# What is the sum of Squares? A Comprehensive Guide

Finding the sum of squares of numbers, terms, and functions is an** **important task in** **Mathematics** **and Statistics. In Mathematics, it is called the algebraic sum of squares which is** **pretty** **simple compared to the** **statistical approach** **of finding the** **sum of squares.

To find the **sum of squares** in** **Mathematics, you only have to square all numbers separately and then add the resultant numbers to get the final answer. If you have two numbers only, you can also use a formula that you may have learned in Algebra.

is the **formula** that you can use for finding** **the sum of two numbers.

**(a + b) ^{2} = a^{2} + b^{2} + 2ab**

In case of more than **two numbers**, you have to find the square of all** **numbers separately and then add them to get the final answer**.** If you don’t know how to do so, you must read this** **guide about the sum of squares. We will** **discuss this method in detail as well as share an example for understanding.

## What is the formula for the sum of squares?

**In algebra,** there is no sum of squares formula**.** You have to square the numbers and then add their** **squares**.** But if you are dealing with this type of problem in Statistics**,** you can follow this **sum of square formula.**

** Sum of Squares = ∑ ^{n}(x_{i} - x)^{-2} **

_{ i=1}**Here,**

**represents**the ith term

- represents the
**average**of all numbers of the sequence.

## Types of the sum of squares

In Statistics and Business Mathematics,** two major types** of sum of squares are used. Here are the details about those types.

**Residual Sum of Squares:**In Statistics, the sum of squares represents the error between the regression and the data set is called the**residual sum of squares**. This type of

**Regression sum of Squares:**To show the relationship between modeled data and regression data, the sum of squares regression is used. This type of sum represents whether two values**Sum of Squares Calculator**. This tool can help you in finding**both algebraic and statistical ways.**

## Practical Example of Calculating Sum of Squares

To let you** **understand** **the algebraic sum of squares, we have solved an** **example here.

**example1**:

**Find the sum of squares of 2, 5, 8, and 11.**

**Solution**:

First of all, we have to **find the squares **of the numbers given in the question.

**Square of 2 = 4**

**Square of 5 = 25**

**Square of 8 = 64**

**Square of 11 =121**

Now, we have to** add the squares** of all numbers to get the answer for the sum of squares. ,

**Sum of squares = 4 + 25 + 64 + 121**

**= 214**

## Conclusion

By checking the above example and formula for the **Statistical sum of squares,** you may have learned about the **solution. **We hope our guide has helped you in understanding the topic of the sum of squares properly** **with this** **discussion.

But if you are unable to understand any of the** ****types of sum of squares,** you can use the** **Sum of Squares Calculator. **This online calculator** will help you in completing your work within seconds.

**FAQ**

**FAQ**

**What is the total sum of squares?**

The** reciprocal** of a **negative fraction** is the fraction that gives **“-1”** as the answer when it is** multiplied **by the original fraction.

**How to find the reciprocal of a negative fraction?**

The total** **sum of squares is the **addition of squares** of the numbers given in a data set.

**What is the purpose of the sum of squares?**

In Statistics, there are **two different types** of sum of squares mentioned below:

**Residual Sum of Squares**

**Regression Sum of Squares**

**What is the Sum of Squares Error?**

It shows how far is the **predicted value** from the mean value for a data set.

**How Does the Sum of Squares Help in Finance?**

In Finance**,** the sum of squares shows the **variation** in the **asset value**.

**How do you find the sum of squares between groups?**

We can find the sum of squares between the group by **dividing**** **the sum of squares by the degree of freedom.

**Why do we minimize the sum of squared residuals?**

We do **minimize**** **the sum of squared residual to make it more **accurate** and **suitable **for the data.

**Is the residual sum of squares a cost function?**

**Yes,** the residual sum of squares is a cost function.

**Does the perfect regression model have sum square errors?**

No, the error** **will be **“0” **in the case of a** perfect regression model.**