3.2.4—Linearising relationships

Rewrite a nonlinear relation as Y=mX+c, then plot the transformed variables. The gradient and intercept must be converted back to the original parameters.

Choose transformations from the model, not from the data alone; label axes and preserve units. A straight plot tests compatibility with the model over the measured range.

For y=a/x+b, plotting y against 1/x gives gradient a and intercept b.

A high correlation after transformation does not prove the mechanism, and the fitted intercept may be a transformed constant.