Chapter 15 Multiple Regression

Aug 26, 2012

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The equation that describes how the dependent variable y is related to the independent variables x1, x2, . . . xp and an error term is:. Multiple Regression Model. . y = b0 b1x1 b2x2 . . . bpxp e. where:b0, b1, b2, . . . , bp are the parameters, ande is a random variable called

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Chapter 15 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

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

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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Chapter 4 Multiple Regression

Chapter 4 Multiple Regression . Multiple Regression Overview. What is it? Why use it?. Multiple Regression. Y’ = b 0 + b 1 X 1 + b 2 X 2 + . . . + b n X n + e . Y = Dependent Variable = # of credit cards

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Chapter 13 Multiple Regression

Chapter 13 Multiple Regression. Section 13.1 Using Several Variables to Predict a Response. Regression Models. The model that contains only two variables, x and y , is called a bivariate model. Regression Models. Suppose there are two predictors, denoted by and .

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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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Chapter 13: Multiple Regression

Chapter 13: Multiple Regression. Section 13.1: How Can We Use Several Variables to Predict a Response?. Learning Objectives. Regression Models The Number of Explanatory Variables Plotting Relationships Interpretation of Multiple Regression Coefficients

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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 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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Chapter 15 Multiple Regression

Chapter 15 Multiple Regression. Multiple Regression Model. Least Squares Method. Multiple Coefficient of Determination. Model Assumptions. Testing for Significance. Using the Estimated Regression Equation for Estimation and Prediction. Categorical Independent Variables.

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Chapter 15: Multiple Linear Regression

Chapter 15: Multiple Linear Regression. In Chapter 15:. 15.1 The General Idea 15.2 The Multiple Linear Regression Model 15.3 Categorical Explanatory Variables in Regression Models 15.4 Regression Coefficients 15.5 ANOVA for Multiple Linear Regression

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Chapter 13 Multiple Regression

Chapter 13 Multiple Regression. Multiple Regression Model Least Squares Method Multiple Coefficient of Determination Model Assumptions Testing for Significance Using the Estimated Regression Equation for Estimation and Prediction Qualitative Independent Variables.

688 views • 39 slides

Chapter 13 Multiple Regression

Chapter 13 Multiple Regression. Multiple Regression Model. Least Squares Method. Multiple Coefficient of Determination. Model Assumptions. Testing for Significance. Using the Estimated Regression Equation for Estimation and Prediction. Qualitative Independent Variables.

592 views • 27 slides

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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Chapter 12 Multiple Regression

Chapter 12 Multiple Regression. Learn…. T o use Multiple Regression Analysis to predict a response variable using more than one explanatory variable. Section 12.1. How Can We Use Several Variables to Predict a Response?. Regression Models.

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15. Multiple Regression

15. Multiple Regression. How do we actually request the regressions in SPSS? How do we use regression to explicate a bivariate relationship with a third variable? What do we look for once we have run the relevant regressions?. Example of Simple and Multiple Regression. DV (Effect). IV

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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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