Final answer:
The standard deviation of the error in a regression model is known as the standard deviation of the residuals or the standard error. It quantifies the typical distance between the observed values and the predictions from the regression model.
Step-by-step explanation:
A standard deviation of the error of the regression model is called the standard deviation of the residuals or sometimes simply the standard error. The standard deviation of the residuals is a measure of how spread out the errors in the model are. In other words, it indicates the typical distance between the observed values and the regression line. This is calculated using the square root of the sum of squared errors (SSE) divided by the degrees of freedom, which is typically the number of data points minus the number of parameters estimated (often n-2, where n is the number of data points).
It's crucial to understand that variability of data and model accuracy are assessed using this statistical value. The Student's t-distribution can further elaborate on the understanding of standard deviation with regard to smaller samples or when population parameters are unknown. Lastly, sampling variability of a statistic like the mean can be described using its standard error, which is the standard deviation of the sampling distribution.