In which order does polyfit command display coefficients?

Hello everyone,

I have a question that arose when reading the polyfit explanation. It says: "p = polyfit(x,y,n) returns the coefficients for a polynomial p(x) of degree n that is a best fit for the data in y. The coefficients in p are in descending powers".

The following example (from the same small article), however, shows that the coefficients are ascending from p1 to pn:

p(x)=p1*xn+p2*xn−1+...+pn*x+pn+1.".

I am confused. If my polyfit output for a first degree polynomial is 1.33 and -4.5, in which order would they appear in the corresponding equation?

Thank you!

[SL: edited to remove some extraneous hyperlinks]

Answer 1

[Star Strider]

The 1.33 value is the slope, and the -4.5 value is the intercept, so they would appear as [1.33 -4.5]. , corresponding to and respectively.

I interpret the coefficients as:

[Nick Krebbers]

Thank you! So basically we insert them in the equation in the same order as they appear in the output, from leftmost to rightmost.

[Star Strider]

As always, my pleasure!

That is how I would do it, with ‘leftmost’ being the coefficient of the highest-order of the polynomial, and ‘rightmost’ being the constant (intercept) term. The polyval function interprets them this way, so it automatically produces the correct result.