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## Main Question or Discussion Point

I am currently working on a gamma ray spectroscopy lab in which i have just fit a polynomial to my calibration points. The calibration points are in a relatively straight line, from x=40 to x=450, and y=34 to y=1300 for the first and last end points respectively. Where X is channel number, and Y is energy. The calibration will change Channel number to energy on the rest of my spectrum graphs.

I noticed while increasing the polynomial's degree from first, to second, to third order that the slope of the line decreased at twice the X value of the last calibration point. Taking it from the perspective of my data, the third order polynomial fit my data better when extrapolating data at twice the region i had fit my line to.

Is this because a third order is inherently a better estimate of extrapolated data because it fits a given data set more accurately? Im afraid i dont understand how increasing the degree of a line that is (supposedly) linear would increase its validity past the fit. Was this just luck?

(Equation of my line, 2.787e+ooo*Ch-5.952e-005*Ch^2, i assume the first term is the first order, and second is the second order term. i have forgotten to printout the graph with the third order fit, but it has a second order term of the same magnitude)

I noticed while increasing the polynomial's degree from first, to second, to third order that the slope of the line decreased at twice the X value of the last calibration point. Taking it from the perspective of my data, the third order polynomial fit my data better when extrapolating data at twice the region i had fit my line to.

Is this because a third order is inherently a better estimate of extrapolated data because it fits a given data set more accurately? Im afraid i dont understand how increasing the degree of a line that is (supposedly) linear would increase its validity past the fit. Was this just luck?

(Equation of my line, 2.787e+ooo*Ch-5.952e-005*Ch^2, i assume the first term is the first order, and second is the second order term. i have forgotten to printout the graph with the third order fit, but it has a second order term of the same magnitude)