Combining multiple regression formulas into one single formula

[Mayank Priyadarshi]

I am trying to devise a formula for tracheal tube depth based on weight. I have three published regression formulas from three different datasets.

1. Depth= 5 + 1*weight (based on 70 patients)
2. Depth= 4.65 + 1.5*weight (based on 38 patients)
3. Depth= 5.5 + 1.2*weight (based on 101 patients)

I do not have the original datasets for any of these formulas. Is there a way to combine these 3 formulas and have one formula instead?

[Felix Bittmann]

I can think of two ideas. Either you read all studies carefully and use the numbers provided by the study with the best quality, according to your judgement. Or you could compute the weighted average of the coefficients.

[Nick Cox]

A short answer is Not easily. If any study reports minimum and maximum observed weights it might be instructive to plot each fitted line over the observed range.

(The presumption is that each study is using the same units of measurement, although they are unstated.)

[Mayank Priyadarshi]

Thank you for the inputs. Much appreciated!