Sum of squares function information

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 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...

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...

minimising a sum of squares function S = ∑ 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}\left(Y_{i}-\beta...

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...

{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 ) + sinc...

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

problem of minimizing an objective function that has the form of a sum: Q ( w ) = 1 n ∑ i = 1 n Q i ( w ) , {\displaystyle Q(w)={\frac {1}{n}}\sum _{i=1}^{n}Q_{i}(w)...

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...

(/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...

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

)}/2} SUM(x2): The sum of squares of the values is important in order to calculate the Standard Deviation of groups SUM ⁡ ( X 2 ⊎ Y 2 ) = SUM ⁡ ( X 2...

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...

3, A(x) = 0, and B(x) = x + 1, we can verify that the squares grow as expected, like the squares: a n ∼ B ( r ) r α Γ ( β ) n β − 1 ( 1 r ) n = 1 + 1 1...

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...

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...