Hi duration17

Welcome to the board

According to the smiley, you don't seem to like the x^{1,2}.

Instead of a quadratic polynomial regression think of it as an OLS with 2 explaining variables. In that case you would get 2 slopes and the independent term, right?

Well, x^2 is your second explaining variable.

Now for the x^{1,2}

The function LINEST has two main parameters, the first is the Y values, and the second is a range with the values of all the explaining variables.

Assuming Y in A2:A6, with 2 explaining variables the Xs values could be B2:C6. That's what is in the example I post. I can use

In E4:

=LINEST(A2:A6,B2:C6)

However, the third column has, in fact, the square values of the second column because we are trying to explain Y with X and X^2.

It seems a bit dumb to write a third column with values that can be calculated from the second column. That's why we can use

In E3

=LINEST(A2:A6,B2:B6^{1,2})

The B2:B6^{1,2} means raise each value in B5:B6 first to the power of 1 and then to the power of 2. This calculates the values of B and C and so we don't need the column C.

This way we can calculate the OLS without writing the third column.

I'm sure this is not a good explanation but I hope it contributes to your better understanding of this OLS calculation.

Kind regards

PGC