chapter 5 linear models linear models are studied intensively because: easiest to understand and...

7

Chapter 5 Linear Models Linear Models are studied intensively because: •Easiest to understand and analyze •Relationships are often linear •Variables with non-linear relationship can often be transformed into linear relationship through an appropriate transformation •Even when a relationship is non-linear, a linear model may provide an accurate approximation for a limited range of values.

Upload: walter-rogers

Post on 21-Dec-2015

218 views

Category:

Documents

4 download

Report

Download

Embed Size (px):

TRANSCRIPT

Page 1: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

Chapter 5 Linear Models

Linear Models are studied intensively because:

•Easiest to understand and analyze•Relationships are often linear•Variables with non-linear relationship can often be transformed into linear relationship through an appropriate transformation•Even when a relationship is non-linear, a linear model may provide an accurate approximation for a limited range of values.

Page 2: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

• Least Square Line: • Let X and Y be two quantitative variables.• Let (x1, y1), (x2, y2), …, (xn, yn) be data

points collected on n individuals

• Goal: Find a linear model in the form Y = a + b X

that represents the given data set

Page 3: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

Page 4: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

Page 5: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

Page 6: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

Formulas for computing b and a

• b = Sxy/Sxx

• a = average(y) – b average(x)

• Sxy = Sum(xy) –Sum(x)Sum(y)/n• Sxx = Sum(x^2) –(Sum(x))^2/n

Page 7: Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with

5 Linear Models

• Remarks:

• 1. Use linear regression if the scatter plot looks reasonably straight

• 2. Check for outliers which could drastically influence regression lines

• 3. If data seem to cluster in scatter plot, look data more carefully

• 4. Large magnitude of slope indicates steeper line• 5. Negative slope shows negative association• 6. Positive slope shows positive association

Master of statistics, KU Leuven · Linear regression models −→Linear mixed models Generalized linear models −→Generalized linear mixed models Non-linear regression models

Non-Linear Models

Classification: Linear Models

Linear Models 1 - iut.ac.irrikhtehgaran.iut.ac.ir/sites/rikhtehgaran.iut.ac.ir/files//files... · Linear Models 1 Isfahan University ... Bapat (2000), Linear Algebra and Linear Models,

Linear Models I

General Linear Models; Generalized Linear Models Hal Whitehead BIOL4062/5062

Linear models and linear mixed effects models in R: …bodowinter.com/tutorial/bw_LME_tutorial1.pdf · Linear models and linear mixed effects models in R: Tutorial 11 Bodo Winter

GENERALISED LINEAR MODELS IN ACTUARIAL WORK · models. The class of generalised linear models includes, as special cases, linear regression, analysis-of-variance models, log-linear

Linear models questions.pdf

HIERARCHICAL LINEAR MODELS

Linear Models - WordPress.com

Comparison of empirical models with intensively observed data … · 2020. 7. 19. · Earth System Sciences Comparison of empirical models with intensively observed data for prediction

Linear models and linear mixed effects models in R ... · Linear models and linear mixed models are an impressively powerful and flexible tool for understanding the world. This tutorial

GENERALIZED LINEAR MODELS IN BIOMEDICAL …€¦ · GENERALIZED LINEAR MODELS IN BIOMEDICAL STATISTICAL APPLICATIONS by ... GENERALIZED LINEAR MODELS IN BIOMEDICAL ... life-testingproblems,

Linear & Generalized Linear Mixed Models · Cross-sectional data −→Hierarchical data Linear regression models −→Linear mixed models Generalized linear models −→Generalized

Linear Models Notes

Using Hierarchical Linear Models to Measure Growth · Using Hierarchical Linear Models to Measure Growth Measurement Incorporated Hierarchical Linear Models Workshop

PubH8401 Linear Models

Limma = linear models for microarray data Linear models ...web.math.ku.dk/.../Robinson-limma-linear-models-ku-2009.4upnotes.… · represented by linear models oFor one-channel platforms,

Generalized Linear Models and Extensions · 2010. 12. 16. · Session 1 - Generalized linear models † Introduction † Motivating examples † History † Generalized linear models

Linear Hierarchical Models

LINEAR PREDICTION MODELS

Linear Optimization Models

Linear Models & Clustering

Introduction to Generalized Linear Models · Generalized linear models extend the general linear model framework to address both of these issues. Introduction Generalized Linear Models

Linear regression models

Extending the Linear Models 2: Linear Mixed-E ects Models Lab

CREATING LINEAR MODELS FOR DATA · 12! Creating)linear)models)for)data)!)!!)!)!!!!)! !)!!!!!

GENERAL LINEAR MODELS

Linear Models & Linear Regression

Lecture 10: Linear Mixed Models (Linear Models with …sayan/Sta613/2017/lec/LMM.pdf · c (Claudia Czado, TU Munich) – 0 – Lecture 10: Linear Mixed Models (Linear Models with

BOOTSTRAPPING LINEAR MODELS

Applying Generalized Linear Models - LEG-UFPRinternas:biblioteca:lindsey... · Applying Generalized Linear Models James K. Lindsey Springer. Preface Generalized linear models provide

Generalized Linear Models