The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning...
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sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals...
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elsewhere, sums of squares occur in a number of contexts: For partitioning of variance, see Partition of sums of squares For the "sum of squared deviations"...
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and the error term.[page needed] The main difference between the sum of squares of the within-subject factors and between-subject factors is that within-subject...
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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}...
36 KB (6,609 words) - 11:11, 5 January 2025
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...
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total sum of squares is the sum of the so-called "within-samples" sum of squares and "between-samples" sum of squares, i.e., partitioning of the sum of squares...
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each of the T i {\displaystyle T_{i}} will be zero. It is now possible to calculate three sums of squares: Individual I = ∑ x 2 {\displaystyle I=\sum x^{2}}...
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combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ...
29 KB (3,396 words) - 22:30, 27 March 2025
Integer partition Jacobi's four-square theorem Gauss circle problem P. T. Bateman (1951). "On the Representation of a Number as the Sum of Three Squares" (PDF)...
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In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression (SSR – not to be...
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expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA)...
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squares Partial least squares regression Partial leverage Partial regression plot Partial residual plot Particle filter Partition of sums of squares Parzen...
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according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was...
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The sum of the reciprocals of the primes of the form 4n + 1 is divergent. By Fermat's theorem on sums of two squares, it follows that the sum of reciprocals...
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matrix, and partition of the sum of squares in statistics problems, especially in the analysis of variance, quotition and partition, two ways of viewing the...
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magic square is a multiple of the order of the smaller squares. Such squares can usually be partitioned into smaller non-overlapping magic sub-squares. Inlaid...
283 KB (22,399 words) - 20:37, 1 April 2025
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because...
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In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the...
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multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums of the subsets are...
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of two distinct isolated primes (2 and 503); unusual number; square-free number; number of compositions (ordered partitions) of 22 into squares; sum of...
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Integral (redirect from Sum rule in integration)
integral is defined in terms of Riemann sums of functions with respect to tagged partitions of an interval. A tagged partition of a closed interval [a, b]...
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The United Nations Partition Plan for Palestine was a proposal by the United Nations to partition Mandatory Palestine at the end of the British Mandate...
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: 10–13 and : 3–5 for surveys. The problem of partitioning a rectilinear polygon to a smallest number of squares (in contrast to arbitrary rectangles) is...
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sums to the magic constant, 4 × 4 pandiagonal magic squares are most-perfect magic squares. In addition, the two numbers at the opposite corners of any...
36 KB (2,450 words) - 18:05, 20 September 2024
can be measured with two sums of squares formulas: The sum of squares of residuals, also called the residual sum of squares: S S res = ∑ i ( y i − f i...
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combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different definitions of rank appear in...
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combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets...
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unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the true...
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Block matrix (redirect from Matrix partition)
\sum _{i=1}^{p}m_{i}=m} , and ∑ j = 1 q n j = n {\displaystyle \sum _{j=1}^{q}n_{j}=n} . The elements A i j {\displaystyle A_{ij}} of the partition are...
29 KB (4,799 words) - 22:17, 6 March 2025