BIOSTATISTICS Linear regression. Copyright ©2011, Joanna Szyda INTRODUCTION 1.Linear regression equation 2.Estimation of linear regression coefficients.

Slides:



Advertisements
Similar presentations
Kin 304 Regression Linear Regression Least Sum of Squares
Advertisements

Linear Equations Review. Find the slope and y intercept: y + x = -1.
Regresi Linear Sederhana Pertemuan 01 Matakuliah: I0174 – Analisis Regresi Tahun: Ganjil 2007/2008.
Regression Analysis Module 3. Regression Regression is the attempt to explain the variation in a dependent variable using the variation in independent.
Definition  Regression Model  Regression Equation Y i =  0 +  1 X i ^ Given a collection of paired data, the regression equation algebraically describes.
Chapter 4 Part I - Introduction to Simple Linear Regression Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions Philip.
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 303 Chapter 10 Least Squares Regression Analysis.
Introduction to Linear and Logistic Regression. Basic Ideas Linear Transformation Finding the Regression Line Minimize sum of the quadratic residuals.
1 Chapter 17: Introduction to Regression. 2 Introduction to Linear Regression The Pearson correlation measures the degree to which a set of data points.
15: Linear Regression Expected change in Y per unit X.
Simple Linear Regression Analysis
1 1 Slide Simple Linear Regression Chapter 14 BA 303 – Spring 2011.
Introduction to Linear Regression and Correlation Analysis
Simple Linear Regression. Types of Regression Model Regression Models Simple (1 variable) LinearNon-Linear Multiple (2
Chapter 11 Simple Regression
Statistics for Business and Economics 8 th Edition Chapter 11 Simple Regression Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Ch.
Linear Trend Lines Y t = b 0 + b 1 X t Where Y t is the dependent variable being forecasted X t is the independent variable being used to explain Y. In.
1 FORECASTING Regression Analysis Aslı Sencer Graduate Program in Business Information Systems.
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.
Regression analysis Control of built engineering objects, comparing to the plan Surveying observations – position of points Linear regression Regression.
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 12-1 Correlation and Regression.
1 Dr. Jerrell T. Stracener EMIS 7370 STAT 5340 Probability and Statistics for Scientists and Engineers Department of Engineering Management, Information.
MTH 161: Introduction To Statistics
Statistical Methods Statistical Methods Descriptive Inferential
Regression using lm lmRegression.R Basics Prediction World Bank CO2 Data.
Simple Linear Regression. Deterministic Relationship If the value of y (dependent) is completely determined by the value of x (Independent variable) (Like.
Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.
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.
Intro to Regression POL 242. Summary Regression is the process by which we fit a line to depict the relationship between two variables (usually both interval.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.
Chapter 11 Correlation and Simple Linear Regression Statistics for Business (Econ) 1.
Get out the Notes from Monday Feb. 4 th, Example 2: Consider the table below displaying the percentage of recorded music sales coming from music.
Chapter 6 (cont.) Difference Estimation. Recall the Regression Estimation Procedure 2.
© 2001 Prentice-Hall, Inc.Chap 13-1 BA 201 Lecture 18 Introduction to Simple Linear Regression (Data)Data.
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Simple Linear Regression Analysis Chapter 13.
Multiple Regression Analysis Regression analysis with two or more independent variables. Leads to an improvement.
Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Chapter Describing the Relation between Two Variables 4.
The General Linear Model. Estimation -- The General Linear Model Formula for a straight line y = b 0 + b 1 x x y.
Chapter 14 Introduction to Regression Analysis. Objectives Regression Analysis Uses of Regression Analysis Method of Least Squares Difference between.
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Introduction Many problems in Engineering, Management, Health Sciences and other Sciences involve exploring the relationships between two or more variables.
Chapter 8 Linear Regression.
CHAPTER 3 Describing Relationships
Simple Linear Regression
Unit 4 LSRL.
LSRL.
Least Squares Regression Line.
Linear Regression Special Topics.
Regression Chapter 6 I Introduction to Regression
Chapter 5 LSRL.
SIMPLE LINEAR REGRESSION MODEL
Chapter 3.2 LSRL.
The Least-Squares Regression Line
Correlation and Regression-II
AP Stats: 3.3 Least-Squares Regression Line
Least Squares Regression Line LSRL Chapter 7-continued
Least-Squares Regression
Chapter 1 Linear Functions
The Multiple Regression Model
Chapter 5 LSRL.
Chapter 5 LSRL.
Least-Squares Regression
Least-Squares Regression
Section 5 Multiple Regression.
Example on the Concept of Regression . observation
3 4 Chapter Describing the Relation between Two Variables
Multivariate Analysis Regression
Find the y-intercept and slope
Introductory Statistics Introductory Statistics
Presentation transcript:

BIOSTATISTICS Linear regression

Copyright ©2011, Joanna Szyda INTRODUCTION 1.Linear regression equation 2.Estimation of linear regression coefficients Least squares Weighted least squares 3.Examples of regression equations Multiple regression Polynomials Logarithmic regression 4.Results interpretation

LINEAR REGRESSION EQUATION

Copyright ©2011, Joanna Szyda REGRESSION EQUATION 1.Dependent variable 2.Independent variable BODY WEIGHT ADIPOSE TISSUE DATA SET

Copyright ©2011, Joanna Szyda REGRESSION EQUATION INTERCEPT

Copyright ©2011, Joanna Szyda REGRESSION EQUATION x i -x i-1 y i -y i-1 slope

Copyright ©2011, Joanna Szyda no dependence gradient = 0 changes in the same direction gradient > 0 changes in opposite directions gradient < 0 EXAMPLES how much will the dependent variable change when the independent variable increases by 1 unit REGRESSION EQUATION SLOPE

Copyright ©2011, Joanna Szyda ERROR error intercept REGRESSION EQUATION

Copyright ©2011, Joanna Szyda small errorlarge error REGRESSION EQUATION ERROR

Copyright ©2011, Joanna Szyda observed value (y) predicted value (ŷ) REGRESSION EQUATION

Copyright ©2011, Joanna Szyda Dependent variableIndependent variable intercept slope REGRESSION EQUATION

Copyright ©2011, Joanna Szyda dependent variableindependent variable intercept slope HOW TO INTERPRET THOSE VALUES ??? REGRESSION EQUATION

ESTIMATION OF REGRESSION COEFFICIENTS

Copyright ©2011, Joanna Szyda LEAST SQUARES HOW TO ESTIMATE REGRESSION COEFFICIENTS ? SO THAT DISTANCES BETWEEN OBSERVED AND PREDICTED VALUES WERE AS SMALL AS POSSIBLE - least squares method

Copyright ©2011, Joanna Szyda  ( ) 2 → minimum LEAST SQUARES

Copyright ©2011, Joanna Szyda LEAST SQUARES

Copyright ©2011, Joanna Szyda LEAST SQUARES

Copyright ©2011, Joanna Szyda WEIGHTING OF OBSERVATIONS WEIGHTED LEAST SQUARES HOW TO ESTIMATE REGRESSION COEFFICIENTS WHEN y ARE MEASURED WITH DIFFERENT ACCURACY?

Copyright ©2011, Joanna Szyda WEIGHTED LEAST SQUARES

EXAMPLES OF REGRESSION EQUATIONS

Copyright ©2011, Joanna Szyda EXAMPLES OF REGRESSION EQUATIONS MULTIPLE REGRESSION BODY WEIGHTAGE ADIPOSE TISSUE

Copyright ©2011, Joanna Szyda POLYNOMIALS 1st grade polynomial 2nd grade polynomial 3rd grade polynomial EXAMPLES OF REGRESSION EQUATIONS

Copyright ©2011, Joanna Szyda LOGHARITMIC REGRESSION EXAMPLES OF REGRESSION EQUATIONS

RESULT INTERPRETATION

Copyright ©2011, Joanna Szyda RESULT INTERPRETATION

Copyright ©2011, Joanna Szyda 1.Time between calls diminishes with temparature rise 2.Temperature increase by 1°C results in call interval shorter by 0.21 s. 3.At 10°C frogs call every 6.26 s. on average: RESULT INTERPRETATION

Copyright ©2011, Joanna Szyda RESULT INTERPRETATION

Copyright ©2011, Joanna Szyda 1.Model: 2.Partners who in 2003 were on average 40 years old and where a husband was 15 years older than his wife, have on average 2.42 children: 3.Partners who in 2003 were on average 25 years old and where a husband was 4 years older than his wife, have on average 2.66 children: RESULT INTERPRETATION

LINEAR REGRESSION

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.