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