Hat operator
The hat operator is a mathematical notation with various uses in different branches of science and mathematics.In statistics, the hat matrix H projects the observed values y of response variable to the predicted values ŷ:Cross product
In screw theory, one use of the hat operator is to represent the cross product operation. Since the cross product is a linear transformation, it can be represented as a matrix. The hat operator takes a vector and transforms it into its equivalent matrix.
For example, in three dimensions,Estimated value
In statistics, the hat is used to denote an estimator or an estimated value. For example, in the context of errors and residuals, the "hat" over the letter ε indicates an observable estimate of an unobservable quantity called ε.
In simple linear regression with observations of independent variable data and dependent variable data, and assuming a model of, can lead to an estimated model of the form where is minimized via least squares by finding optimal values of and for the observed data.The Fourier transform of a function is traditionally denoted by.
