## Error term and Residuals

Regular Contributor
Posts: 168

# Error term and Residuals

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

Posts: 2,053

## Re: Error term and Residuals

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
Regular Contributor
Posts: 168

## Re: Error term and Residuals

I understood residuals now.

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

Posts: 2,053

## Re: Error term and Residuals

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
Regular Contributor
Posts: 168

## Re: Error term and Residuals

Thanks.

Where that 'e' comes from?

Super User
Posts: 20,731

## Re: Error term and Residuals

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, $y_i$.

Posts: 2,655

## Re: Error term and Residuals

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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