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Course Description
Statistical techniques can be used to address new situations. This is important in a rapidly evolving risk management world. Analysts with a strong analytical background understand that a large data set can represent a treasure trove of information to be mined and can yield a strong competitive advantage. This course provides budding analysts with a foundation in multiple reression. Participants will learn about these statistical techniques using data on the demand for insurance, lottery sales, healthcare expenditures, and other applications. Although no specific knowledge of actuarial or risk management is presumed, the approach introduces applications in which statistical techniques can be used to analyze real data of interest.
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Chapter 1. Regression and the Normal Distribution
FreeRegression analysis is a statistical method that is widely used in many fields of study, with actuarial science being no exception. This chapter introduces the role of the normal distribution in regression and the use of logarithmic transformations in specifying regression relationships.
Course Introduction100 xpFitting a normal distribution100 xpFitting Galton's height data100 xpVisualizing child's height distribution100 xpVisualizing distributions100 xpVisualizing injury claims with density plots100 xpSummarizing distributions100 xpSummarizing injury claims with box and qq plots100 xpEffects on distributions of removing the largest claim100 xpTransformations100 xpDistribution of transformed bodily injury claims100 xp - 2
Chapter 2. Basic Linear Regression
FreeThis chapter considers regression in the case of only one explanatory variable. Despite this seeming simplicity, many deep ideas of regression can be developed in this framework. By limiting ourselves to the one variable case, we can illustrate the relationships between two variables graphically. Graphical tools prove to be important for developing a link between the data and a predictive model.
Correlation100 xpCorrelations and the Wisconsin lottery100 xpMethod of least squares100 xpLeast squares fit using housing prices100 xpUnderstanding Variability100 xpSummarizing measures of uncertainty100 xpEffects of linear transforms on measures of uncertainty100 xpStatistical inference100 xpStatistical inference and Wisconsin lottery100 xpDiagnostics100 xpAssessing outliers in lottery sales100 xp - 3
Chapter 3. Multiple Linear Regression
FreeThis chapter introduces linear regression in the case of several explanatory variables, known as multiple linear regression (MLR). Many basic linear regression concepts extend directly, including goodness of fit measures such as the coefficient of determination and inference using t-statistics. Multiple linear regression models provide a framework for summarizing highly complex, multivariate data. Because this framework requires only linearity in the parameters, we are able to fit models that are nonlinear functions of the explanatory variables, thus providing a wide scope of potential applications.
Term life data100 xpMethod of least squares100 xpLeast squares and term life data100 xpInterpreting coefficients as proportional changes100 xpInterpreting coefficients as elasticities100 xpStatistical inference and multiple linear regression100 xpStatistical inference and term life100 xpBinary variables100 xpBinary variables and term life100 xpCategorical variables100 xpCategorical variables and Wisconsin hospital costs100 xpHypothesis testing100 xpHypothesis testing and term life100 xpHypothesis testing and Wisconsin hospital costs100 xp - 4
Chapter 4. Variable Selection
FreeThis chapter describes tools and techniques to help you select variables to enter into a linear regression model, beginning with an iterative model selection process. In applications with many potential explanatory variables, automatic variable selection procedures are available that will help you quickly evaluate many models. Nonetheless, automatic procedures have serious limitations including the inability to account properly for nonlinearities such as the impact of unusual points; this chapter expands upon the Chapter 2 discussion of unusual points. It also describes collinearity, a common feature of regression data where explanatory variables are linearly related to one another. Other topics that impact variable selection, including out-of-sample validation, are also introduced.
An iterative approach to data analysis and modeling100 xpInsert exercise title here50 xpAutomatic variable selection procedures100 xpData-snooping in stepwise regression100 xpResidual analysis100 xpResidual analysis and risk manager survey100 xpUnusual observations100 xpOutlier example100 xpHigh leverage and risk manager survey100 xpCollinearity100 xpCollinearity and term life100 xpSelection criteria100 xpCross-validation and term life100 xp - 5
Chapter 5. Interpreting Regression Results
FreeAn application, determining an individual's characteristics that influence its health expenditures, illustrates the regression modeling process from start to finish. Subsequently, the chapter summarizes what we learn from the modeling process, underscoring the importance of variable selection.
Case study - MEPS health expenditures100 xpSummarizing data100 xpFit a benchmark multiple linear regression model100 xpVariable selection100 xpModel comparisons using cross-validation100 xpOut of sample validation100 xpWhat the modeling procedure tells us100 xpWhat modeling procedures tell us50 xpThe importance of variable selection100 xp
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