Multiple Regression

Jul 20, 2012

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Multiple Regression. Multiple regression is an extension of bivariate regression to include more than one independent variable.Limitations of bivariate regression: - often simplistic - biased estimates if relevant predictors are omitted - lack of fit does not show that X is unrelated to Y. McGra

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Multiple Regression

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Multiple Regression

Multiple Regression. In multiple regression, we consider the response , y, to be a function of more than one predictor variable, x1, …, xk Easiest to express in terms of matrices. Multiple Regression. Let Y be a col vector whose rows are the observations of the response Let X be a matrix.

1.11k views • 45 slides

Multiple Regression

What is Multiple Regression? . y = b0 b1x1 b2x2.... bkxk.? One dependent variableSeveral independent variables x1,x2..xk. Assumptions. Quantitative dataIndependent observationEach value of IV, the distribution of the DV must be normalThe variance of the distribution of the DV should be co

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Multiple Regression

Multiple Regression. Dr. Andy Field. Aims. Understand When To Use Multiple Regression . Understand the multiple regression equation and what the betas represent. Understand Different Methods of Regression Hierarchical Stepwise Forced Entry

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Multiple Regression

Multiple Regression . Control of Confounding Variables. Randomization Matching Adjustment Direct Indirect Mantel-Haenszel Multiple Regression Linear Logistic Poisson Cox. Stratified methods . Limitations of the Stratified Methods.

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MULTIPLE REGRESSION

MULTIPLE REGRESSION. OVERVIEW. What Makes it Multiple? Additional Assumptions Methods of Entering Variables Adjusted R 2 Using z-Scores Categorical Predictors. WHAT MAKES IT MULTIPLE?. Predict from a combination of two or more predictor (X) variables

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Multiple Regression

Multiple Regression. W&W, Chapter 13, 15(3-4). Introduction. Multiple regression is an extension of bivariate regression to take into account more than one independent variable. The most simple multivariate model can be written as: Y =  0 +  1 X 1 +  2 X 2 + 

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Multiple Regression

Multiple Regression. The Basics. Multiple Regression (MR). Predicting one DV from a set of predictors, the DV should be interval/ratio or at least assumed I/R if using Likert scale for instance. Assumptions. Y must be normally distributed (no skewness or outliers) X’s

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Multiple Regression

Multiple Regression. Introduction. In this chapter we extend the simple linear regression model, and allow for any number of independent variables. We expect to build a model that fits the data better than the simple linear regression model. Introduction. We shall use computer printout to

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Multiple Regression

STAT 101 Dr. Kari Lock Morgan. Multiple Regression. SECTIONS 9.2, 10.1, 10.2 Multiple explanatory variables (10.1) Partitioning variability – R 2 , ANOVA (9.2) Conditions – residual plot (10.2). Exam 2 Grades: In-Class. Exam 2 Re-grades.

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Multiple Regression

STAT 101 Dr. Kari Lock Morgan 11/27/12. Multiple Regression. SECTION 10.3 Categorical variables Variable selection Confounding variables revisited. US States.

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MULTIPLE REGRESSION

MULTIPLE REGRESSION. OVERVIEW. What Makes it Multiple? Additional Assumptions Methods of Entering Variables Adjusted R 2 Using z-Scores. WHAT MAKES IT MULTIPLE?. Predict from a combination of two or more predictor (X) variables.

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Multiple Regression

Multiple Regression. SPH 247 Statistical Analysis of Laboratory Data. Cystic Fibrosis Data. Cystic fibrosis lung function data lung function data for cystic fibrosis patients (7-23 years old) age a numeric vector. Age in years. sex a numeric vector code. 0: male, 1:female.

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Multiple regression

Multiple regression. An example. Theory. Optimism causes political participation. General optimism Specific optimism. Dependent variable. polpartbes _ | count | Freq. Percent Cum. ------------+-----------------------------------

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Multiple Regression

Multiple Regression. Using Additional Explanatory Variables. Try this …. Look at the relationship between average driving distance & scoring average for 146 LPGA golfers in 2009. The least-squares regression line is ŷ = 87.95 – 0.0609x. Interpret the slope :.

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Multiple Regression

Multiple Regression. Chapter 18. 18.1 Introduction. In this chapter we extend the simple linear regression model, and allow for any number of independent variables. We expect to build a model that fits the data better than the simple linear regression model.

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Multiple Regression

Multiple Regression. Chapter 17. Introduction. In this chapter we extend the simple linear regression model, and allow for any number of independent variables. We expect to build a model that fits the data better than the simple linear regression model. Introduction.

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Multiple regression:

Multiple regression:. Yi = B 0 + B 1 X 1 +B 2 X 2 + B 3 X 3 +e where each of the Betas estimate the effect of one independent variable. This allows the regression to "control" for each of the other factors simultaneously

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Multiple Regression

Multiple Regression. Multiple Regression. The test you choose depends on level of measurement: Independent Variable Dependent Variable Test Dichotomous Continuous Independent Samples t-test Dichotomous Nominal Nominal Cross Tabs Dichotomous Dichotomous

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Multiple Regression

Multiple Regression. What Techniques Can Tell Us. Chi Square- Do groups differ (nominal data)? T Test Do Groups/Variables differ? Gamma/Lambda/Kendall’s Tau etc Are variables related to each other? (nominal data) Correlation Are variables related to each other? (ratio/interval data).

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Multiple Regression

Multiple Regression. Class 22. Multiple Regression (MR). Y = b o + b 1 + b 2 + b 3 + ……b x + ε. Multiple regression (MR) can incorporate any number of predictors in model. “Regression plane” with 2 predictors, after that it becomes increasingly difficult to visualize result.

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Multiple regression

Multiple regression. Regression. Problem: to draw a straight line through the points that best explains the variance. Regression. Problem: to draw a straight line through the points that best explains the variance. Regression.

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Multiple Regression

University of Warwick, Department of Sociology, 2014/15 SO 201: SSAASS (Surveys and Statistics) (Richard Lampard ) Week 6 Regression: ‘Loose Ends’. Multiple Regression. GHQ = (-0.47 x INCOME) + (-1.95 x HOUSING) + 5.74 For B = 0.47, t = -1.51 (& p = 0.139 > 0.05)

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