How to change confidence intervals using fit and Curve Fitting App?

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Hello, I have an issue fitting some data to a simple y=ax equation. The issue, I believe, is that with 95% confidence, the fit is correct, but I'd like to improve it. In the below pictures, you can see the four data points I'm trying to fit to a straight line. If I chose the starting point for a as -0.1, it says that -0.1 is good and within 95% confidence. If I set it as -0.5, the same thing happens. How can I improve this if possible?
The second and fourth data point may be bad, meaning that I'm expecting the answer to this to be closer to the -0.5.
Additionally, the data that is being plotted here, from a physical sense, should pass through 0,0.

Accepted Answer

Matt J
Matt J on 12 Apr 2022
Edited: Matt J on 12 Apr 2022
The confidence intervals are a function of the input x,y data and the model function, and nothing else. The confidence interval tightness that you can achieve depends entirely on how well the x,y data agrees with the model you've specified.
If the 2nd and 4th data points are bad, you should remove them. I do not see any indication that the curve fails to pass through (0,0).
Matt J
Matt J on 14 Apr 2022
Edited: Matt J on 14 Apr 2022
Yes, but even with analytical solvers like polyfit, it is still good to measure your data in natural units, where natural means that they aren't all super large or super small, or with orders of magnitude difference between the x and y values.

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