An error term is a residual variable produced by a statistical or mathematical model, arising when the model does not fully represent the actual relationship between independent and dependent variables. This error term quantifies the discrepancy in empirical analysis.
Commonly referred to as the residual, disturbance, or remainder term, it is represented by symbols like e, ε, or u in various models.
Key Insights
- The error term signifies uncertainty within a statistical model, such as a regression model.
- It accounts for the lack of perfect goodness of fit in a model.
- Heteroskedastic conditions describe periods where the variance of the error term fluctuates widely.
Understanding an Error Term
The error term indicates the margin of error within a statistical model. It reflects the total deviations from the regression line, explaining the variance between the model’s theoretical values and actual results. This line is analyzed to determine correlations between one independent variable and one dependent variable.
Error Term in a Formula
An error term signals that the model isn’t perfectly accurate, leading to variations in real-world results. Consider this multiple linear regression function:
[ Y = αX + βρ + ϵ ]
Where:
- α, β = Constant parameters
- X, ρ = Independent variables
- ϵ = Error term
If the actual Y differs from the predicted Y during empirical tests, the error term is not zero, implying other influencing factors.
What Do Error Terms Reveal?
In a stock price analysis over time, the error term is the discrepancy between the expected price and observed price. If the price matches the expectation precisely, the error term is zero and falls on the trend line.
Deviations from the trend line indicate other influences on the dependent variable (price), such as changes in market sentiment. The farthest data points from the trend line define the largest margin of error.
In a heteroskedastic model, the error term’s variance can vary significantly, posing challenges in interpreting statistical models correctly.
Linear Regression, Error Term, and Stock Analysis
Linear regression links current trends of a security or index, establishing relationships between dependent and independent variables like the security price and time. The resulting trend line serves as a predictive model.
Unlike a moving average, the linear regression line adjusts quicker and more dramatically because it fits directly to data points rather than averaging them.
Differentiating Error Terms and Residuals
While often used interchangeably, error terms and residuals differ fundamentally. Error terms are generally unobservable. Conversely, residuals can be observed and calculated, making them easier to quantify and visualize. In effect, while an error term indicates how observed data deviates from the entire population, a residual shows deviations from sample population data.
Related Terms: residuals, regression line, market sentiment, heteroskedasticity, variance.
