Search results
Results from the WOW.Com Content Network
If a vector of predictions is generated from a sample of data points on all variables, and is the vector of observed values of the variable being predicted, with ^ being the predicted values (e.g. as from a least-squares fit), then the within-sample MSE of the predictor is computed as
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
Help; Learn to edit; Community portal; Recent changes; Upload file; Special pages
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
Physical scientists often use the term root mean square as a synonym for standard deviation when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. [8] [9] This is useful for electrical engineers in calculating the "AC only" RMS of a signal.
The following statements explain the meaning of the remaining columns: The sum of the entries in the first column (a 2) is the sum of the squares of the distance from sample to sample mean; The sum of the entries in the last column (b 2) is the sum of squared distances between the measured sample mean and the correct population mean
Help; Learn to edit; Community portal; Recent changes; Upload file; Special pages