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Sum of: Formula: Squares of two numbers: x 2 + y 2 = (x+y) 2-2ab: Squares of three numbers: x 2 + y 2 +z 2 = (x+y+z) 2-2xy-2yz-2xz: Squares of first ‘n’ natural numbers: Σn 2 = [n(n+1)(2n+1)]/6: Squares of first even natural numbers: Σ(2n) 2 = [2n(n+1)(2n+1)]/3: Squares of first odd natural numbers: Σ(2n-1) 2 = [n(2n+1)(2n-1)]/3
- 12 min
- What Is The Sum of Squares?
- Sum of Squares Formula
- SS in Regression Analysis
The sum of squares (SS) is a statistic that measures the variability of a dataset’s observations around the mean. It’s the cumulative total of each data point’s squared difference from the mean. Larger values indicate a greater degree of dispersion. However, it is an unscaled measure that doesn’t adjust for the number of data points. Adding new dat...
The sum of squares formula is the following: Where: 1. Σ represents the sum for all observations from 1 to n. 2. n is the samplesize. 3. Xᵢ is an individual data point. 4. X̅ (pronounced “X-bar”) is the mean of the data points. The sum of squares formula provides us with a measure of variability or dispersion in a data set. The process for how to f...
In regression analysis, the sum of squares (SS) is particularly helpful because it separates variability into three types: total SS, regression SS, and error SS. After explaining them individually, I’ll show you how they work together.
In statistics : Sum of squares of n data points = ∑ ni=0 (x i - x̄) 2. In algebra : Sum of squares = a 2 + b 2 = (a + b) 2 - 2ab. Sum of squares of n natural numbers formula: 1 2 + 2 2 + 3 2 + ... + n 2 = [n (n+1) (2n+1)] / 6. Where, ∑ = represents sum. x i = each value in the set. x̄ = mean of the values.
Mar 17, 2024 · The sum of squares is a statistical measure of deviation from the mean. It is also known as variation. It is calculated by adding together the squared differences of each data point. To determine...
Jul 3, 2023 · The sum of squares is a statistical measure of variability. It indicates the dispersion of data points around the mean and how much the dependent variable deviates from the predicted values in regression analysis. We decompose variability into the sum of squares total (SST), the sum of squares regression (SSR), and the sum of squares error (SSE).
Sum of squares (SS) is a statistical tool that is used to identify the dispersion of data as well as how well the data can fit the model in regression analysis. The sum of squares got its name because it is calculated by finding the sum of the squared differences.
Jacobi's four-square theorem gives the number of ways that a number can be represented as the sum of four squares. For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function. Fermat's theorem on sums of two squares says which primes are sums of two squares.
