With linear regression, the distribution of slopes and intercepts will always be Gaussian, so long as you haven't violated any assumption of the analysis. If you repeated the experiment many times, you'd get different slopes and intercepts in each experiment, and these would follow a Gaussian distribution. This means that the 95% confidence intervals of best-fit values can be interpreted at face value, and that you can compare slopes (or Y-intercepts) with a t test.

With nonlinear regression, a parameter may not be Gaussian, even if you meet all the assumptions of nonlinear regression. It depends on the equation you select. There is no general way to know whether a parameter follows a Gaussian distribution or not. But it matters. If a parameter does approximate a Gaussian distribution, then you can:

	•	Accept the 95% confidence intervals at face value. There is a 95% chance that the interval contains the true value. If a parameter does not follow a Gaussian distribution, there may be less than a 95% chance that the interval contains the true value.

	•	Perform a t test to compare two treatments, either pooling several experiments or using the result of one pair of experiments. See Comparing fits to two sets of data (same equation).