Transforming original data must follow the chosen axes. If a model is correct, its transformed points lie on one straight line. Two distinct points fix a candidate line; an extra point tests it. Write the transformed data pairs, calculate m=Delta Y/Delta X, then c=Y-mX. Recover the constants by matching the linear form. Use a further datum to check rather than refitting silently. For y=a+b/x, data (x,y)=(1,8),(2,5) become (1/x,y)=(1,8),(1/2,5). Gradient 6 and intercept 2 give y=2+6/x. Check: the intercept is at transformed X=0, which may not represent any finite original x. Do not call the first measured point the intercept.

Transforming original data must follow the chosen axes. If a model is correct, its transformed points lie on one straight line. Two distinct points fix a candidate line; an extra point tests it.

Write the transformed data pairs, calculate \(m=\Delta Y/\Delta X\), then \(c=Y-mX\). Recover the constants by matching the linear form. Use a further datum to check rather than refitting silently.

For \(y=a+b/x\), data \((x,y)=(1,8),(2,5)\) become \((1/x,y)=(1,8),(1/2,5)\). Gradient 6 and intercept 2 give \(y=2+6/x\).

Check: the intercept is at transformed \(X=0\), which may not represent any finite original \(x\). Do not call the first measured point the intercept.

Recovering and checking laws from data

Recovering and checking laws from data