Variance Of Y Hat Proof

The fitted regression linemodel is Yˆ 13931 07874X For any new subjectindividual withX its prediction of EYis Yˆ b0 b1X.

Variance of y hat proof. VarXY VarXVarY Proof. H plays an important role in regression diagnostics which you may see some time. 2 Least Squares in Matrix Form Our data consists of npaired observations of the predictor variable Xand the response variable Y ie X 1Y 1X nY n.

V 1 V P n. CorrXY 1 Y aX b for some constants a and b. The variances of 0 and 1 are.

Unfortunately there is generally no simple formula for the variance of a quadratic form unless the random vector is Gaussian. The sum of squared residuals RSS is e0e2 e1 e2. For a given model with independent variables and a dependent variable the hat matrix is the projection matrix to project vector y onto the column space of X.

A related matrix is the hat matrix which makes yˆ the predicted y out of y. Disk failures A RAID-like disk array consists of n drives each of which will fail independently with probability p. The corresponding regression line is thus.

E0e y Xfl0y Xfl y0y fl0X0y y0Xflfl0X0Xfl y0y 2fl0X0y fl0X0Xfl 4 where this development uses the fact that the transpose of a scalar. It describes the influence each response value has on each fitted value. We can determine four ways in which we can get a narrow confidence interval for μ Y.

Begingroup DavidMarx That step should be Var-barxhatbeta_1barybarx2Varhatbeta_1bary I think and then once I substitute in for hatbeta_1 and bary not sure what to do for this but Ill think about it more that should put me on the right path I hope. Y t α 2 n 2 M S E 1 n x x 2 x i x 2. Let the model be Y X Beta Epsilon where all elements of Epsilon have mean 0 and variance sigma2.