Swizzle rate versus speed for RipStik
Correlation is introduced in MS 150 Statistics using data from swizzle rates versus speed gathered in class. While the example is somewhat silly, generating the data is fun and perhaps memorable for the students. More memorable than fifty solid minutes of lecture.
I used an 800 centimeter run as I have done for the past couple of terms. 800 provides enough distance for the swizzle count to be reasonable - shorter distances would reduce the swizzle count which would inevitably increase the error in the count. A difference between two and three is a 50% difference, out at 11 and 12 the difference is under 10%.
The ground is fairly level, but there is a hint of a slope and I ride up against that small slope to avoid the acceleration of gravity.
Data, which varies term to term, is available in a spreadsheet.
The data has a positive relationship. In this course the focus remains on grasping the basic concepts around a linear regression. Even in this small data set, however, the potentially logistic nature of the data can be seen.
Desmos was used to generate the above regression. Desmos is perhaps the most powerful graphical tool for arbitrary function regressions available. When riding the board one has the distinct impression that the relationship is roughly logistic. There is a minimum speed below which one cannot easily remain balanced. There is simply a top end where the amplitude of the swizzle is too small to generate additional propulsive velocity. Using Desmos multiterm data appears to support logistic behavior.
I used an 800 centimeter run as I have done for the past couple of terms. 800 provides enough distance for the swizzle count to be reasonable - shorter distances would reduce the swizzle count which would inevitably increase the error in the count. A difference between two and three is a 50% difference, out at 11 and 12 the difference is under 10%.
The ground is fairly level, but there is a hint of a slope and I ride up against that small slope to avoid the acceleration of gravity.
Data, which varies term to term, is available in a spreadsheet.
Desmos was used to generate the above regression. Desmos is perhaps the most powerful graphical tool for arbitrary function regressions available. When riding the board one has the distinct impression that the relationship is roughly logistic. There is a minimum speed below which one cannot easily remain balanced. There is simply a top end where the amplitude of the swizzle is too small to generate additional propulsive velocity. Using Desmos multiterm data appears to support logistic behavior.
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