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

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The Simple Regression Model Conditions for the SRM Inference in Regression 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 Inference in Regression 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 Inference in Regression 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 Inference in Regression 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 Inference in Regression 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 Inference in Regression 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.
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