ALRLec2 - Chapter 2 Simple Linear Regression Simple linear...

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1 Chapter 2 Simple Linear Regression Simple linear regression model E[Y|X=x] = β 1 + β 0 x Var[Y|X=x] = σ 2 Another way of writing the same model Y = β 1 + β 0 x + e y i = β 1 + β 0 x i + e i i = 1,2,…,n Assumption of e i E[e i |x i ] = 0 Var[e i |x i ] = σ 2 e i ’s are independent of each other Note we did not assume e i ’s normal distributed 2.1 Ordinary Least Squares (OLS) Parameters: unknown quantities in the model 2 01 ,,    Estimates: computable functions of data ^ 2 ^ 0 ^ 1 , , Fitted value for case i, ^ i y ˆˆ ˆ ii yx   Residual () i i i i i e y y y x 2.2 Least Squares Residual Sum of Squares (RSS) ^^ 22 11 ˆ nn i i i e y x  
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2 Find 01 ,  to minimize 2 0 1 0 1 1 ( , ) ( ) n ii i RSS y x   Appendix A.3 1 0 1 1 2 ( ) 0 2 ( ) 0 n i n i i i i RSS yx RSS x y x     ( 1 ) 11 0 nn y n x   ( 2 ) 2 1 1 1 0 n n n i i i i i i i x y x x ( 1) & ( 2)
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ALRLec2 - Chapter 2 Simple Linear Regression Simple linear...

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