a fractional factorial design. Show how the design may be divided into eight blocks of eight runs each so that no main effect or two-factor interaction is confounded with any block effect. I looked up the answer on page 8 for the Box Hunter and Hunter textbook. I used one generator 7 = 12346, and the blocks were generated as (I need three blocking factors to generate 8 blocks (2 3 ) of 8 runs each for a total of =64 runs): B 1 = 137 B 2 = 126 B 3 = 1234 Clearly on main factors or two factor interactions interact with those bock effects.

6 6. Fit the followind PECVD deposition data with a linear model using regression techniques, and perform analysis of variance to evaluate the quality of your model. Is the linear model sufficient? Observation (u) Time (x u, min) Thickness (y u, μm) Formally I cannot talk about model sufficiency because without experimental replication I cannot directly test for it. Under these circumstances, my job is to find the simplest significant model, and to exclude all insignificant terms. Analysis shows that a linear model is clearly significant. This is true with or without the intercept term, which, on its own it is not significant. A quadratic term is clearly insignificant.

7 7 Response Thickness (full model) Thickness Actual Thickness Predicted P<.0001 RSq=0.97 RMSE=3.241 Model Error Prob > F C. Total <.0001 Parameter Estimates Term Estimate Std Error t Ratio Prob> t Intercept Time <.0001 (Time-.3333)*(Time-.3333) Thickness Residual Time Thickness Leverage Residua Thickness Predicted Time Leverage, P<.0001 Time*Time Thickness Leverage Residua Time*Time Leverage, P=0.9221

8 8 Response Thickness (Intercept and Linear Term Only) Thickness Actual Thickness Predicted P<.0001 RSq=0.97 RMSE=3.007 Model Error Prob > F C. Total <.0001 Parameter Estimates Term Estimate Std Error t Ratio Prob> t Intercept Time < Thickness Residual Time 0 Thickness Leverage Residua Thickness Predicted Time Leverage, P<.0001

9 9 Response Thickness (Intercept forced to zero, Linear Term Only) Thickness Actual Thickness Predicted P<.0001 RSq=. RMSE= Model Error Prob > F C. Total <.0001 Tested against reduced model: Y=0 Parameter Estimates Term Estimate Std Error t Ratio Prob> t Intercept Zeroed Time <.0001 Thickness Residual Time Thickness Leverage Residua Thickness Predicted Time Leverage, P<.0001

### SMA 6304 / MIT / MIT Manufacturing Systems. Lecture 10: Data and Regression Analysis. Lecturer: Prof. Duane S. Boning

SMA 6304 / MIT 2.853 / MIT 2.854 Manufacturing Systems Lecture 10: Data and Regression Analysis Lecturer: Prof. Duane S. Boning 1 Agenda 1. Comparison of Treatments (One Variable) Analysis of Variance

### Regression Analysis. Simple Regression Multivariate Regression Stepwise Regression Replication and Prediction Error EE290H F05

Regression Analysis Simple Regression Multivariate Regression Stepwise Regression Replication and Prediction Error 1 Regression Analysis In general, we "fit" a model by minimizing a metric that represents

### EE290H F05. Spanos. Lecture 5: Comparison of Treatments and ANOVA

1 Design of Experiments in Semiconductor Manufacturing Comparison of Treatments which recipe works the best? Simple Factorial Experiments to explore impact of few variables Fractional Factorial Experiments

### Stat 328 Final Exam (Regression) Summer 2002 Professor Vardeman

Stat Final Exam (Regression) Summer Professor Vardeman This exam concerns the analysis of 99 salary data for n = offensive backs in the NFL (This is a part of the larger data set that serves as the basis

### STAT 350: Summer Semester Midterm 1: Solutions

Name: Student Number: STAT 350: Summer Semester 2008 Midterm 1: Solutions 9 June 2008 Instructor: Richard Lockhart Instructions: This is an open book test. You may use notes, text, other books and a calculator.

### Plasma Etch Tool Gap Distance DOE Final Report

Plasma Etch Tool Gap Distance DOE Final Report IEE 572 Doug Purvis Mei Lee Gallagher 12/4/00 Page 1 of 10 Protocol Purpose: To establish new Power, Pressure, and Gas Ratio setpoints that are acceptable

### a. The least squares estimators of intercept and slope are (from JMP output): b 0 = 6.25 b 1 =

Stat 28 Fall 2004 Key to Homework Exercise.10 a. There is evidence of a linear trend: winning times appear to decrease with year. A straight-line model for predicting winning times based on year is: Winning

### Design of Engineering Experiments Chapter 5 Introduction to Factorials

Design of Engineering Experiments Chapter 5 Introduction to Factorials Text reference, Chapter 5 page 170 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA

### Formula for the t-test

Formula for the t-test: How the t-test Relates to the Distribution of the Data for the Groups Formula for the t-test: Formula for the Standard Error of the Difference Between the Means Formula for the

### Addition of Center Points to a 2 k Designs Section 6-6 page 271

to a 2 k Designs Section 6-6 page 271 Based on the idea of replicating some of the runs in a factorial design 2 level designs assume linearity. If interaction terms are added to model some curvature results

Assignment 9 Answer Keys Problem 1 (a) First, the respective means for the 8 level combinations are listed in the following table A B C Mean 26.00 + 34.67 + 39.67 + + 49.33 + 42.33 + + 37.67 + + 54.67

### Analysis of Covariance

Analysis of Covariance Using categorical and continuous predictor variables Example An experiment is set up to look at the effects of watering on Oak Seedling establishment Three levels of watering: (no

Answer Keys to Homework#10 Problem 1 Use either restricted or unrestricted mixed models. Problem 2 (a) First, the respective means for the 8 level combinations are listed in the following table A B C Mean

### Section Least Squares Regression

Section 2.3 - Least Squares Regression Statistics 104 Autumn 2004 Copyright c 2004 by Mark E. Irwin Regression Correlation gives us a strength of a linear relationship is, but it doesn t tell us what it

### Chapter 6 The 2 k Factorial Design Solutions

Solutions from Montgomery, D. C. (004) Design and Analysis of Experiments, Wiley, NY Chapter 6 The k Factorial Design Solutions 6.. A router is used to cut locating notches on a printed circuit board.

### Statistical Modelling in Stata 5: Linear Models

Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester 07/11/2017 Structure This Week What is a linear model? How good is my model? Does

### 20g g g Analyze the residuals from this experiment and comment on the model adequacy.

3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15??? Error??? Total 19 196.04 3.11. A pharmaceutical

### 23. Fractional factorials - introduction

173 3. Fractional factorials - introduction Consider a 5 factorial. Even without replicates, there are 5 = 3 obs ns required to estimate the effects - 5 main effects, 10 two factor interactions, 10 three

### Intro to Linear Regression

Intro to Linear Regression Introduction to Regression Regression is a statistical procedure for modeling the relationship among variables to predict the value of a dependent variable from one or more predictor

### Simple Linear Regression Using Ordinary Least Squares

Simple Linear Regression Using Ordinary Least Squares Purpose: To approximate a linear relationship with a line. Reason: We want to be able to predict Y using X. Definition: The Least Squares Regression

### What If There Are More Than. Two Factor Levels?

What If There Are More Than Chapter 3 Two Factor Levels? Comparing more that two factor levels the analysis of variance ANOVA decomposition of total variability Statistical testing & analysis Checking

### 3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value.

3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15??? Error??? Total 19 196.04 Completed table is: One-way

### Design of Engineering Experiments Part 5 The 2 k Factorial Design

Design of Engineering Experiments Part 5 The 2 k Factorial Design Text reference, Special case of the general factorial design; k factors, all at two levels The two levels are usually called low and high

### Multiple Predictor Variables: ANOVA

Multiple Predictor Variables: ANOVA 1/32 Linear Models with Many Predictors Multiple regression has many predictors BUT - so did 1-way ANOVA if treatments had 2 levels What if there are multiple treatment

### 19. Blocking & confounding

146 19. Blocking & confounding Importance of blocking to control nuisance factors - day of week, batch of raw material, etc. Complete Blocks. This is the easy case. Suppose we run a 2 2 factorial experiment,

### Data Set 1A: Algal Photosynthesis vs. Salinity and Temperature

Data Set A: Algal Photosynthesis vs. Salinity and Temperature Statistical setting These data are from a controlled experiment in which two quantitative variables were manipulated, to determine their effects

### Lecture 10. Factorial experiments (2-way ANOVA etc)

Lecture 10. Factorial experiments (2-way ANOVA etc) Jesper Rydén Matematiska institutionen, Uppsala universitet jesper@math.uu.se Regression and Analysis of Variance autumn 2014 A factorial experiment

### Design & Analysis of Experiments 7E 2009 Montgomery

Chapter 5 1 Introduction to Factorial Design Study the effects of 2 or more factors All possible combinations of factor levels are investigated For example, if there are a levels of factor A and b levels

### Simple Linear Regression

Simple Linear Regression 1 Correlation indicates the magnitude and direction of the linear relationship between two variables. Linear Regression: variable Y (criterion) is predicted by variable X (predictor)

### TOPIC 9 SIMPLE REGRESSION & CORRELATION

TOPIC 9 SIMPLE REGRESSION & CORRELATION Basic Linear Relationships Mathematical representation: Y = a + bx X is the independent variable [the variable whose value we can choose, or the input variable].

### Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras

Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras Lecture - 39 Regression Analysis Hello and welcome to the course on Biostatistics

### CHAPTER 5 NON-LINEAR SURROGATE MODEL

96 CHAPTER 5 NON-LINEAR SURROGATE MODEL 5.1 INTRODUCTION As set out in the research methodology and in sequent with the previous section on development of LSM, construction of the non-linear surrogate

### Acknowledgements. Outline. Marie Diener-West. ICTR Leadership / Team INTRODUCTION TO CLINICAL RESEARCH. Introduction to Linear Regression

INTRODUCTION TO CLINICAL RESEARCH Introduction to Linear Regression Karen Bandeen-Roche, Ph.D. July 17, 2012 Acknowledgements Marie Diener-West Rick Thompson ICTR Leadership / Team JHU Intro to Clinical

### Factorial 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

### 9 Correlation and Regression

9 Correlation and Regression SW, Chapter 12. Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then retakes the

### Lecture 3 Linear random intercept models

Lecture 3 Linear random intercept models Example: Weight of Guinea Pigs Body weights of 48 pigs in 9 successive weeks of follow-up (Table 3.1 DLZ) The response is measures at n different times, or under

### Intro to Linear Regression

Intro to Linear Regression Introduction to Regression Regression is a statistical procedure for modeling the relationship among variables to predict the value of a dependent variable from one or more predictor

### " M A #M B. Standard deviation of the population (Greek lowercase letter sigma) σ 2

Notation and Equations for Final Exam Symbol Definition X The variable we measure in a scientific study n The size of the sample N The size of the population M The mean of the sample µ The mean of the

### Design and Analysis of

Design and Analysis of Multi-Factored Experiments Module Engineering 7928-2 Two-level Factorial Designs L. M. Lye DOE Course 1 The 2 k Factorial Design Special case of the general factorial design; k factors,

### Unit 11: Multiple Linear Regression

Unit 11: Multiple Linear Regression Statistics 571: Statistical Methods Ramón V. León 7/13/2004 Unit 11 - Stat 571 - Ramón V. León 1 Main Application of Multiple Regression Isolating the effect of a variable

### Chapter 5 Introduction to Factorial Designs Solutions

Solutions from Montgomery, D. C. (1) Design and Analysis of Experiments, Wiley, NY Chapter 5 Introduction to Factorial Designs Solutions 5.1. The following output was obtained from a computer program that

### Chapter 6 The 2 k Factorial Design Solutions

Solutions from Montgomery, D. C. () Design and Analysis of Experiments, Wiley, NY Chapter 6 The k Factorial Design Solutions 6.. An engineer is interested in the effects of cutting speed (A), tool geometry

### Stat 411/511 ESTIMATING THE SLOPE AND INTERCEPT. Charlotte Wickham. stat511.cwick.co.nz. Nov

Stat 411/511 ESTIMATING THE SLOPE AND INTERCEPT Nov 20 2015 Charlotte Wickham stat511.cwick.co.nz Quiz #4 This weekend, don t forget. Usual format Assumptions Display 7.5 p. 180 The ideal normal, simple

### MODELS WITHOUT AN INTERCEPT

Consider the balanced two factor design MODELS WITHOUT AN INTERCEPT Factor A 3 levels, indexed j 0, 1, 2; Factor B 5 levels, indexed l 0, 1, 2, 3, 4; n jl 4 replicate observations for each factor level

### Suppose we needed four batches of formaldehyde, and coulddoonly4runsperbatch. Thisisthena2 4 factorial in 2 2 blocks.

58 2. 2 factorials in 2 blocks Suppose we needed four batches of formaldehyde, and coulddoonly4runsperbatch. Thisisthena2 4 factorial in 2 2 blocks. Some more algebra: If two effects are confounded with

### Simple Linear Regression

Simple Linear Regression MATH 282A Introduction to Computational Statistics University of California, San Diego Instructor: Ery Arias-Castro http://math.ucsd.edu/ eariasca/math282a.html MATH 282A University

### Inferences 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

### Fractional Factorial Designs

Fractional Factorial Designs ST 516 Each replicate of a 2 k design requires 2 k runs. E.g. 64 runs for k = 6, or 1024 runs for k = 10. When this is infeasible, we use a fraction of the runs. As a result,

### Project Report for STAT571 Statistical Methods Instructor: Dr. Ramon V. Leon. Wage Data Analysis. Yuanlei Zhang

Project Report for STAT7 Statistical Methods Instructor: Dr. Ramon V. Leon Wage Data Analysis Yuanlei Zhang 77--7 November, Part : Introduction Data Set The data set contains a random sample of observations

### 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008

MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/term

### Regression. Estimation of the linear function (straight line) describing the linear component of the joint relationship between two variables X and Y.

Regression Bivariate i linear regression: Estimation of the linear function (straight line) describing the linear component of the joint relationship between two variables and. Generally describe as a

### STATISTICS 110/201 PRACTICE FINAL EXAM

STATISTICS 110/201 PRACTICE FINAL EXAM Questions 1 to 5: There is a downloadable Stata package that produces sequential sums of squares for regression. In other words, the SS is built up as each variable

### Institutionen för matematik och matematisk statistik Umeå universitet November 7, Inlämningsuppgift 3. Mariam Shirdel

Institutionen för matematik och matematisk statistik Umeå universitet November 7, 2011 Inlämningsuppgift 3 Mariam Shirdel (mash0007@student.umu.se) Kvalitetsteknik och försöksplanering, 7.5 hp 1 Uppgift

### 2.830 Homework #6. April 2, 2009

2.830 Homework #6 Dayán Páez April 2, 2009 1 ANOVA The data for four different lithography processes, along with mean and standard deviations are shown in Table 1. Assume a null hypothesis of equality.

### Chapter 13 Experiments with Random Factors Solutions

Solutions from Montgomery, D. C. (01) Design and Analysis of Experiments, Wiley, NY Chapter 13 Experiments with Random Factors Solutions 13.. An article by Hoof and Berman ( Statistical Analysis of Power

### Lecture 2. The Simple Linear Regression Model: Matrix Approach

Lecture 2 The Simple Linear Regression Model: Matrix Approach Matrix algebra Matrix representation of simple linear regression model 1 Vectors and Matrices Where it is necessary to consider a distribution

### Question Possible Points Score Total 100

Midterm I NAME: Instructions: 1. For hypothesis testing, the significant level is set at α = 0.05. 2. This exam is open book. You may use textbooks, notebooks, and a calculator. 3. Do all your work in

### STAT 572 Assignment 5 - Answers Due: March 2, 2007

1. The file glue.txt contains a data set with the results of an experiment on the dry sheer strength (in pounds per square inch) of birch plywood, bonded with 5 different resin glues A, B, C, D, and E.

### EXAMINATIONS OF THE HONG KONG STATISTICAL SOCIETY

EXAMINATIONS OF THE HONG KONG STATISTICAL SOCIETY MODULE 4 : Linear models Time allowed: One and a half hours Candidates should answer THREE questions. Each question carries 20 marks. The number of marks

### Estimation of etch rate and uniformity with plasma impedance monitoring. Daniel Tsunami

Estimation of etch rate and uniformity with plasma impedance monitoring Daniel Tsunami IC Design and Test Laboratory Electrical & Computer Engineering Portland State University dtsunami@lisl.com 1 Introduction

### STATISTICAL DATA ANALYSIS IN EXCEL

Microarra Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 5 Linear Regression dr. Petr Nazarov 14-1-213 petr.nazarov@crp-sante.lu Statistical data analsis in Ecel. 5. Linear regression OUTLINE Lecture

### Open book and notes. 120 minutes. Covers Chapters 8 through 14 of Montgomery and Runger (fourth edition).

IE 330 Seat # Open book and notes 10 minutes Covers Chapters 8 through 14 of Montgomery and Runger (fourth edition) Cover page and eight pages of exam No calculator ( points) I have, or will, complete

### Business Statistics. Lecture 9: Simple Regression

Business Statistics Lecture 9: Simple Regression 1 On to Model Building! Up to now, class was about descriptive and inferential statistics Numerical and graphical summaries of data Confidence intervals

### Regression Models for Time Trends: A Second Example. INSR 260, Spring 2009 Bob Stine

Regression Models for Time Trends: A Second Example INSR 260, Spring 2009 Bob Stine 1 Overview Resembles prior textbook occupancy example Time series of revenue, costs and sales at Best Buy, in millions

### Introduction to Machine Learning Prof. Sudeshna Sarkar Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Introduction to Machine Learning Prof. Sudeshna Sarkar Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module 2 Lecture 05 Linear Regression Good morning, welcome

### Exam Applied Statistical Regression. Good Luck!

Dr. M. Dettling Summer 2011 Exam Applied Statistical Regression Approved: Tables: Note: Any written material, calculator (without communication facility). Attached. All tests have to be done at the 5%-level.

### Applied Regression Modeling: A Business Approach Chapter 3: Multiple Linear Regression Sections

Applied Regression Modeling: A Business Approach Chapter 3: Multiple Linear Regression Sections 3.4 3.6 by Iain Pardoe 3.4 Model assumptions 2 Regression model assumptions.............................................

### 2-way analysis of variance

2-way analysis of variance We may be considering the effect of two factors (A and B) on our response variable, for instance fertilizer and variety on maize yield; or therapy and sex on cholesterol level.

### LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION

LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION In this lab you will learn how to use Excel to display the relationship between two quantitative variables, measure the strength and direction of the

### Inference for Regression Inference about the Regression Model and Using the Regression Line, with Details. Section 10.1, 2, 3

Inference for Regression Inference about the Regression Model and Using the Regression Line, with Details Section 10.1, 2, 3 Basic components of regression setup Target of inference: linear dependency

### Introduction to Regression

Introduction to Regression Using Mult Lin Regression Derived variables Many alternative models Which model to choose? Model Criticism Modelling Objective Model Details Data and Residuals Assumptions 1

### 1 A Review of Correlation and Regression

1 A Review of Correlation and Regression SW, Chapter 12 Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then

### CHAPTER 6 MACHINABILITY MODELS WITH THREE INDEPENDENT VARIABLES

CHAPTER 6 MACHINABILITY MODELS WITH THREE INDEPENDENT VARIABLES 6.1 Introduction It has been found from the literature review that not much research has taken place in the area of machining of carbon silicon

### Stat 6640 Solution to Midterm #2

Stat 6640 Solution to Midterm #2 1. A study was conducted to examine how three statistical software packages used in a statistical course affect the statistical competence a student achieves. At the end

### * Tuesday 17 January :30-16:30 (2 hours) Recored on ESSE3 General introduction to the course.

Name of the course Statistical methods and data analysis Audience The course is intended for students of the first or second year of the Graduate School in Materials Engineering. The aim of the course

### Difference 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

### DOE Wizard Screening Designs

DOE Wizard Screening Designs Revised: 10/10/2017 Summary... 1 Example... 2 Design Creation... 3 Design Properties... 13 Saving the Design File... 16 Analyzing the Results... 17 Statistical Model... 18

### Multiple Regression and Model Building Lecture 20 1 May 2006 R. Ryznar

Multiple Regression and Model Building 11.220 Lecture 20 1 May 2006 R. Ryznar Building Models: Making Sure the Assumptions Hold 1. There is a linear relationship between the explanatory (independent) variable(s)

### Workshop 7.4a: Single factor ANOVA

-1- Workshop 7.4a: Single factor ANOVA Murray Logan November 23, 2016 Table of contents 1 Revision 1 2 Anova Parameterization 2 3 Partitioning of variance (ANOVA) 10 4 Worked Examples 13 1. Revision 1.1.

### STAT 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,

### Simple Linear Regression

Simple Linear Regression September 24, 2008 Reading HH 8, GIll 4 Simple Linear Regression p.1/20 Problem Data: Observe pairs (Y i,x i ),i = 1,...n Response or dependent variable Y Predictor or independent

### DEMAND ESTIMATION (PART III)

BEC 30325: MANAGERIAL ECONOMICS Session 04 DEMAND ESTIMATION (PART III) Dr. Sumudu Perera Session Outline 2 Multiple Regression Model Test the Goodness of Fit Coefficient of Determination F Statistic t

### ST505/S697R: Fall Homework 2 Solution.

ST505/S69R: Fall 2012. Homework 2 Solution. 1. 1a; problem 1.22 Below is the summary information (edited) from the regression (using R output); code at end of solution as is code and output for SAS. a)

### 10.0 REPLICATED FULL FACTORIAL DESIGN

10.0 REPLICATED FULL FACTORIAL DESIGN (Updated Spring, 001) Pilot Plant Example ( 3 ), resp - Chemical Yield% Lo(-1) Hi(+1) Temperature 160 o 180 o C Concentration 10% 40% Catalyst A B Test# Temp Conc

### Variance. Standard deviation VAR = = value. Unbiased SD = SD = 10/23/2011. Functional Connectivity Correlation and Regression.

10/3/011 Functional Connectivity Correlation and Regression Variance VAR = Standard deviation Standard deviation SD = Unbiased SD = 1 10/3/011 Standard error Confidence interval SE = CI = = t value for

### lm statistics Chris Parrish

lm statistics Chris Parrish 2017-04-01 Contents s e and R 2 1 experiment1................................................. 2 experiment2................................................. 3 experiment3.................................................

### Regression: Main Ideas Setting: Quantitative outcome with a quantitative explanatory variable. Example, cont.

TCELL 9/4/205 36-309/749 Experimental Design for Behavioral and Social Sciences Simple Regression Example Male black wheatear birds carry stones to the nest as a form of sexual display. Soler et al. wanted

### 1. (Problem 3.4 in OLRT)

STAT:5201 Homework 5 Solutions 1. (Problem 3.4 in OLRT) The relationship of the untransformed data is shown below. There does appear to be a decrease in adenine with increased caffeine intake. This is

### Linear Regression with Multiple Regressors

Linear Regression with Multiple Regressors (SW Chapter 6) Outline 1. Omitted variable bias 2. Causality and regression analysis 3. Multiple regression and OLS 4. Measures of fit 5. Sampling distribution

### Ch 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

### FACTORIAL DESIGNS and NESTED DESIGNS

Experimental Design and Statistical Methods Workshop FACTORIAL DESIGNS and NESTED DESIGNS Jesús Piedrafita Arilla jesus.piedrafita@uab.cat Departament de Ciència Animal i dels Aliments Items Factorial

### Multiple Regression: Example

Multiple Regression: Example Cobb-Douglas Production Function The Cobb-Douglas production function for observed economic data i = 1,..., n may be expressed as where O i is output l i is labour input c

### Introduction to Crossover Trials

Introduction to Crossover Trials Stat 6500 Tutorial Project Isaac Blackhurst A crossover trial is a type of randomized control trial. It has advantages over other designed experiments because, under certain

### STA 4210 Practise set 2a

STA 410 Practise set a For all significance tests, use = 0.05 significance level. S.1. A multiple linear regression model is fit, relating household weekly food expenditures (Y, in \$100s) to weekly income

### Holiday Assignment PS 531

Holiday Assignment PS 531 Prof: Jake Bowers TA: Paul Testa January 27, 2014 Overview Below is a brief assignment for you to complete over the break. It should serve as refresher, covering some of the basic

### Regression ( Kemampuan Individu, Lingkungan kerja dan Motivasi)

Regression (, Lingkungan kerja dan ) Descriptive Statistics Mean Std. Deviation N 3.87.333 32 3.47.672 32 3.78.585 32 s Pearson Sig. (-tailed) N Kemampuan Lingkungan Individu Kerja.000.432.49.432.000.3.49.3.000..000.000.000..000.000.000.

### MSc / PhD Course Advanced Biostatistics. dr. P. Nazarov

MSc / PhD Course Advanced Biostatistics dr. P. Nazarov petr.nazarov@crp-sante.lu 04-1-013 L4. Linear models edu.sablab.net/abs013 1 Outline ANOVA (L3.4) 1-factor ANOVA Multifactor ANOVA Experimental design

### How To: Analyze a Split-Plot Design Using STATGRAPHICS Centurion

How To: Analyze a SplitPlot Design Using STATGRAPHICS Centurion by Dr. Neil W. Polhemus August 13, 2005 Introduction When performing an experiment involving several factors, it is best to randomize the