Linear Discriminant Analysis (LDA). Goal To classify observations into 2 or more groups based on k discriminant functions (Dependent variable Y is categorical.

Slides:

Advertisements

Similar presentations

Kin 304 Regression Linear Regression Least Sum of Squares

Advertisements

Chap 12-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 12 Simple Regression Statistics for Business and Economics 6.

BA 275 Quantitative Business Methods

Simple Regression Model

Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What.

Linear Regression Using Excel 2010 Linear Regression Using Excel ® 2010 Managerial Accounting Prepared by Diane Tanner University of North Florida Chapter.

Some Terms Y =  o +  1 X Regression of Y on X Regress Y on X X called independent variable or predictor variable or covariate or factor Which factors.

Chapter 13 Multiple Regression

LINEAR REGRESSION: Evaluating Regression Models Overview Assumptions for Linear Regression Evaluating a Regression Model.

LINEAR REGRESSION: Evaluating Regression Models. Overview Assumptions for Linear Regression Evaluating a Regression Model.

St. Louis City Crime Analysis 2015 Homicide Prediction Presented by: Kranthi Kancharla Scott Manns Eric Rodis Kenneth Stecher Sisi Yang.

Chapter 12 Multiple Regression

1 An example. 2 AirlinePercentage on time Complaints Southwest Continental Northwest US Airways United American

Linear Regression Example Data

Empirical Estimation Review EconS 451: Lecture # 8 Describe in general terms what we are attempting to solve with empirical estimation. Understand why.

Chapter 14 Introduction to Linear Regression and Correlation Analysis

Chapter 6 (cont.) Regression Estimation. Simple Linear Regression: review of least squares procedure 2.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 13-1 Chapter 13 Introduction to Multiple Regression Statistics for Managers.

Quantitative Demand Analysis

Chapter 2 Overview of the Data Mining Process 1. Introduction Data Mining – Predictive analysis Tasks of Classification & Prediction Core of Business.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 12-1 Chapter 12 Simple Linear Regression Statistics for Managers Using.

Extending that Line into the Future St. Louis CMG February 12, 2008 Wayne Bell – UniGroup, Inc.

Statistics for Business and Economics 8 th Edition Chapter 11 Simple Regression Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Ch.

OPIM 303-Lecture #8 Jose M. Cruz Assistant Professor.

1 1 Slide © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole.

1 1 Slide Multiple Regression n Multiple Regression Model n Least Squares Method n Multiple Coefficient of Determination n Model Assumptions n Testing.

Brain Mapping Unit The General Linear Model A Basic Introduction Roger Tait

You want to examine the linear dependency of the annual sales of produce stores on their size in square footage. Sample data for seven stores were obtained.

Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 12-1 Correlation and Regression.

Chap 12-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition Chapter 12 Introduction to Linear.

Applied Quantitative Analysis and Practices LECTURE#22 By Dr. Osman Sadiq Paracha.

EQT 373 Chapter 3 Simple Linear Regression. EQT 373 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value.

Applied Quantitative Analysis and Practices LECTURE#23 By Dr. Osman Sadiq Paracha.

Ch4 Describing Relationships Between Variables. Section 4.1: Fitting a Line by Least Squares Often we want to fit a straight line to data. For example.

Regression. Population Covariance and Correlation.

Class 23 The most over-rated statistic The four assumptions The most Important hypothesis test yet Using yes/no variables in regressions.

Logistic Regression Database Marketing Instructor: N. Kumar.

Statistics for Business and Economics 8 th Edition Chapter 11 Simple Regression Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Ch.

Chapter 13 Multiple Regression

Discussion of time series and panel models

Regression Analysis Part C Confidence Intervals and Hypothesis Testing

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.

Statistics for Business and Economics 8 th Edition Chapter 11 Simple Regression Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Ch.

Simple Linear Regression In the previous lectures, we only focus on one random variable. In many applications, we often work with a pair of variables.

Lecture 10: Correlation and Regression Model.

Multiple Regression. Simple Regression in detail Y i = β o + β 1 x i + ε i Where Y => Dependent variable X => Independent variable β o => Model parameter.

PLC Group: Mr. Keefe Mr. Brewer Mr. Skramstad Student Reading Habits and its Impact on CST.

 Input parameters 1, 2, …, n  Values of each denoted X 1, X 2, X n  For each setting of X 1, X 2, X n observe a Y  Each set (X 1, X 2, X n,Y) is one.

Applied Quantitative Analysis and Practices LECTURE#25 By Dr. Osman Sadiq Paracha.

Linear Discriminant Analysis and Logistic Regression.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 14-1 Chapter 14 Introduction to Multiple Regression Basic Business Statistics 10 th Edition.

© 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license.

Houston, Texas FAT CITY, USA Gloria Lobo-Stratton Sharon Lovdahl Dennis Glendenning.

Class 22. Understanding Regression EMBS Part of 12.7 Sections 1-3 and 7 of Pfeifer Regression note.

Introduction to Multiple Regression Lecture 11. The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & 2 or more.

Real Estate Sales Forecasting Regression Model of Pueblo neighborhood North Elizabeth Data sources from Pueblo County Website.

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 + 

Multiple Regression Analysis Regression analysis with two or more independent variables. Leads to an improvement.

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 14-1 Statistics for Managers Using Microsoft® Excel 5th Edition Chapter.

Regression Modeling Applications in Land use and Transport.

Samantha Bellah Adv. Stats Final Project Real Estate Forecasting Regression Model Market: Highland Park Neighborhood Data Sources: Zillow.com E:\PuebloRESales2014Q1Q2.xlsx.

Simple linear regression and correlation Regression analysis is the process of constructing a mathematical model or function that can be used to predict.

Construction Engineering 221 Probability and Statistics.

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

Chapter 12 Simple Regression Statistika.  Analisis regresi adalah analisis hubungan linear antar 2 variabel random yang mempunyai hub linear,  Variabel.

Chapter 12 – Discriminant Analysis

Modeling in R Sanna Härkönen.

BIVARIATE REGRESSION AND CORRELATION

Multiple Regression A curvilinear relationship between one variable and the values of two or more other independent variables. Y = intercept + (slope1.

Simple Linear Regression

Presentation transcript:

Linear Discriminant Analysis (LDA)

Goal To classify observations into 2 or more groups based on k discriminant functions (Dependent variable Y is categorical with k classes.) Assumptions Multivariate Normal Distribution variables are distributed normally within the classes/groups. Similar Group Covariances Correlations between and the variances within each group should be similar.

Dependent Variable Must be categorical with 2 or more classes (groups). If there are only 2 classes, the discriminant analysis procedure will give the same result as the multiple regression procedure.

Independent Variables Continuous or categorical independent variables If categorical, they are converted into binary (dummy) variables as in multiple linear regression

Output Example: Assume 3 classes (y=1,2,3) of the dependent. Yx11x12x13x14f1f2f3Pred. Y … … …..

Binary Dependent - Regression If only 2 classes of dependent, can do multiple regression Sample data shown below: StatusAge (18-30)Age (50+)Income YX1X2X … …

Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations24 ANOVA dfSSMSFSignificance F Regression E-05 Residual Total Coefficients Standard Errort StatP-valueLower 95%Upper 95% Intercept X X Income

Classification StatusAge (18-30)Age (50+)Income YX1X2X3Predicted YClass Classification Rule in this case: If Pred. Y > 0.5 then Class = 1; else Class = 0. This model yielded 2 misclassifications out of 24. How good is R-square?

Crosstab of Pred. Y and Y For large datasets, one can format the Predicted Y variable and create a crosstab with Y to see how accurately the model classifies the data (fictitious results shown here). The Good and Bad columns represent the number of actual Y values. Predicted Y *1000GoodBad 900to to to to to to to to to to to to to to to to to to to

Kolmogorov-Smirnov Test Use the crosstabs shown in last slide to conduct the KS Test to determine 1. Cutoff score, 2. Classification accuracy, and 3. Forecasts of model performance.