method of least squares उदाहरण वाक्य

To bring them into agreement, the small inconsistencies ( usually only a few cm ) are adjusted using the method of least squares that is, eliminated in a statistically plausible manner.
These equations are solved by the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times, and a new estimated hypocenter is computed.
Important papers of his include " On series expansions determined by the methods of least squares ", and " Investigations of the number of primes less than a given number ".
When the name is used, the " Gaussian distribution " was named after Carl Friedrich Gauss, who introduced the distribution in 1809 as a way of rationalizing the method of least squares as outlined above.
In 1810, after reading Gauss's work, Laplace, after proving the central limit theorem, used it to give a large sample justification for the method of least square and the normal distribution.

The method of least squares leads to a consideration of problems in an inner product space, involving projection onto subspaces, and thus the problem of minimizing the squared errors can be reduced to a problem in numerical linear algebra.
The minor planet was named in memory of Finnish scientist Henrik Johan Walbeck ( 1793 1822 ), astronomer and geodesist at the old Academia Aboensis who used the method of least squares to derive a good value for the Earth's flattening.
When the method of least squares is used to estimate " ? " 0 and ? 1, then the residuals \ scriptstyle \ widehat \ varepsilon, unlike the errors \ scriptstyle \ varepsilon, cannot be independent since they satisfy the two constraints
Adrain, Gauss, and Legendre all motivated the method of least squares by the problem of reconciling disparate physical measurements; in the case of Gauss and Legendre, the measurements in question were astronomical, and in Adrain's case they were survey measurements.
:Assuming that the application of physics is correct ( I don't understand the " experimental " set-up ), and that the measurements are subject to about the same ( normal ) error distribution with ? = 0, the method of least squares is applicable and appropriate.