I'm curious as to what methods excel uses when it calculates a polynomial
curve of best fit, i.e. if you graphed two sets of values and added a
trendline in the graph of the polynomial type, how does it determine the
constant coefficients of the function it produces?

For the equation y = a + bx + cx² + dx³ and a list of observations X
and Y it uses a multiple regression:

=LINEST(Y,X^{1,2,3})

To see the result array-enter (with ctrl+shift+enter) in a 4x1 range or
highlight the formula and press F9.

Jon H wrote:

I'm curious as to what methods excel uses when it calculates a polynomial
curve of best fit, i.e. if you graphed two sets of values and added a
trendline in the graph of the polynomial type, how does it determine the
constant coefficients of the function it produces?

The chart trendline and the worksheet functions LINEST, SLOPE, INTERCEPT, etc
all do least squares fitting

Jerry

"Jon H" wrote:

I'm curious as to what methods excel uses when it calculates a polynomial
curve of best fit, i.e. if you graphed two sets of values and added a
trendline in the graph of the polynomial type, how does it determine the
constant coefficients of the function it produces?