G89.2229 Multiple Regression Week 6 Wednesday

Jul 04, 2013

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G89.2229 Lect 6W. Constructing polynomial fits. Two approaches for constructing polynomial fitsSimply create squared, cubed versions of XCenter first: Create squared, cubed versions of (X-C)Xc=(X-`X)Xc and Xc2 will have little or no correlationBoth approach yield identical fitsCentered polynom

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G89.2229 Multiple Regression Week 6 Wednesday

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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.

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Notes 6: Multiple Linear Regression

Notes 6: Multiple Linear Regression. 1. The Multiple Linear Regression Model 2. Estimates and Plug-in Prediction 3. Confidence Intervals and Hypothesis Tests 4. Fits, residuals, R-squared, and the overall F-test 5. Categorical Variables as Regressors

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g89.2229 multiple regression week 14 monday

G89.2229 Lect 14M. Overview of Course. For some outcome Y and explanatory variables X'=[X1 X2 ... Xp],We considered E(Y | X)To be modeled descriptivelyAs a structural modelAdditive models for E(Y | X)Main effects linear modelsAdditive polynomial modelsLinear models with interactions. G89.2229 Lect 14M.

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G89.2229 Multiple Regression Week 7 Wednesday

G89.2229 Lect 7W. Representing Interaction in the Regression Equation. If we believe that the effect of X1 varies as a function of level of a second variable, X2, we can build a simple multiplicative interactive effect.Y=b0 b1X1 b2X2 b3(X1*X2) eThis multiplicative term creates a curved surface in

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G89.2229 Multiple Regression Week 4 Monday

G89.2229 Lect 4M. Suppression. Sometimes the semipartial effect for X1 (i.e. b1) in Y = b0 b1X1 b2X2 e is larger in absolute magnitude than the bivariate effect in Y = b0 b1X1 eThis has been called suppressionExample:X1 is stressY is distressX2 is copingClassic pattern is when one of

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Multiple Regression

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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G89.2229 Multiple Regression Week 11 Wednesday

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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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G89.2229 Multiple Regression Week 3 Wednesday

G89.2229 Lect 3W. The geometry of E(Y|X1 X2) = b0 b1X1 b2X2. E(Y|X1 X2)= b0 b1X1 b2X2 describes a plane.For every change in either X1 or X2, E(Y|X1 X2) changes linearlyThe distribution of X1 and X2 does not affect the form of the plane itself, but it does affect the estimates of b0, b1, an

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6-3 Multiple Regression

6-3 Multiple Regression. 6-3.1 Estimation of Parameters in Multiple Regression. 6-3 Multiple Regression. 6-3.1 Estimation of Parameters in Multiple Regression. The least squares function is given by. The least squares estimates must satisfy. 6-3 Multiple Regression.

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Notes 6: Multiple Linear Regression

2. 1. The Multiple Linear Regression Model. The plug-in predictive interval for the price of a housegiven its size is quite large.Is this

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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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G89.2229 Multiple Regression Week 11 Monday

G89.2229 Lect 11M. Binary outcomes in psychology. Psychologists tend to study quantitative processes such as reaction time, strength of attitudes, achievement scores, and severity of depressionIn some cases the outcome is binary or categoricalDecisions (e.g. to sit next to certain person)Passing

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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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Chapter 6: Multiple Linear Regression

Chapter 6: Multiple Linear Regression. Data Mining for Business Intelligence Shmueli, Patel & Bruce. Topics. Explanatory vs. predictive modeling with regression Example: prices of Toyota Corollas Fitting a predictive model Assessing predictive accuracy Selecting a subset of predictors.

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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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