A little math or some things you can do with regression equations

Given a regression equation for method comparison data, here are some simple things can one do, besides the usual. In what follows, Y is defined as the new method and X as the reference method.

If the slope is greater than 1.0 and the intercept greater than 0, Y will never equal X, when X is positive, Y will always be greater.

If the slope is less than 1.0 and the intercept less than 0, Y will never equal X, when X is positive, Y will always be less than X.

If in an Excel file, the slope is in cell A2 and the intercept in cell A3, the point where Y=X is given by the cell formula: = A3/(1-A2).

One can also prepare a table of biases for relevant regions. For example, for a sodium assay,

1.07 Slope X Y Diff. Pct. Bias
-10.2 Intercept 100 96.8 -3.2 -3.2%
145.7143 Y=X 110 107.5 -2.5 -2.3%
120 118.2 -1.8 -1.5%
130 128.9 -1.1 -0.8%
140 139.6 -0.4 -0.3%
145.7 145.7 0 0
150 150.3 0.3 0.2%
160 161 1 0.6%
170 171.7 1.7 1.0%
180 182.4 2.4 1.3%
190 193.1 3.1 1.6%
200 203.8 3.8 1.9%

 

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