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 = a2 + b2 + 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(xi - x)-2
i=1
Here,
- represents the ith term of the sequence.
- 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 sum shows whether two variables from the data set are in a linear relationship or not.
- 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 from the dataset are connected or not. You can find the sum of squares in Statistics using different approaches and formulas. If you don’t know how to do so, you can use the Sum of Squares Calculator. This tool can help you in finding the sum of squares in 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
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.
