THE LOGIC OF REGRESSION. OUTLINE 1.The Rules of the Game: Interval-Scale Data and PRE (Strength) 2.Understanding the Regression Line (Form) 3.Example:

Slides:

Advertisements

Similar presentations

The Role of r2 in Regression Target Goal: I can use r2 to explain the variation of y that is explained by the LSRL. D4: 3.2b Hw: pg 191 – 43, 46, 48,

Advertisements

Regresi Linear Sederhana Pertemuan 01 Matakuliah: I0174 – Analisis Regresi Tahun: Ganjil 2007/2008.

 Coefficient of Determination Section 4.3 Alan Craig

Chapter 10 Curve Fitting and Regression Analysis

Simple Regression. Major Questions Given an economic model involving a relationship between two economic variables, how do we go about specifying the.

Sociology 601 Class 17: October 28, 2009 Review (linear regression) –new terms and concepts –assumptions –reading regression computer outputs Correlation.

Chapter 15 (Ch. 13 in 2nd Can.) Association Between Variables Measured at the Interval-Ratio Level: Bivariate Correlation and Regression.

LINEAR REGRESSION: What it Is and How it Works Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r.

LINEAR REGRESSION: What it Is and How it Works. Overview What is Bivariate Linear Regression? The Regression Equation How It’s Based on r.

REGRESSION What is Regression? What is the Regression Equation? What is the Least-Squares Solution? How is Regression Based on Correlation? What are the.

Correlation and Regression Analysis

CHAPTER 3 Describing Relationships

REGRESSION Predict future scores on Y based on measured scores on X Predictions are based on a correlation from a sample where both X and Y were measured.

INTERPRETING REGRESSION COEFFICIENTS. OUTLINE 1.Back to Basics 2.Form: The Regression Equation 3.Strength: PRE and r 2 4.The Correlation Coefficient r.

Chapter 12 Section 1 Inference for Linear Regression.

Week 9: Chapter 15, 17 (and 16) Association Between Variables Measured at the Interval-Ratio Level The Procedure in Steps.

Exploring relationships between variables Ch. 10 Scatterplots, Associations, and Correlations Ch. 10 Scatterplots, Associations, and Correlations.

Chapter 5 Regression. Chapter outline The least-squares regression line Facts about least-squares regression Residuals Influential observations Cautions.

Introduction to Linear Regression and Correlation Analysis

Relationship of two variables

Ch 3 – Examining Relationships YMS – 3.1

Chapter 3 concepts/objectives Define and describe density curves Measure position using percentiles Measure position using z-scores Describe Normal distributions.

Managerial Economics Demand Estimation. Scatter Diagram Regression Analysis.

Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.

AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION.

Section 5.2: Linear Regression: Fitting a Line to Bivariate Data.

Simple Linear Regression. Deterministic Relationship If the value of y (dependent) is completely determined by the value of x (Independent variable) (Like.

10B11PD311 Economics REGRESSION ANALYSIS. 10B11PD311 Economics Regression Techniques and Demand Estimation Some important questions before a firm are.

PS 225 Lecture 20 Linear Regression Equation and Prediction.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 3 Describing Relationships 3.2 Least-Squares.

STA291 Statistical Methods Lecture LINEar Association o r measures “closeness” of data to the “best” line. What line is that? And best in what terms.

Examining Bivariate Data Unit 3 – Statistics. Some Vocabulary Response aka Dependent Variable –Measures an outcome of a study Explanatory aka Independent.

CHAPTER 5 Regression BPS - 5TH ED.CHAPTER 5 1. PREDICTION VIA REGRESSION LINE NUMBER OF NEW BIRDS AND PERCENT RETURNING BPS - 5TH ED.CHAPTER 5 2.

ECON 338/ENVR 305 CLICKER QUESTIONS Statistics – Question Set #8 (from Chapter 10)

Essential Statistics Chapter 51 Least Squares Regression Line u Regression line equation: y = a + bx ^ –x is the value of the explanatory variable –“y-hat”

SWBAT: Calculate and interpret the residual plot for a line of regression Do Now: Do heavier cars really use more gasoline? In the following data set,

Chapter 10: Determining How Costs Behave 1 Horngren 13e.

Residuals Recall that the vertical distances from the points to the least-squares regression line are as small as possible.  Because those vertical distances.

CHAPTER 3 Describing Relationships

Regression Analysis Deterministic model No chance of an error in calculating y for a given x Probabilistic model chance of an error First order linear.

1 1 Slide The Simple Linear Regression Model n Simple Linear Regression Model y =  0 +  1 x +  n Simple Linear Regression Equation E( y ) =  0 + 

Simple Linear Regression The Coefficients of Correlation and Determination Two Quantitative Variables x variable – independent variable or explanatory.

Method 3: Least squares regression. Another method for finding the equation of a straight line which is fitted to data is known as the method of least-squares.

Chapter 14 Introduction to Regression Analysis. Objectives Regression Analysis Uses of Regression Analysis Method of Least Squares Difference between.

CHAPTER 5: Regression ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation.

Chapter 15 Association Between Variables Measured at the Interval-Ratio Level.

Bivariate Regression. Bivariate Regression analyzes the relationship between two variables. Bivariate Regression analyzes the relationship between two.

CHAPTER 3 Describing Relationships

Simple Linear Regression

CHAPTER 3 Describing Relationships

Statistics 101 Chapter 3 Section 3.

CHAPTER 3 Describing Relationships

Chapter 5 LSRL.

Ordinary Least Squares (OLS) Regression

Multiple Regression.

PRINCIPLES OF MULTIPLE REGRESSION

Quantitative Methods Simple Regression.

Statistics in Data Mining on Finance by Jian Chen

Probability and Statistics for Computer Scientists Second Edition, By: Michael Baron Section 11.1: Least squares estimation CIS Computational.

Correlation and Simple Linear Regression

Least-Squares Regression

CHAPTER 3 Describing Relationships

Unit 4 Vocabulary.

Correlation and Simple Linear Regression

Chapter 5 LSRL.

Least-Squares Regression

Correlation and Regression

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.

Correlation and Simple Linear Regression

Presentation transcript:

THE LOGIC OF REGRESSION

OUTLINE 1.The Rules of the Game: Interval-Scale Data and PRE (Strength) 2.Understanding the Regression Line (Form) 3.Example: Education and Voter Turnout 4.On the Importance of Visual Inspection (Scattergram)

READINGS Pollock, Essentials, review chs. 5-6, read ch. 7 (pp ) Pollock, SPSS Companion, ch. 8 Course Reader, Selections 3-4 (Ideology and Law, Correlates of Democracy)

REGRESSION ANALYSIS: THE BASIC GOALS Taking full advantage of interval-scale data Measuring form, strength, and significance of statistical relationships Specify associations between dependent and independent variables

THE RULES OF THE GAME PRE = (E 1 – E 2 )/E 1 1.Guessing Y without knowing X: mean value of Y E 1 = Σ(Y i –Y) 2 2.Guessing Y given knowledge of X: Y i = a + bX i Stipulations: a linear relationship, such that sum of squared deviations of observed values of Y from predicted values is minimal—thus, the line of “least squares”

E 1 = sum of squared deviations from the mean E 2 = sum of squared deviations from the regression line PRE = (E 1 – E 2 )/E 1 Which measures the strength of the relationship The regression line—that is, the equation— measures the form of the relationship.

Understanding the Regression Line 1.Path of the mean values of Y upon X 2.Estimated “average” values of Y for values of X 3.A line that cuts through the exact middle of the scattergram 4.A very precise statement of the form of a relationship

Path of Mean Values of Y for Values of X

Scattergram and Least-Squares Line

Visualizing Line of Least Squares

Variations in Relationships

Elements of the Regression Equation

Example: % High School Graduates (X) and % Turnout (Y)

Regression Equation: High School Graduates and Turnout

Estimated turnout = (% graduates) When X is zero, predicted y = Question: Where is X when predicted value of Y = 0? Answer: Around 30.2 (compare to minimal value of X) Slope = +.87 (for every 1 percent increase in high- school graduates, an increase of.87 percent in turnout)

What About Wyoming?

On the Importance of the Scattergram 1. Visual confirmation of observed relationship 2.Identify patterns in deviations from the line—that is, in patterns among “residual values” 3.This is crucial since different arrays of data can produce identical regression lines (same form, that is, but different strength) 4.Identification of “outliers” (extreme cases)