Quiz4 - E(Y |x)= μ Y |x = β β 1 x Simple Linear...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 2

Quiz4 - E(Y |x)= μ Y |x = β β 1 x Simple Linear...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online