Hi - I always had little patience for math. Can anyone who is good at math/calculus advise on calculating appropriate trend lines? Exponential decay, linear etc.

I understand the basic formula for exponential decay is y = a(1 - r)x, but what if the rate of change is not constant or in one direction - or +?

Any suggested formula for my data so far -- which goes up and down?

Pre TSM: 63
W1: 22
W2: 34
W3: 46.5
W4: 50
W5: 38.5
W6: 35.5
W7: 39
W8: 33.5
W9: 28.5
W10: 23
W11: 16.5
W12: 19
W13: 17

Thanks...I hope any discussion here will also be useful to others looking at charting trend lines.

Merlot, possible fit scenarios for the exponential decay would be:

1. Single two-parameters exponent: y = A*exp(-b*x) where "exp(-b*x)" stands for the constant e to the power of "-b*x". This describes steady decay from a maximal starting point where y=A to essentially zero with a rate constant of the decay equal to b. Rate constant has a physical time meaning: the amplitude "y" drops by 2.72 times over period of 1/b. E.g., in my weekly fit, b=0.3 which means that my consumption is dropping 2.7 fold over approximately 3.3 weeks.

2. The decay straight to zero is a wrong fit for those trending to a moderation instead of abstinence. In this case the more appropriate exponential function would be three-parameters: y = A0+A*exp(-b*x).
It's the same as above except that decay stabilized on a level of A0, never reaching zero. E.g., in my weekly fit it is now 13.8 units.

3. More complex (and probably esoteric) case would be described by a double exponential decay where there are in total five parameters: y = A0+A1*exp(-b*x)+A2*exp(-c*x). This would describe what probably happened in my case: first very quick decay down to the level of A0+A2 that happens with a rate constant b followed by a slower decay to a baseline A0 with a rate constant of c.

#3 requires much more data and much more precise data to give a meaningful fit that is for sure different from #2. This is rarely the case and that is why I settled for a single exponent decaying to a non-zero baseline. Still, to give you an idea how it looks, here are the parameters for the fit to my weekly data:
A0=13.02
A1=33.24
b=2.51
A2=31.76
c=0.16
So if this trend is solid and continues, the inference is that before TSM my consumption was A0+A1+A2=78.02, it dropped down to 48.9 over period of 1/b=0.4 weeks, eventually reached a new baseline of A0+A2=44.8 and decayed from there to 13.02 per week with a rate of 2.7-fold every 1/c=6.25 weeks.

Your data don't yet show a trend to any definite function and, in particular, that 22 units dip at first week throws off the fits. Formal fit to a single exponent down to zero says that you started with A=49.6 units per week and it decays to zero 2.7-fold every 15 weeks (but this is not a good fit and the numbers need to be taken with a pound of salt). You are experiencing a steady decline and that's all that really matters!

Wow, thanks for all of that Nutella. It appears it is too early for me to use an exponential formula. Once I have a whole lot more data I'll revisit those options. Perhaps a 4 or 5 week moving average trend line would work with the first data point using pre-TSM units and then adding and subtracting a week.