I have a set of prediction scatter data y vs x in black crosses below. 
For the prediction to be 'accurate', the points ought to fall on the 1:1 line.
I am trying to quantify a correction scheme to transform the data in order to lie on the 1:1 line. I have tried introducing error terms with simple variables but they could not give me the correct result.
For example, the trend below shows y = 0.3 x + 0.5.
A corrected trend may have the form of: y = 0.3 (x + k) + 0.5, where k is an 'error' term. I know this form is incorrect however.
Any one has any ideas how could I do this?
Thank you
Regards Ben