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# lecture9 - Simple Linear Regression Analysis Multiple...

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Simple Linear Regression Analysis Multiple Linear Regression STA113: Probability and Statistics in Engineering Linear Regression Analysis - Chapters 12 and 13 in Devore Artin Armagan Department of Statistical Science November 18, 2009 Armagan

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Simple Linear Regression Analysis Multiple Linear Regression Outline 1 Simple Linear Regression Analysis Using simple regression to describe a linear relationship Inferences From a Simple Regression Analysis Assessing the Fit of the Regression Line Prediction with a Sample Linear Regression Equation 2 Multiple Linear Regression Using Multiple Linear Regression to Explain a Relationship Inferences From a Multiple Regression Analysis Assessing the Fit of the Regression Line Comparing Two Regression Models Multicollinearity Armagan
Simple Linear Regression Analysis Multiple Linear Regression Using simple regression to describe a linear relationship Inferences From a Simple Regression Analysis Assessing the Fit of the Regression Line Prediction with a Sample Linear Regression Equation Purpose and Formulation Regression analysis is a statistical technique used to describe relationships among variables. In the simplest case where bivariate data are observed, the simple linear regression is used. The variable that we are trying to model is referred to as the dependent variable and often denoted by y . The variable that we are trying to explain y with is referred to as the independent or explanatory variable and often denoted by x . If a linear relationship between y and x is believed to exist, this relationship is expressed through an equation for a line: y = b 0 + b 1 x Armagan

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Simple Linear Regression Analysis Multiple Linear Regression Using simple regression to describe a linear relationship Inferences From a Simple Regression Analysis Assessing the Fit of the Regression Line Prediction with a Sample Linear Regression Equation Purpose and Formulation Above equation gives an exact or a deterministic relationship meaning there exists no randomness. In this case recall that having only two pairs of observations ( x , y ) would suffice to construct a line. However many things we observe have a random component to it which we try to understand through various probability distributions. Armagan
Simple Linear Regression Analysis Multiple Linear Regression Using simple regression to describe a linear relationship Inferences From a Simple Regression Analysis Assessing the Fit of the Regression Line Prediction with a Sample Linear Regression Equation Example 1 2 3 4 5 6 4 6 8 10 12 x y 1 2 3 4 5 6 2 4 6 8 10 12 x y y = 1 + 2 x ˆ y = - 0 . 2 + 2 . 2 x Armagan

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Simple Linear Regression Analysis Multiple Linear Regression Using simple regression to describe a linear relationship Inferences From a Simple Regression Analysis Assessing the Fit of the Regression Line Prediction with a Sample Linear Regression Equation Least Squares Criterion to Fit a Line We need to specify a method to find the “best” fitting line to the observed data.
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lecture9 - Simple Linear Regression Analysis Multiple...

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