I'm trying to compare fits to data in a certain way. I start with the initial data and fit and compute the [itex]\chi[/itex]^2 value for example: x: 1 2 3 4 y: 2.1 3.9 6.0 10.1 I get the linear fit, [itex]\chi[/itex]^2 value and degrees of freedom=3. Now with what I'm working with, I don't actually know the values of x. The above values of x are just assumed (but the y values are known). I'm looking to reduce the [itex]\chi[/itex]^2 value so I let the fourth x value (4) equal 5 instead and then make a new linear fit with a new [itex]\chi[/itex]^2 value. It's obvious that the new [itex]\chi[/itex]^2 value will be smaller than the original but do I lose a degree of freedom by choosing the last x value to be 5 instead of assuming its 4? I want to be able to compare the [itex]\chi[/itex]^2/(degrees of freedom) value for the original case (final x=4) and the adjusted case (final x=5). I'm confused for either case. E.g. If the degrees of freedom remain the same, I can keep adding more and more points to get a better fit without any penalty. On the other hand, if the degrees of freedom are reduced, if I were to add more points, would the degrees of freedom eventually hit 0?