Finding polynomials from a set of coordinates

[Han]

http://support.hp.com/us-en/document/c01939749

EDIT: I don't have my HP50G in front of me and the screenshots in the link above do not list polynomial fit as a choice, so the link above my not apply directly to you if you are looking for a polynomial fit. So if there is no polynomial fit option, you would need to do it by hand using the Vandermonde matrix. https://en.wikipedia.org/wiki/Polynomial_regression

EDIT #2:

[[ 8 ] [ 5 ] [ 11 ] [ 16 ] [ 18 ] [ 14]]
[ 0 4 8 12 16 20 ]
VANDERMONDE
/

returns

[[ 8 ]
[ '-439/120' ]
[ '203/192' ]
[ '-151/1536' ]
[ '13/3072' ]
[ '-3/40960' ]]

This is a list of the cefficients \( a_0, a_1, \dotsm, a_5 \) of the polynomial
\[ a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3 \cdot x^3 + a_4 \cdot x^4 + a_5 \cdot x^5 \]
That is, \( a_0 = 8 \), \( a_1 = -\frac{439}{120} \), \( a_2 = \frac{203}{192} \), \( a_3 = -\frac{151}{1536} \), \(a_4 = \frac{13}{3072} \), and \(a_5 = -\frac{3}{40960} \).