Answer :
Final answer:
The average of the residuals, the differences between the observed and predicted values in a dataset, is always zero, regardless of the shape of the scatter diagram. This property derives from the method of least squares used in linear regression models.
Explanation:
In statistics, when we speak of residuals, we refer to the difference between the observed value and the predicted value for a specific observation in a dataset. When we plot the residuals in a scatter diagram, regardless of its shape, the average of the residuals is always zero. This fact, defined as a property of the residuals in linear regression models, is due to the method of least squares, which minimizes the sum of squared residuals. This in turn ensures that the sum, and consequently the average, of the residuals is zero.
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