Fun with Fitbit Math

“I wonder how many steps I need for one calorie?,” I idly thought. I have a Fitbit data, I wonder how many ways there are to approach this. Let the math geekdom commence!

Assumption: Fitbit uses a linear algorithm. You get some credit for living, and then extra credit for steps. Exercise figures in, but I’m treating that as a second order problem not in scope.
1) Do a scatter plot to confirm linear relationship. Yes, it seems pretty linear. A quick correlation on the data gives .9666, very high.
2) Keep looking at the Fitbit until I have just hit any particular calorie. Count steps until it increments again.
3) Similarly, look at the data. Find two entries with similar steps, and calculate the difference.
a. Observations 12 and 13: A difference of 16 steps was 144 calories
b. Observations 13 and 14: A difference of 52 steps was -138 calories. Uh oh.
c. Observations 20 and 21: A difference of 81 steps was ~-300 calories. Uh oh.
d. Conclusions: Maybe not so linear? This approach didn’t work at all.
4) Pick two observations that seem kinda typical. The linear equations is y=mx+b, 2 equations in 2 variables. Check results against a few other observations, see if it holds up.
5) General Linear modeling. Which here degrades to the simple case, and Excel has that built into the graphing. The equations is 0.0726x+1933.4.

Conclusion: I get 1,981 calories for just existing, and each step gets me another .7 calories. Or it takes 1,377 steps to get a hundred calories.

Maybe it’s time for Muttrox to get back to work.

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