Fitting Data from a matrix to polynomial

I need help making a polynomial from given data from a matrix. Report the coefficients in the standard manner and describe/discuss how you chose the polynomial order. Also report the 95% confidence intervals for the coefficients.

0.0	                 180.48242260204557
1.0472413857496277	-2.8019794514594967E-14
1.9636664333660168	-37.722506925880054
2.9199038223613516	-5.852371530184997
4.0287872569295	        30.4136814365995
5.109651311245777	42.12479894850814
5.840958234437185	14.115802094499417
7.059020731794682	-39.236345500485974
7.9997668633757595	-83.13969153340369
8.799863970074767	-54.46835207407943
10.16543599143651	126.84527900958814

Answer 1

[Matt J]

A very relevant example:

https://www.mathworks.com/help/curvefit/fit.html#bto_zh5-3

Answer 2

[Walter Roberson]

XY = [0.0	        180.48242260204557
1.0472413857496277	-2.8019794514594967E-14
1.9636664333660168	-37.722506925880054
2.9199038223613516	-5.852371530184997
4.0287872569295	        30.4136814365995
5.109651311245777	42.12479894850814
5.840958234437185	14.115802094499417
7.059020731794682	-39.236345500485974
7.9997668633757595	-83.13969153340369
8.799863970074767	-54.46835207407943
10.16543599143651	126.84527900958814]
X = XY(:,1); Y = XY(:,2);