Testing whether the slope of a linear regression line differs from 1 (or some other value)?

Prism and InStat test whether a slope of a linear regression line differs significantly from zero. But you need to use extra steps to test whether the slope differs from some other value.

Using nonlinear regression (Prism 4 or later)

Instead of choosing linear regression, choose nonlinear regression analysis and choose to fit a straight line. The results will be the same as linear regression, but Prism gives you more choices with "nonlinear" regression.

One choice is to compare the best-fit value of any parameter to a theoretical value. Go to the Compare tab of the nonlinear regression parameters dialog, check the option to ask compare the best-fit value of a parameter to a theoretical value, and then choose Slope and enter the theoretical value (1.0).

Alternative approach: Manual calculations

Here is an alternative approach. First run linear regression. Then test whether the slope differs from a specific value manually:

Calculate a t ratio as:
   (best fit slope - hypothetical slope) / standard error of slope

The hypothetical slope is 1.0 or whatever value you want. The standard error of the slope is reported by both InStat and Prism.

Then use  GraphPad QuickCalcs to determine the two-tailed P value corresponding to that t ratio. Or use this Excel formula: =TDIST(tratio, df, 2).

The number of degrees of freedom is reported by Prism or InStat and equals number of data points minus two.

Elsewhere, we explain how to test for differences among slopes or intercepts with two or more linear regression lines.