# How to Calculate Residual Sum of Squares?

How do you find the residual sum of squares (RSS)?

## Find Minimum Residual Sum (RSS)

In statistics, Minimum Residual sum is the measurement of difference between data and an estimation model. It is otherwise called as residual sum of squares(RSS), sum of squared residuals (SSR) or the sum of squared errors of prediction. It is mainly used as an optimality criterion (i.e., measurement of fitness of data to the given hypothesis) to make parameter selection and model selection. The model better fits the data, when it has smaller the residual sum of squares; when it has greater the residual sum, the model poorly fits the data. The tutorial will teach you the ways on how to calculate the Residual sum of squares (RSS) in simple steps.

**Formula : **

Where,

X,Y - set of values,

Î± , Î² - constant values,

n - Set value counts

**Steps to Follow** :

**Step 1:**

Lets consider two population groups X and Y. The set of value of X = 1, 5, 3 and Y = 2, 6, 4. Constant value, Î± = 2, Î² = 3. Find the Residual Sum Of Square(RSS) values for the two population groups.

x = 1, 5, 3

y = 2, 6, 4

Î± = 2

Î² = 3

**Step 2: **Substitute the given values in the formula,

RSS = Î£(2- (2 + (3 x 1)))^{2 }+ (6 - (2 + (3 x 5)))^{2} + (4 - (2 + (3 x 3)))^{2}

= Î£(2-(2 + 3))^{2} + (6 -(2 +15))^{2} + (4 - (2 + 9))^{2}= Î£(2-(5))^{2} + (6 - (17))^{2} + (4-(11))^{2}

= Î£(-3)^{2} + (-11)^{2} + (-7)^{2}

= Î£(9) + (121) + (49)

RSS = 179

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