Difference between Residuals & Errors.

Source: Deep Learning on Medium

Difference between Residuals & Errors.

In statistics,

RESIDUAL ERROR/RESIDUAL:
The residual error(e) is the difference between the predicted value (ŷ) and the observed value(y).

Residual = “Observed value” — “predicted value”
e = y — ŷ

(i.e.)An entity’s value was predicted as 2.5 but the actual value of that entity was 2, then residual error,e is 2–2.5 (i.e.) -0.5.
e = 2–2.5 = -0.5

ERROR:
Whereas in case of error(E) it is the entity values deviation from the true value.
Also note that the mean value in this considered example for error is unobserved(i.e.) it may or may not exist in the population.

Error = “Observed Value” — “Unobserved Value[OR]Mean”
E=X-mean

(i.e.)The mean height value of group of persons is 20 and you have selected one among them whose height is 22, then the error is 22–20 which is 2.
E = 22–20 = 2

Note:
In case of both RESIDUAL/ERROR concepts,

We are ought to calculate the value hence “Observed Value” is the first element.