Sentence examples for variances are given from inspiring English sources

New formulations for the recursive residuals for models having uncorrelated errors with equal variances are given in terms of the observation vector or the usual least-squares residuals, which do not require the computation of least-squares parameter estimates and for which the transformation matrices are expressed wholly in terms of the rows of the Theil Z matrix.

(2) The sensors with higher observation noise variances are given less power.

It is easy to show that and are zero-mean RVs and that their variances are given by (13).

Eigenvalues and cumulative explained variances are given at the bottom of the table.

The eigenvectors (principal components) can be viewed as composite traits (linear combinations of the original traits) that are genetically uncorrelated (i.e., their covariances are zero) and whose genetic variances are given by the corresponding eigenvalues.

The estimated values of the Class I and Class II reflectances and their respective variances are given by the following expressions and where W(i) is the weight of the ith photon packet in MCML, which is a quantity affected by the absorption coefficient at the scattering points, and L i) is the product of the likelihood rations of all the biased scatterings that affected the ith photon packet.

To summarize, the statistical analysis showed that (i) the basis for the analysis of variance (homogeneity of variances) is given, (ii) only the combination of gold NP and an alternating magnetic field increases significantly at a 0.001 level the hydrolysis of aspirin, and (iii) neither gold NP nor alternating magnetic fields alone lead to a significant effect on the hydrolysis.

where the mean and the variance are given by (29).

Details regarding the analyses of variance are given in Additional file 1: Table S1.

The corresponding phase noise power spectrum and phase noise variance are given by (31).

where the mean and the variance are given by,,, and denotes the SNR.