Difference of Squares Formula | Regression Sum of Squares Formula

Algebra is one of the most important parts of mathematics when seen together with analysis, geometry, and the number theory. This is useful in the study of symbols or rules and their manipulation. In Algebra mathematics, we study polynomials, functions, different algebraic properties, or functions that further helps in solving tough problems.

One of the most important concepts in Maths is polynomials and their factorization. This is easy to factorize polynomial equations with algebraic formulas. Differences and sum of squares are two common concepts in maths that are helpful in factoring a Polynomial equation. When you learn quadratics, you will study the different type of polynomial equations too. In this post, we will focus on the difference of squares formula and the regression sum of squares formulas.

The difference of Squares Formula

In the case of elementary mathematics, the difference of squares is defined as the subtraction of two squares with a minus sign in between.

\[\ a^{2}-b^{2}\]

Let us check how to factorize it based on the below-given identity. This is not possible to factorize the equation ahead.

\[\ a^{2}-b^{2}=(a+b)(a-b)\;or\;(a-b)(a+b)\]

Regression Sum of Squares Formula

When residuals for the sum of squares are added together, they are termed as the regression sum of square. In mathematics, it is also named as the explained sum too. Here, is given a quick formula to calculate the regression sum of squares in mathematics.

\[\ SSR=\sum\left(\widehat{y}-\overline{y}\right)^{2}\]

Sum of Squares Formula

The sum of squares in mathematics is a statistical technique that is used in regression analysis to calculate the dispersion of multiple data points. In the case of the regression analysis, the objective is to determine how perfectly a data series will fit into a function to check how was it generated. This is the easiest way to check how well the function will fit into the equation. The sum of squares formula is given as –

\[\large a^{2}+b^{2}=\left(a+b\right)^{2}-2ab\]

The Sum of Squares Formula for N values is given as,

\[\large 1^{2}+2^{2}+3^{2}…….n^{2}=\frac{n\left(n-1\right)\left(2n-1\right)}{6}\]

The other name for this popular mathematical concept is the variation that is generally used to measure the deviation from the mean. The mean is the average of a set of numbers and the term that is used frequently throughout the series.

But calculating only a specific mean for the series is not helpful in many cases. You should also check the amount of deviation for a given set of measurements. Also, you need to check how each value is different from the mean and find some insights too how regression model was created from the values. In this way, the sum of squares formula is used to check either there is some relationship exists between two variables or not. If you are not able to explain the relationship among two variables then it will be named as the residual sum of squares.

This is the reason why the sum of squares is named as variation how can you define the variation in mathematics between independent value and the mean. To find the sum of squares for a given set of data points, you have to careful and follow the guidelines as discussed earlier. The best solution will minimize the deviation and gives you a more accurate solution.