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Unformatted text preview: E(Y |x)= μ Y |x = β + β 1 x Simple Linear Regression Model : Y= β + β 1 x+ – Assumes random, independent, mean 0, ε constant variance Method of Least Squares: Y i = β + β 1 x i + ε i , i=1, 2, …, n where: = - β0 y β1x = =-( = )( = ) =- β1 i 1nyixi i 1nyi i 1nxi ni 1nxi2 ( = ) = =- ( - ) = ( - ) = i 1nxi 2n i 1nxi x yi y i 1n xi x 2 SxySxx Estimated regression line is = + y β0 β1x Residuals: = - ei yi yi Residual sum of squares: = - = SSE yi yi2 ei2 =- σ2 SSEn 2 Unbiased estimators , β0 β1 , meaning distributions are centered at t rue values of β 1 and β and are normal. = + , = Vβ0 σ21n x2Sxx Vβ1 σ2Sxx = , = ( + ) seβ1 σ2Sxx seβ0 σ2 1n x2Sxx = = - =-( ) SST Syy yi y2 yi2 yi 2n =( - ) + - = + yi y 2 yi yi2 SSR SSE = - R2 1 SSESST (coefficient of determination) Regression models are used primarily for interpolation . That is, when predicting a new observation on the response (or estimating the mean response) at a particular value of the regressor x, we should only use values of x that are within the range...
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- Spring '06
- Regression Analysis, linear regression model