Lect21 - The Simple Regression Model Conditions for the SRM...

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The Simple Regression Model Conditions for the SRM Outline The Simple Regression Model Conditions for the SRM Inference in Regression Inference about the Slope Inference about the Intercept 1 / 19 ISOM 2500 Lect 21: The Simple Regression Model
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The Simple Regression Model Conditions for the SRM The Capital Asset Pricing Model (CAPM) How does the return, R t , on a specific stock relate to the return, M t , of the whole market? The Capital Asset Pricing Model (CAPM) has the form that R t = β 0 + β 1 M t + ε t and says that β 0 = 0. Today we’ll test the CAPM for Berkshire Hathaway. 2 / 19 ISOM 2500 Lect 21: The Simple Regression Model
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The Simple Regression Model Conditions for the SRM The Simple Regression Model The Simple Regression Model (SRM) models the association in the population between a predictor X and response Y by the following equation: Y = β 0 + β 1 X + ε, ε N ( 0 , σ 2 ε ) , or, equivalently, the following two components: 1. Linear on Average 2. Normality of the Deviations from the Mean 3 / 19 ISOM 2500 Lect 21: The Simple Regression Model
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The Simple Regression Model Conditions for the SRM Linear on Average The mean of Y given X = x is called the conditional mean of Y given X = x , written as μ y | x = E ( Y | X = x ) . A primary question that one’d like to answer in regression analysis is: How does μ y | x depend on x ? The SRM says that μ y | x depends linearly on x : μ y | x = β 0 + β 1 x . 4 / 19 ISOM 2500 Lect 21: The Simple Regression Model
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The Simple Regression Model Conditions for the SRM Deviations from the Mean A second question that one’d like to answer in regression analysis is: how does the response deviate from its conditional mean? The deviations of responses around μ y | x are called errors , and denoted by ε The SRM makes three assumptions about ε : 1. Independent: the error for one observation is independent of the error for any other observation 2. Equal variance: All errors have the same variance, Var ( ε ) = σ 2 ε . 3. Normal: The errors are normally distributed. 5 / 19 ISOM 2500 Lect 21: The Simple Regression Model
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The Simple Regression Model Conditions for the SRM Simple Regression Model (SRM) Y = β 0 + β 1 X + ε, ε N ( 0 , σ 2 ε ) , 1. The observations are independent of one another 2. have equal variance around the regression line, 3. and are normally distributed around the regression line.
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This note was uploaded on 12/20/2011 for the course ACCT/MGMT 2010 taught by Professor A during the Spring '11 term at HKUST.

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Lect21 - The Simple Regression Model Conditions for the SRM...

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