Evaluating Regression Models

Oct 19, 2013

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Good Models and Explaining" Variance. What do we mean when we say a model is good" or explains" the dependent variable?Explanation exists in our theory, not in any data we might observe.Thus explained" variance cannot be measured with a statistic (or with data). What do we mean when we say we

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Evaluating Regression Models

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Multilevel Regression Models

Multilevel Regression Models . sean f. reardon 17 june, 2004. Outline. What/Why Multilevel Regression? The Basic Multilevel Regression Model Growth Models A Taste of Advanced Topics. Part I.A. What are multilevel data and multilevel analysis?.

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Regression Models

Regression Models. Chapter 4. To accompany Quantitative Analysis for Management , Tenth Edition , by Render, Stair, and Hanna Power Point slides created by Jeff Heyl. © 2009 Prentice-Hall, Inc. . Learning Objectives. After completing this chapter, students will be able to:.

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Linear Regression Models

Linear Regression Models. Based on Chapter 3 of Hastie, Tibshirani and Friedman Slides by David Madigan. Linear Regression Models. Here the X ’s might be:. Raw predictor variables (continuous or coded-categorical) Transformed predictors ( X 4 =log X 3 )

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 8 – Multicollinearity, Diagnostics. Multiple Regression Models. Multicollinearity

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 7 – Multiple Regression Analysis. Model Assumptions.

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 3 – Model Fit and Correlation. Correlation and Linear Association. Height (inches) and Income ($/mo.) in first post-MBA

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models . Part 5 – Elasticities and Functional Form. Linear Regression Models. Model building Linear models – cost functions

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Statistics and Data Analysis. Part 10 – Qualitative Data. Modeling Qualitative Data. A Binary Outcome Yes or No – Bernoulli Survey Responses: Preference Scales

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 1 – Simple Linear Model. Theory. Demand Theory: Q = f(Price) “The Law of Demand” Demand curves slope downward

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models . Part 4 – Prediction. Prediction. Use of the model for prediction Use “x” to predict y based on y = β 0 + β 1 x + ε Sources of uncertainty

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LINEAR REGRESSION: Evaluating Regression Models

LINEAR REGRESSION: Evaluating Regression Models. Overview. Standard Error of the Estimate Goodness of Fit Coefficient of Determination Regression Coefficients. Standard Error of the Estimate. Index of how far off predictions are expected to be Larger r means smaller standard error

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 6 – Multiple Regression. Multiple Regression Agenda. The concept of multiple regression Computing the regression equation

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 2 – Inference About the Regression. The Linear Regression Model. 1. The linear regression model

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Regression Models

Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 9 – Model Building. Multiple Regression Models. Using Binary Variables Logs and Elasticities Trends in Time Series Data

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Regression Models

Regression Models. Fit data Time-series data: Forecast Other data: Predict. Use in Data Mining. One of major analytic models Linear regression The standard – ordinary least squares regression Can use for discriminant analysis Can apply stepwise regression

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Linear regression models

Linear regression models. Simple Linear Regression. History. Developed by Sir Francis Galton (1822-1911) in his article “Regression towards mediocrity in hereditary structure”. Purposes:.

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Nonlinear Regression Models

Nonlinear Regression Models. Nonlinear Regression Models. Lets revisit the AR(1) model of autocorrelation: y t = x t β +e t [ i ] e t = ρ e t-1 + ν t → ν t = e t - ρ e t-1 ρ y t-1 = ρ x t-1 β + ρ e t-1 (t=2,3,…,T) → y t − ρ y t-1 = x t β − ρ x t-1 β +e t - ρ e t-1

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Regression Models

Population Deterministic Regression Model Y i =  0 +  1 X i Y i only depends on the value of X i and no other factor can affect Y i . Population Probabilistic Regression Model Y i =  0 +  1 X i +  i , i = 1, 2, ... , n. E(Y |X i )=  0 +  1 X i ,

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Multiple Regression Models

Multiple Regression Models. Exploring an example: “Chapter 4: Multiple Regression II” data.

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Evaluating the Uncertainty of Land-Use Regression Models

Halûk Özkaynak US EPA, Office of Research and Development National Exposure Research Laboratory, RTP, NC Presented at the CMAS Special Symposium on Air Quality October 13, 2010. Evaluating the Uncertainty of Land-Use Regression Models. Land-Use Regression (LUR) Models.

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Regression Models

Regression Models. Chapter 4. Learning Objectives. After completing this chapter, students will be able to:. Identify variables and use them in a regression model Develop simple linear regression equations from sample data and interpret the slope and intercept

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Regression Models

Regression Models. Residuals and Diagnosing the Quality of a Model. Visualizing Regression Models. Criteria of quality. Residuals (or what we don’t explain) should be “noise” Independent variables measure different phenomena We haven’t left out something important.

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