1 Response Surface A Response surface model is a special type of multiple regression model with: Explanatory variables Interaction variables Squared variables.

Slides:

Advertisements

Similar presentations

Questions From Yesterday

Advertisements

© Copyright 2001, Alan Marshall1 Regression Analysis Time Series Analysis.

Stat 112: Lecture 7 Notes Homework 2: Due next Thursday The Multiple Linear Regression model (Chapter 4.1) Inferences from multiple regression analysis.

Probabilistic & Statistical Techniques Eng. Tamer Eshtawi First Semester Eng. Tamer Eshtawi First Semester

Simple Regression Model

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

1 Home Gas Consumption Interaction? Should there be a different slope for the relationship between Gas and Temp after insulation than before insulation?

1 Multiple Regression Response, Y (numerical) Explanatory variables, X 1, X 2, …X k (numerical) New explanatory variables can be created from existing.

Using process knowledge to identify uncontrolled variables and control variables as inputs for Process Improvement 1.

Lecture 23: Tues., Dec. 2 Today: Thursday:

Stat 112: Lecture 10 Notes Fitting Curvilinear Relationships –Polynomial Regression (Ch ) –Transformations (Ch ) Schedule: –Homework.

Statistics for Managers Using Microsoft® Excel 5th Edition

Lecture 23: Tues., April 6 Interpretation of regression coefficients (handout) Inference for multiple regression.

The Basics of Regression continued

Stat 112: Lecture 19 Notes Chapter 7.2: Interaction Variables Thursday: Paragraph on Project Due.

Gordon Stringer, UCCS1 Regression Analysis Gordon Stringer.

Stat 112: Lecture 8 Notes Homework 2: Due on Thursday Assessing Quality of Prediction (Chapter 3.5.3) Comparing Two Regression Models (Chapter 4.4) Prediction.

Lecture 24: Thurs. Dec. 4 Extra sum of squares F-tests (10.3) R-squared statistic (10.4.1) Residual plots (11.2) Influential observations (11.3,

MATH408: Probability & Statistics Summer 1999 WEEKS 8 & 9 Dr. Srinivas R. Chakravarthy Professor of Mathematics and Statistics Kettering University (GMI.

IE-331: Industrial Engineering Statistics II Spring 2000 WEEK 1 Dr. Srinivas R. Chakravarthy Professor of Operations Research and Statistics Kettering.

Improving Stable Processes Professor Tom Kuczek Purdue University

1 Chapter 10 Correlation and Regression We deal with two variables, x and y. Main goal: Investigate how x and y are related, or correlated; how much they.

Multiple Linear Regression Response Variable: Y Explanatory Variables: X 1,...,X k Model (Extension of Simple Regression): E(Y) =  +  1 X 1 +  +  k.

3 CHAPTER Cost Behavior 3-1.

© 2004 Prentice-Hall, Inc.Chap 15-1 Basic Business Statistics (9 th Edition) Chapter 15 Multiple Regression Model Building.

Coefficient of Determination R2

Linear Trend Lines = b 0 + b 1 X t Where is the dependent variable being forecasted X t is the independent variable being used to explain Y. In Linear.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 12.4.

1 Multivariate Linear Regression Models Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of.

Multiple Linear Regression. Purpose To analyze the relationship between a single dependent variable and several independent variables.

1 Prices of Antique Clocks Antique clocks are sold at auction. We wish to investigate the relationship between the age of the clock and the auction price.

Web example squares-means-marginal-means-vs.html.

Basic Concepts of Correlation. Definition A correlation exists between two variables when the values of one are somehow associated with the values of.

Why Model? Make predictions or forecasts where we don’t have data.

Lesson Multiple Regression Models. Objectives Obtain the correlation matrix Use technology to find a multiple regression equation Interpret the.

Chapter 5 Residuals, Residual Plots, & Influential points.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

© Buddy Freeman, 2015 Multiple Linear Regression (MLR) Testing the additional contribution made by adding an independent variable.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 13 Multiple Regression Section 13.3 Using Multiple Regression to Make Inferences.

Controlling Variables

Stat 112 Notes 10 Today: –Fitting Curvilinear Relationships (Chapter 5) Homework 3 due Thursday.

Warm Up Feel free to share data points for your activity. Determine if the direction and strength of the correlation is as agreed for this class, for the.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 14-1 Chapter 14 Multiple Regression Model Building Statistics for Managers.

Regression Analysis: Part 2 Inference Dummies / Interactions Multicollinearity / Heteroscedasticity Residual Analysis / Outliers.

EXCEL DECISION MAKING TOOLS BASIC FORMULAE - REGRESSION - GOAL SEEK - SOLVER.

Lesson 14 - R Chapter 14 Review. Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 14-1 Chapter 14 Multiple Regression Model Building Statistics for Managers.

Stat 112 Notes 6 Today: –Chapters 4.2 (Inferences from a Multiple Regression Analysis)

Chapters 8 Linear Regression. Correlation and Regression Correlation = linear relationship between two variables. Summarize relationship with line. Called.

EXCEL DECISION MAKING TOOLS AND CHARTS BASIC FORMULAE - REGRESSION - GOAL SEEK - SOLVER.

REGRESSION REVISITED. PATTERNS IN SCATTER PLOTS OR LINE GRAPHS Pattern Pattern Strength Strength Regression Line Regression Line Linear Linear y = mx.

1 Simple Linear Regression Example - mammals Response variable: gestation (length of pregnancy) days Explanatory: brain weight.

HW 23 Key. 24:41 Promotion. These data describe promotional spending by a pharmaceutical company for a cholesterol-lowering drug. The data cover 39 consecutive.

Stat 112 Notes 8 Today: –Chapters 4.3 (Assessing the Fit of a Regression Model) –Chapter 4.4 (Comparing Two Regression Models) –Chapter 4.5 (Prediction.

1. Analyzing patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers, and influential points.

Chapter 11: Linear Regression E370, Spring From Simple Regression to Multiple Regression.

MATH 7174: Statistics & Modeling for Teachers June 11, 2014

REGRESSION (R2).

Basic Estimation Techniques

Regression Techniques

Simple Linear Regression

Stats Club Marnie Brennan

Model Selection In multiple regression we often have many explanatory variables. How do we find the “best” model?

Section 3.3 Linear Regression

AP Statistics, Section 3.3, Part 1

Chapter 5 LSRL.

Least-Squares Regression

Multiple Linear Regression

Multivariate Linear Regression Models

A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. Find the correlation coefficient & interpret.

Presentation transcript:

1 Response Surface A Response surface model is a special type of multiple regression model with: Explanatory variables Interaction variables Squared variables

2 Response Surface A response surface model is often used to approximate a complicated relationship between a response variable and several explanatory variables.

3 Response Surface In order to get reliable data for a response surface model, a designed experiment is often used to collect the data on the explanatory variables and the response.

4 Designed Experiment In a designed experiment, the experimenter chooses values of the explanatory variables to investigate and measures the response for the chosen combinations of explanatory variables.

5 Tennis Ball Experiment In the manufacture of tennis balls certain additives are thought to affect the bounciness of the tennis ball. Response: A measure of bounce.

6 Tennis Ball Experiment Explanatory variables Amount of silica Amount of sulfur Amount of silane

7 Tennis Ball Experiment Each explanatory variable has three levels Silica: 0.7, 1.2, 1.7 Sulfur: 1.8, 2.3, 2.8 Silane: 40, 50, 60

8 Tennis Ball Experiment A total of 15 combinations of silica, sulfur and silane are examined and the bounce response is measured for each combination. The target bounce response is 450.

9 SilicaSulfurSilaneBounce

10 Response Surface Model

11 JMP – Fit Model Put Bounce in for the Y response. Highlight silica, sulfur and silane in Select Columns. Macros – Response Surface

12

13

14 Summary The model is useful. F= , P-value < R 2 = , virtually all of the variation in Bounce is explained by the model.

15

16 Statistical Significance The interaction between Silica and Silane is not statistically significant. The squared term for Silane is not statistically significant.

17 Reduced Model Remove the interaction term: Silica*Silane. Remove the squared term: Silane*Silane.

18

19 Summary The model is useful. F= , P-value < R 2 = , virtually all of the variation in Bounce is explained by the model. Only slightly lower than R 2 for the full model.

20 Statistical Significance All variables in the model are statistically significant. This is the best response surface model.

21 Prediction What combinations of silica, sulfur and silane will give you the target bounce of 450, on average?

22

23

24 Prediction There are several combinations that will give a predicted bounce of 450. Silica = 1.0, Sulfur = 1.948, Silane = 50 Silica = 0.8, Sulfur = 2.251, Silane = 40