What value is the sum of the residuals of a linear regression close to? Justify

Question 26. What value is the sum of the residuals of a linear regression close to? Justify

The sum of the residuals of a linear regression is 0. Linear regression works on the theory that the errors (residuals) are normally distributed with a mean of 0, i.e.

Here, Y is the dependent variable or target,

β is the vector of the regression coefficient,

X is the feature matrix comprising all the features as the columns,

ε is the residual term like ε ~ N(0, σ2).

So, the sum of all the residuals is the expected value of the residuals times the total no of data points. Subsequently the expectation of residuals is 0, the sum of all the residual terms is zero.

Note: N(μ,σ2) is the standard notation for a normal distribution having mean μ and standard deviation σ2.