First a big caveat--this procedure of using max/min slope lines is only for IB Physics. It's not used at the university level or by real physicists, because there are much more precise ways to generate estimates of uncertainty in a regression setting. For the IB Physics course, here's what you do when the raw data isn't linear: 1. find the transformation of x that creates a linear function with y, 2. propagate uncertainties through that transformation of x, 3. construct the max & min slope lines and compute the uncertainty as this video shows. For example, if your graph curves upward / looks convex, you could try creating a plot of y against x^2. If that isn't linear, you could try y against x^3. Once you get your linear function (let's say it's y = kx^3 + b), you propagate your x-axis uncertainties through the operation of raising to the power of 3. The uncertainty rules tell us that (uncty in x^3) / x^3 = 3 (uncty in x) / x. Solving for (uncty in x^3), we get (uncty in x^3) = x^3 * (uncty in x) / x. So you find your column of x values, look at the header to see what the absolute uncertainty ∆x was, and you compute 3*(∆x)/[each value of x] to get the uncertainty in each value of x^3. Now, you have a linear graph with properly scaled error bars for which you can perform this procedure. I have some videos where I go through this procedure in Excel using some sample data. It starts out with a log-log procedure you can optionally use to find the correct transformation that will linearize your data: ruclips.net/video/YZF0XjipJK4/видео.html ruclips.net/video/dcK_kS9k__E/видео.html But one caution: you don't want to just follow the linearization process blindly. It's always a better approach is to follow the guidance of physics theory. If your variables are distance d and time t, and you know from the kinematic equations that d depends on t^2, then t^2 is automatically the correct transformation to use, not t^3 or t^1.5, etc. Here's a video on that: ruclips.net/video/0HB2hCs7a3A/видео.html
Thank you for that great video! I was wondering how we would do this for a parabolic trendline?
First a big caveat--this procedure of using max/min slope lines is only for IB Physics. It's not used at the university level or by real physicists, because there are much more precise ways to generate estimates of uncertainty in a regression setting.
For the IB Physics course, here's what you do when the raw data isn't linear: 1. find the transformation of x that creates a linear function with y, 2. propagate uncertainties through that transformation of x, 3. construct the max & min slope lines and compute the uncertainty as this video shows.
For example, if your graph curves upward / looks convex, you could try creating a plot of y against x^2. If that isn't linear, you could try y against x^3. Once you get your linear function (let's say it's y = kx^3 + b), you propagate your x-axis uncertainties through the operation of raising to the power of 3. The uncertainty rules tell us that (uncty in x^3) / x^3 = 3 (uncty in x) / x. Solving for (uncty in x^3), we get (uncty in x^3) = x^3 * (uncty in x) / x. So you find your column of x values, look at the header to see what the absolute uncertainty ∆x was, and you compute 3*(∆x)/[each value of x] to get the uncertainty in each value of x^3. Now, you have a linear graph with properly scaled error bars for which you can perform this procedure.
I have some videos where I go through this procedure in Excel using some sample data. It starts out with a log-log procedure you can optionally use to find the correct transformation that will linearize your data:
ruclips.net/video/YZF0XjipJK4/видео.html
ruclips.net/video/dcK_kS9k__E/видео.html
But one caution: you don't want to just follow the linearization process blindly. It's always a better approach is to follow the guidance of physics theory. If your variables are distance d and time t, and you know from the kinematic equations that d depends on t^2, then t^2 is automatically the correct transformation to use, not t^3 or t^1.5, etc. Here's a video on that:
ruclips.net/video/0HB2hCs7a3A/видео.html
@@danielm9463 Thank you so much for the thorough explanation!
This guy is a genius !! your illustrations made it clear wow thank you.
ib written in the title like a true nerd, here to help the feeble, sleep-deprived ib students. thank you kind sir
Haha, this comment is very spot on in every way. Good luck with your classes!!!!!!
such a lifesaver
Super concise explanation. Appreciate the extra verification of the concepts I needed
same
Omg you saved my life!!! Thank you!!
Absolute Legend
AAAAHHH I LOVE YOU BROO!!
damn your explanation is very easy to understand, thank you.
Thank you, saved my life!!!
Woah thank you sooo much. Life saver!
Nice
Thank u!
thx bro