the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where...

theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares, such that...

Least squares For the "sum of squared differences", see Mean squared error For the "sum of squared error", see Residual sum of squares For the "sum of squares...

The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual...

least squares function approximation applies the principle of least squares to function approximation, by means of a weighted sum of other functions. The...

Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of four squares (of integers)...

Least trimmed squares (LTS), or least trimmed sum of squares, is a robust statistical method that fits a function to a set of data whilst not being unduly...

a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals...

four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as a sum of four non-negative integer squares....

seventeenth problem, for the representation of positive polynomials as a sum of squares of rational functions Square-free polynomial Cube (algebra) Metric tensor...

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters...

A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables...

squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a...

analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard...

of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding...

(n)+\sum _{d|m}\mu (d)\sum _{d'|n}\mu (d')\\&=\mu (mn)-\mu (m)\mu (n)+0\end{aligned}}} The sum of the Möbius function over all positive divisors of n (including...

least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the...

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...

minimising a sum of squares function S = ∑ i = 1 n ε i 2 = ∑ i = 1 n ( Y i − β 0 − β 1 ϕ 1 ( X i 1 ) − ⋯ − β p ϕ p ( X i p ) ) 2 . {\displaystyle S=\sum _{i=1}^{n}\varepsilon...

(/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but...

needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences...

a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is...

Square-summable may refer to: Square-integrable functions Square-summable sequences; see Hilbert space § Sequence spaces This disambiguation page lists...

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems...

is unknown. The sum of squares of the residuals, on the other hand, is observable. The quotient of that sum by σ2 has a chi-squared distribution with...

{sinc} (3)+\operatorname {sinc} (4)+\cdots ={\frac {\pi -1}{2}}.} The sum of the squares also equals ⁠π − 1/2⁠: ∑ n = 1 ∞ sinc 2 ⁡ ( n ) = sinc 2 ⁡ ( 1 ) +...

Ramanujan's sum. A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function. The sum of positive...

variance involves summing the squares of quantities. There are only finitely many positive integers that are not sums of distinct squares. The largest one...

perfect squares. Three squares are not sufficient for numbers of the form 4k(8m + 7). A positive integer can be represented as a sum of two squares precisely...

least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost function relating...