How to Calculate Residual Sum of Squares

Residual Sum of Squares (RSS) - Definition, Formula, Example

Definition:

Residual sum of squares (RSS) is also known as the sum of squared residuals (SSR) or sum of squared errors (SSE) of prediction. It is an amount of the difference between data and an estimation model.

Formula:

Residual Sum of Squares Formula
Where,
X,Y - set of values, α , β - constant values, n - Set value counts
Example:

Consider two population groups, where X = 1,2,3,4 and Y=4,5,6,7 , constant value α = 1, β = 2. Find the Residual Sum Of Square(RSS) values for the two population groups.

Given,

X = 1,2,3,4 Y = 4,5,6,7 α = 1 β = 2

Solution:

Substitute the given values in the formula,

Residual Sum of Squares Formula
RSS = ∑(4-(1+(2x1)))2 + (5-(1+(2x2)))2 + (6-(1+(2x3))2 + (7-(1+(2x4))2
= ∑(1)2 + (0)2 + (-1)2 + (-2)2
= 6

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