Cov(x Y Hat)

ϵX1i X1i ˆα0 ˆα1X2i.

Cov(x y hat). Method of moments the GMM estimator based on the third- or higher- order joint cumulants of observable variables. CovXYSDXSDYSDYSDX covXYVARX this is the same as equation for hat b1 on page 518 The intercept b0 is estimated by putting x0 in the regression line. CovXY 1 2 VarX YVarXVarY 1 2 Substituting this into the above formula we get the answer.

In statistics the projection matrix sometimes also called the influence matrix or hat matrix maps the vector of response values dependent variable values to the vector of fitted values or predicted values. Covβ X T X-1 MSE where MSE SSEDFE SSEn-p. Where ˆα0 and ˆα1 are the OLS estimators of X2i.

C o v X Y. Now instead of measuring the fluctuation of a single variable the covariance measures how two. Y i b0 b1xi 9 where the hat denotes the predicted value of y corresponding to that value of x.

It describes the influence each response value has on each fitted value. Cov X iW i Var X i we can infer the direction of the bias of b 1 that persists in large samples Suppose W i has a positive effect on Y i then 2 0 Suppose X i and W i are positively correlated then Cov i. 1x Covy i P y i n.

The variance of the mean response is given by. ϵYi Yi ˆy0 ˆy1X2i. Alphahat meanybetahatmeanx We get the result the the LSE of the intercept and the slope are 211 and 038.

This is the sample regression function SRF corresponding to the population regression function or PRF 3. A company insures homes in three cities J K L. The coefficient of variation COV is a measure of relative event dispersion thats equal to the ratio between the standard deviation and the mean.