Virhetermillä

Virhetermillä (Finnish for "error term") is a statistical concept used in regression analysis to account for the variability in data that cannot be explained by the independent variables in a model. It represents the difference between the observed values and the values predicted by the regression equation. The error term is crucial because it helps to quantify the accuracy of the model and to understand the extent to which the independent variables explain the dependent variable.

In a simple linear regression model, the error term is denoted as ε (epsilon). The model can be expressed as:

Y = β0 + β1X + ε

where Y is the dependent variable, X is the independent variable, β0 is the y-intercept, β1 is the slope of the regression line, and ε is the error term. The error term is assumed to have the following properties:

1. The expected value of the error term is zero (E(ε) = 0), meaning that errors are randomly distributed around zero.

2. The errors are uncorrelated with each other (no autocorrelation).

3. The errors have constant variance (homoscedasticity).

4. The errors are normally distributed.

The error term is essential for making inferences about the population parameters (β0 and β1) and for conducting hypothesis tests. It also helps in assessing the goodness-of-fit of the model. However, if the error term violates the assumptions mentioned above, it can lead to biased or inefficient estimates and invalid hypothesis tests. Therefore, it is important to check the assumptions of the error term when using regression analysis.