Finding the Closest Match to a Theoretical Curve

[stats_student]

Hi guys, i have been tasked with matching the upper a theoretical curve (seen in the picture-blue) to the upper experimental part. So far in an attempt to do this i have tried changing a single parameter in the equation i used to generate the theoretical curve, so that the sum of the differences between each observed and theoretical value is minimized.

as an example - my calculations are as follows:

(O1-T1)^2 = x
(O2-T2)^2 = y

where O and T stand for observed and theoretical. I then have summed x & y and then in excel change my parameter in the equation until x+y is minimized.

the results i get are shown in the picture.

I'm just wondering if there is a better method at getting the upper part of my curve to match as closely as possible.
Also keep in mind I'm allowed to change any of the parameters in the equation i have used.

any advice would be greatly appreciated thanks.

 

[stats_student]

Oh also the equation i have used is also shown in the picture.

 

[stats_student]

i was thinking maybe a method where i attach weights to each point so that the upper part of the curve is matched more closely? Does a formal procedure for that exist?

 

[stats_student]

Or perhaps i could ignore the bottom part of my curve and do a least squares regression on the upper part only?
not really sure if I'm thinking about this the right way.
any input would be appreciated.

Cheers.