Simple Linear Regression F-Test for Lack-of-Fit

Slides:

Advertisements

Similar presentations

On the application of GP for software engineering predictive modeling: A systematic review Expert systems with Applications, Vol. 38 no. 9, 2011 Wasif.

Advertisements

Partial Least Squares Models Based on Chapter 3 of Hastie, Tibshirani and Friedman Slides by Javier Cabrera.

1 Vol. 01. p Vol. 01. p Vol. 01. p.20.

Simple Linear Regression F-Test for Lack-of-Fit Breaking Strength as Related to Water Pressure for Fiber Webs M.S. Ndaro, X-y. Jin, T. Chen, C-w. Yu (2007).

Analysis of Variance Outlines: Designing Engineering Experiments

1 Vol. 03. p Vol. 03. p Vol. 03. p.21.

1 Vol. 02. p Vol. 02. p Vol. 02. p.19.

1 Vol. 03. p Vol. 03. p Vol. 03. p.16.

1 Vol. 02. p Vol. 02. p Vol. 02. p.30.

1 Vol. 03. p Vol. 03. p Vol. 03. p.35.

1 Vol. 02. p Vol. 02. p Vol. 02. p.10.

1 Vol. 01. p Vol. 01. p Vol. 01. p.14.

Split-Plot Experiment Top Shrinkage by Wool Fiber Treatment and Number of Drying Revolutions J. Lindberg (1953). “Relationship Between Various Surface.

Design of Engineering Experiments - Experiments with Random Factors

2 n Factorial Experiment 4 Factor used to Remove Chemical Oxygen demand from Distillery Spent Wash R.K. Prasad and S.N. Srivastava (2009). “Electrochemical.

1 Econometrics 1 Lecture 1 Classical Linear Regression Analysis.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 26 Regression Analysis-Chapter 17.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 25 Regression Analysis-Chapter 17.

Lesson #32 Simple Linear Regression. Regression is used to model and/or predict a variable; called the dependent variable, Y; based on one or more independent.

Statistics 350 Lecture 23. Today Today: Exam next day Good Chapter 7 questions: 7.1, 7.2, 7.3, 7.28, 7.29.

Introduction to Regression Analysis Straight lines, fitted values, residual values, sums of squares, relation to the analysis of variance.

Statistics 350 Lecture 11. Today Last Day: Start Chapter 3 Today: Section 3.8 Mid-Term Friday…..Sections ; ; (READ)

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

Review of the fundamental concepts of probability Exploratory data analysis: quantitative and graphical data description Estimation techniques, hypothesis.

Linear Regression – Estimating Demand Elasticities U.S. Sugar Consumption H. Schultz (1933). “A Comparison of Elasticities of Demand Obtained.

Linear Lack of Fit (LOF) Test An F test for checking whether a linear regression function is inadequate in describing the trend in the data.

Stats for Engineers Lecture 9. Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution.

Statistical Methods Statistical Methods Descriptive Inferential

Y=a+bx Sum of squares of errors Linear Regression: Method of Least Squares The Method of Least Squares is a procedure to determine the best fit line to.

Thomas Knotts. Engineers often: Regress data  Analysis  Fit to theory  Data reduction Use the regression of others  Antoine Equation  DIPPR.

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

Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.

9.2A- Linear Regression Regression Line = Line of best fit The line for which the sum of the squares of the residuals is a minimum Residuals (d) = distance.

DOX 6E Montgomery1 Design of Engineering Experiments Part 9 – Experiments with Random Factors Text reference, Chapter 13, Pg. 484 Previous chapters have.

Nested Design Comparison of 2 Shampoo Formulations on Hair Combability M.L. Garcia and J. Diaz (1976). “Combability Measurements on Human Hair,” Journal.

1 Statistical Design of Experiments BITS Pilani, November ~ Shilpa Gupta (97A4)

ETM U 1 Analysis of Variance (ANOVA) Suppose we want to compare more than two means? For example, suppose a manufacturer of paper used for grocery.

Dept of Bioenvironmental Systems Engineering National Taiwan University Lab for Remote Sensing Hydrology and Spatial Modeling STATISTICS Linear Statistical.

The general linear test approach to regression analysis.

Linear Prediction Correlation can be used to make predictions – Values on X can be used to predict values on Y – Stronger relationships between X and Y.

Factorial Designs Outlines:  2 2 factorial design  2 k factorial design, k>=3  Blocking and confounding in 2 k factorial design.

Problems. 1.The tensile strength of concrete produced by 4 mixer levels is being studied. The data are: Compute the MS for the mixers and plot the means.

1 Simple Linear Regression and Correlation Least Squares Method The Model Estimating the Coefficients EXAMPLE 1: USED CAR SALES.

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 12 1 MER301: Engineering Reliability LECTURE 12: Chapter 6: Linear Regression Analysis.

Tukey’s 1-Degree of Freedom for Non-Additivity Yields for 8 Business Indices Over 18 Years K.V. Smith(1969). “Stock Price and Economic Indexes for Generating.

1. Complete SRTE on ANGEL 2. Project Due Wed midnight on ANGEL 3. Complete post-test Dec 6, 12pm – Dec 8, 12pm Up to 2% extra credit on your overall grade.

Two-Factor Study with Random Effects In some experiments the levels of both factors A & B are chosen at random from a larger set of possible factor levels.

Statistics 350 Review. Today Today: Review Simple Linear Regression Simple linear regression model: Y i =  for i=1,2,…,n Distribution of errors.

Introduction Many problems in Engineering, Management, Health Sciences and other Sciences involve exploring the relationships between two or more variables.

Simple Linear Regression and Correlation (Continue..,) Reference: Chapter 17 of Statistics for Management and Economics, 7 th Edition, Gerald Keller. 1.

2-Way Random Effects ANOVA Gage Repeatability and Repeatability Experiment for Measuring Drill Holes in Wood Parts Source: M-H. C. Li and A. Al-Refaie.

REGRESSION (R2).

CHAPTER 13 Design and Analysis of Single-Factor Experiments:

ENM 310 Design of Experiments and Regression Analysis

Tensile strength (MPa) Length (m) of fibers/kg

Ch12.1 Simple Linear Regression

1-Way ANOVA with Numeric Factor – Dose-Response

Simple Linear Regression F-Test for Lack-of-Fit

Linear Regression.

Linear Regression.

Transforming to Linearity

Prediction of new observations

2-Way Random Effects ANOVA

So far --> looked at the effect of a discrete variable on a continuous variable t-test, ANOVA, 2-way ANOVA.

Correlation and Regression

Section 2: Linear Regression.

Nonlinear Fitting.

HW# : Complete the last slide

y=a+bx Linear Regression: Method of Least Squares slope y intercept

Cases. Simple Regression Linear Multiple Regression.

Presentation transcript:

Simple Linear Regression F-Test for Lack-of-Fit Breaking Strength as Related to Water Pressure for Fiber Webs M.S. Ndaro, X-y. Jin, T. Chen, C-w. Yu (2007). "Splitting of Islands-in-the-Sea Fibers (PA6/COPET) During Hydroentangling of Nonwovens," Journal of Engineered Fibers and Fabrics, Vol. 2, #4

Data Description Experiment consisted of 30 experimental runs, 5 replicates each at water pressures of 60, 80, 100, 120, 150, 200 when the fiber is hydroentangled Response: Tensile strength (machine direction) of the islands-in-the-sea fibers

Regression Estimates and Sums of Squares