3.154 FAQ-968 How to determine whether the slope in a linear fit is significantly different from a specific value?

Last Update: 8/14/2018

The linear fit reports whether the fitted slope is significantly different from 0 by default. However, you may also want to compare the fitted slope with a specific value other than 0, the theoretical slope value for example. You can manually calculate it as follows:

1. Calculate the t ratio:
   \(t = \frac{b - b_0}{\sigma_b}\)
   where b is the fitted slope value, \(b_0\) can be any value you want to compare with the fitted slope, and \(\sigma_b\) is the standard error of the fitted slope, which can be found in the Parameters table of the linear fit report sheet.
2. Use TCDF function to calculate the two-tailed probability corresponding to this t ratio value:
   \(Prob = TCDF(t, df, 3)\)
   where the degrees of freedom df = the total number of points - 2, 3 means the two-tailed probability is returned.

You can run the above calculation in the Script Window (Window: Script Window).

If the returned Prob < 0.05, it means the fitted Slope is significantly different from the specific value.

Minimum Origin Version Required: Origin 2019

---

Keywords:Linear Curve Fit, linear regression, slope, significant difference, comparison, P value