To change a correlation from a variable with a certain set of units, \(x\), to the same variable with a different set of units, \(x’\), you must relate those variables and substitute that relationship back into the correlation. For example, let’s say you found a helpful correlation, but it used different units than what you would like to use. The correlation is

\[y\,=\,4.6x\,+\,3\]

where \(x\) is a velocity in units of ft/min, and you would like to use \(x’\) with units of m/s. So this is the relationship:

\[x\left(\frac{ft}{min}\right)\,=\,x’\left(\frac{m}{s}\right)\left(\frac{3.785\,ft}{1\,m}\right)\left(\frac{60\,s}{1\,min}\right)\]

\[x\left(\frac{ft}{min}\right)\,=\,227.1\,x’\left(\frac{m}{s}\right)\]

Now we can substitute that back into the equation to get this:

\[y\,=\,4.6\,(227.1\,x’)\,+\,3\]

\[y\,=\,1044.7\,x’\,+\,3\]