COTOR Training Session II GL Data: Long Tails, Volatility, Data Transforms September 11, 2006.

Slides:



Advertisements
Similar presentations
Claude Beigel, PhD. Exposure Assessment Senior Scientist Research Triangle Park, USA Practical session metabolites Part II: goodness of fit and decision.
Advertisements

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression Chapter.
11 Simple Linear Regression and Correlation CHAPTER OUTLINE
Regression Analysis Module 3. Regression Regression is the attempt to explain the variation in a dependent variable using the variation in independent.
Regression Analysis Once a linear relationship is defined, the independent variable can be used to forecast the dependent variable. Y ^ = bo + bX bo is.
Chapter 12 Simple Linear Regression
Chapter 10 Simple Regression.
BA 555 Practical Business Analysis
Chapter 13 Introduction to Linear Regression and Correlation Analysis
Lecture 19: Tues., Nov. 11th R-squared (8.6.1) Review
Part 4 Chapter 13 Linear Regression
Regression Diagnostics - I
Simple Linear Regression Analysis
Chapter 14 Introduction to Linear Regression and Correlation Analysis
Correlation and Regression Analysis
Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. More About Regression Chapter 14.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS & Updated by SPIROS VELIANITIS.
Lecture 5 Correlation and Regression
September 11, 2006 How Valid Are Your Assumptions? A Basic Introduction to Testing the Assumptions of Loss Reserve Variability Models Casualty Loss Reserve.
Advantages of Multivariate Analysis Close resemblance to how the researcher thinks. Close resemblance to how the researcher thinks. Easy visualisation.
Regression and Correlation Methods Judy Zhong Ph.D.
9 - 1 Intrinsically Linear Regression Chapter Introduction In Chapter 7 we discussed some deviations from the assumptions of the regression model.
Introduction to Linear Regression and Correlation Analysis
Regression Analysis Regression analysis is a statistical technique that is very useful for exploring the relationships between two or more variables (one.
Inference for regression - Simple linear regression
Correlation and Linear Regression
Statistics for Business and Economics 8 th Edition Chapter 11 Simple Regression Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Ch.
STATISTICS: BASICS Aswath Damodaran 1. 2 The role of statistics Aswath Damodaran 2  When you are given lots of data, and especially when that data is.
CPE 619 Simple Linear Regression Models Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama.
Simple Linear Regression Models
1 1 Slide © 2005 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
Managerial Economics Demand Estimation. Scatter Diagram Regression Analysis.
Regression Maarten Buis Outline Recap Estimation Goodness of Fit Goodness of Fit versus Effect Size transformation of variables and effect.
Introduction to Linear 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.
ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression 13. 1: Statistical Review Uchechukwu Ofoegbu Temple University.
Go to Table of Content Single Variable Regression Farrokh Alemi, Ph.D. Kashif Haqqi M.D.
Chapter 14 Inference for Regression AP Statistics 14.1 – Inference about the Model 14.2 – Predictions and Conditions.
Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company.
Inference for Regression Chapter 14. Linear Regression We can use least squares regression to estimate the linear relationship between two quantitative.
Multiple Regression Petter Mostad Review: Simple linear regression We define a model where are independent (normally distributed) with equal.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.
STA 286 week 131 Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression.
1 Regression Analysis The contents in this chapter are from Chapters of the textbook. The cntry15.sav data will be used. The data collected 15 countries’
REGRESSION DIAGNOSTICS Fall 2013 Dec 12/13. WHY REGRESSION DIAGNOSTICS? The validity of a regression model is based on a set of assumptions. Violation.
Ch14: Linear Least Squares 14.1: INTRO: Fitting a pth-order polynomial will require finding (p+1) coefficients from the data. Thus, a straight line (p=1)
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.
Chapter 12 Simple Linear Regression n Simple Linear Regression Model n Least Squares Method n Coefficient of Determination n Model Assumptions n Testing.
Lesson Testing the Significance of the Least Squares Regression Model.
Lecturer: Ing. Martina Hanová, PhD.. Regression analysis Regression analysis is a tool for analyzing relationships between financial variables:  Identify.
1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Part II: Theory and Estimation of Regression Models Chapter 5: Simple Regression Theory.
The simple linear regression model and parameter estimation
Chapter 4: Basic Estimation Techniques
Regression and Correlation of Data Summary
Chapter 4 Basic Estimation Techniques
Simple Linear Regression
Regression Analysis AGEC 784.
Correlation and Simple Linear Regression
Linear Regression Models
Correlation and Simple Linear Regression
Chapter 12 Inference on the Least-squares Regression Line; ANOVA
Correlation and Simple Linear Regression
Chapter 14 Inference for Regression
M248: Analyzing data Block D UNIT D2 Regression.
SIMPLE LINEAR REGRESSION
Simple Linear Regression and Correlation
Chapter 14 Inference for Regression
Ch 4.1 & 4.2 Two dimensions concept
Correlation and Simple Linear Regression
Correlation and Simple Linear Regression
Presentation transcript:

COTOR Training Session II GL Data: Long Tails, Volatility, Data Transforms September 11, 2006

COTOR Session II Presenters Doug Ryan MBA Actuaries, Inc. Phil Heckman Heckman Actuarial Consulting

Assumptions and Verification Behavior of mean, variance, distribution (sometimes) Verify by examining –Descriptive statistics –Regression diagnostics –Scatter plots –Residual plots

GL Data: Chain Ladder

What are they? Slope standard error R square: Percentage of variance explained by regression Intercept standard error Degrees of Freedom: # Observations - # Parameters

A Key Diagnostic: Standard Residual Standardize by subtracting mean (should be zero) and divide by standard deviation A z-score –Z = (x – mean)/sd

Two Factor Model One factor model: incremental loss =f(prior cumulative) –Compute separate function for each development age –Can use Excel regression functions Two factor model: incremental loss = f(accident period, development age) –Bornhuetter-Ferguson is an example –Nonlinear function, Use solver

GL Data: Two-Factor Model

GL Data: 3-Factor Model

GL Data: Log Chain Ladder

Why use logarithms? Descriptive statistics indicate data not normal A-priori belief that model is mutiplicative Residuals increase with value of dependent variable

GL Data: Log 2-Factor Model

Iterative Least Squares Start with all weights = 1 Estimate by minimizing weighted sum of squares Calculate new weights = 1/(1+ Old Weight*Squared Error) Reëstimate. Stop when weights stop changing.

GL Data: Summary