Day 16: Propagating Uncertainty for Linear Regressions

I know I’ve been focused a lot on uncertainty lately, but I wanted to share a breakthrough that I shared with my students today. At this point in the year, students are comfortable with estimating measurement uncertainty and calculating it in a couple of ways. They are also comfortable with using the crank-three-times method to propagate uncertainty through a calculation. In previous years, this thread has unwoven once we started determining velocity from a position vs. time graph. What is the uncertainty of the slope? However, this year, I found a way to have LoggerPro calculate the uncertainty of the coefficients of the linear regression! While I had hoped this could be done from the specified error bars, I instead had to enter all trials into LoggerPro and then edit the Linear Fit Options to show the uncertainty. Now we can continue to focus on measurement uncertainty as we build our various models throughout the semester! I created some sample data to illustrate this technique with my class today:

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