# Error Term: Definition, Example, and How to Calculate With Formula

![Error Term](https://www.investopedia.com/thmb/rTjXFIgTrbGFXSiEjUlLVPeKfcY=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/ErrorTerm-FINAL-4d315aae597e449da2689c8d5e363300.png)

*— Investopedia / Jiaqi Zhou*

> **Definition**
>
> An error term is a component in a statistical model that accounts for the difference between the predicted values and the actual outcomes, representing factors not captured by the model’s independent variables.

## What Is an Error Term?

An error term shows the difference between what a model predicts and what actually happens. It exists because models can’t capture every factor that affects the outcome. Also called the residual or disturbance, it’s usually represented by symbols like _e_, _ε_, or _u_ in equations.

### Key Takeaways

*   An error term appears in a statistical model, like a regression model, to indicate the uncertainty in the model.
*   The error term is a residual variable that accounts for a lack of perfect goodness of fit.
*   Heteroskedastic refers to a condition in which the variance of the residual term, or error term, in a regression model varies widely.

## Understanding an Error Term

An error term represents the margin of error within a statistical model; it refers to the [sum of the deviations](https://www.investopedia.com/terms/s/sum-of-squares.asp) within the [regression line](https://www.investopedia.com/terms/r/regression.asp), which provides an explanation for the difference between the theoretical value of the model and the actual observed results. The regression line is [used as a point of analysis](https://www.investopedia.com/terms/s/stepwise-regression.asp) when attempting to determine the correlation between one independent variable and one dependent variable.

## Error Term Use in a Formula

An error term essentially means that the model is not completely accurate and results in differing results during real-world applications. For example, assume there is a [multiple linear regression](https://www.investopedia.com/terms/m/mlr.asp) function that takes the following form: 

﻿ $\begin{aligned} &Y = \alpha X + \beta \rho + \epsilon \\ &\textbf{where:} \\ &\alpha, \beta = \text{Constant parameters} \\ &X, \rho = \text{Independent variables} \\ &\epsilon = \text{Error term} \\ \end{aligned}$﻿

When the actual Y differs from the expected or predicted Y in the model during an empirical test, then the error term does not equal 0, which means there are other factors that influence Y.

## What Do Error Terms Tell Us?

Within a linear regression model tracking a stock’s price over time, the error term is the difference between the expected price at a particular time and the price that was actually observed. In instances where the price is exactly what was anticipated at a particular time, the price will fall on the trend line and the error term will be zero.

Points that do not fall directly on the trend line exhibit the fact that the dependent variable, in this case, the price, is influenced by more than just the independent variable, representing the passage of time. The error term stands for any influence being exerted on the price variable, such as changes in [market sentiment](https://www.investopedia.com/terms/m/marketsentiment.asp).

The two data points with the greatest distance from the trend line should be an equal distance from the trend line, representing the largest margin of error.

If a model is [heteroskedastic](https://www.investopedia.com/terms/h/heteroskedastic.asp), a common problem in interpreting statistical models correctly, it refers to a condition in which the [variance](https://www.investopedia.com/terms/v/variance.asp) of the error term in a regression model varies widely.

## Linear Regression, Error Term, and Stock Analysis

Linear regression is a form of analysis that relates to current trends experienced by a particular security or index by providing a relationship between a dependent and independent variables, such as the price of a security and the passage of time, resulting in a trend line that can be used as a [predictive model](https://www.investopedia.com/terms/p/predictive-modeling.asp).

A linear regression exhibits less delay than that experienced with a [moving average](https://www.investopedia.com/terms/m/movingaverage.asp), as the line is fit to the data points instead of based on the averages within the data. This allows the line to change more quickly and dramatically than a line based on numerical averaging of the available data points.

## The Difference Between Error Terms and Residuals

Although the error term and residual are often used synonymously, there is an important formal difference. An error term is generally unobservable and a residual is observable and calculable, making it much easier to quantify and visualize. In effect, while an error term represents the way observed data differs from the actual [population](https://www.investopedia.com/terms/p/population.asp), a residual represents the way observed data differs from [sample](https://www.investopedia.com/terms/s/sample.asp) population data.