Y Hat Matrix Calculator

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.

Y hat matrix calculator. The n n matrix H XXX1X is often called the hat-matrix. Note that e y Xβˆ 23 y XX0X1X0y 24 I XX0X1X0y 25 My 26 where M and M Makes residuals out of y. This says that Y our dependent variable is composed of a linear part and error.

Instead of having y Z β we get that y P y where P is the hat matrix. Calculate the covariance matrix of β. Y - dependent variable vector n x 1.

Online calculator to perform matrix operations on one or two matrices including addition subtraction multiplication and taking the power determinant inverse or transpose of a matrix. These notes will not remind you of how matrix algebra works. Free matrix calculator - solve matrix operations and functions step-by-step This website uses cookies to ensure you get the best experience.

The hat matrix is also known as the projection matrix because it projects the vector of observations y onto the vector of predictions thus putting the hat on y. Calculate y-hat using the formula above and your given X value. The regression residuals can be written in different ways as y yˆ y Xβˆ y Hy IHy 23.

Y X β u where u N 0 Σ and Σ is symmetric idempotent. Write H on board. Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore referred to as the hat matrix.

The fitted values ŷ in linear least-squares regression are a linear transformation of the observed response variable. With help of this calculator you can. Mdl fitlmXY After fitting I looked at mdlDiagnosticsHatMatrix and found that the generated hat matrix values were different compared to when I calculated them manually using the formula above.