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RamKumar
Fluorite | Level 6

What is the difference between error term and residuals in modeling?

6 REPLIES 6
PaigeMiller
Diamond | Level 26

An error term exists in the model. It is a mathematical construct.

The residual is the actual value of one data point (deviation from the value predicted by the model).

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Paige Miller
RamKumar
Fluorite | Level 6

I understood residuals now.

How does an error term exists in the model? May I request you to give an simple example please.

PaigeMiller
Diamond | Level 26

A simple regression model looks like this

y = b0 + b1*X + e

e is the error term, b0 is the intercept and b1 is the slope

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Paige Miller
RamKumar
Fluorite | Level 6

Thanks.

Where that 'e' comes from?

Reeza
Super User
FYI the Stats course for SAS is free via the SAS Analytics U homepage.

From wikipedia:
http://en.wikipedia.org/wiki/Regression_analysis


Theoretical Model with e : y_i=\beta_0 +\beta_1 x_i +\varepsilon_i,\quad i=1,\dots,n.\!
Fitted model:
 \widehat{y_i} = \widehat{\beta}_0 + \widehat{\beta}_1 x_i.

The residual,  e_i = y_i - \widehat{y}_i , is the difference between the value of the dependent variable predicted by the model,  \widehat{y_i}, and the true value of the dependent variable, y_i.

SteveDenham
Jade | Level 19

I would recommend reading some good introductory regression and linear modeling texts.  You may find this one to be helpful:

Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis, by Frank Harrell, Jr.

Steve Denham

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