I put your data to Excel. x - analog reading, y - gate position. Made a char out of this data. Added a trend line (2nd order poly) and that's what I got: y = -7E-07x2 + 0,0092x - 6,1082. However it looks like poor fitting.
You could improve it by taking more measurements.
Regards,
Jacek
Do it right or don't do it at all.