Using the properties of the arithmetic mean for least squares interpolation

In the present paper some properties of the arithmetic mean have been employed to determine the parameters of the least squares line, plane and hyper plane, without using partial derivatives and solving the equations of the normal system. It is in fact known that when the criterion of least squares is used to identify an interpolating function, the solution to the problem is obtained via the search for the minimum of a function; therefore the use of partial derivatives becomes inevitable. Instead, the method here suggested allows the interpolating model - which is common to many economic and social subjects - to be presented to university students including those without any knowledge of partial derivatives