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The method of least squares is
widely used in practice to
establish the analytical
dependencies of functions
according to its experimental
behavior
...
xn

y

y1

y 2
...

In other words, it is necessary
to move from a table at least
approximately to a formula
that allows it to be used in
research
...


Then the analytical record of
the function is searched in the
form

y  kx  b
...


The idea of this method is
based on minimizing the
function of two arguments
k and b,

representing the sum of the
squared differences of the
table values of the original
function and its values
obtained from the formula

experimental function
values

F(k; b)  (y1  (kx1  b)) 
2

 (y 2  (kx2  b)) 
...

2

values of the function from
the proposed analytical
dependence

More briefly, this function of
two variables can be written as :
n

F(k; b )   ( y i  kx i  b )
...


On the basis of the necessary
condition for the extremum
function of two variables, we
conclude that the desired
point must be stationary, in
which the partial derivatives
are equal to zero
...

1 
; 2 
a 21 c 2
c 2 a 22

The method of least squares is
also suitable when the
experimentally obtained table
corresponds to a nonlinear
function
...


The least squares method
allows the experimentally
obtained function to be
represented by an analytical
dependence

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