We saw that measuring calorie intake with a conventional calorie counter (database lookup) gives an estimate of actual calories consumed with a spread of about 18% while using Pertinacity's proxy gives a spread of about 28%. Also, both measurements are biased by about 20% due to underreporting.

Pertinacity's calorie proxy is less precise than a database lookup but not significantly so. The variability of daily calorie measurements induced by using the Pertinacity proxy is comparable to the natural variability of calorie intake. In exchange for this loss of precision we dramatically improve ease-of-use. Pertinacity is much simpler to use than a conventional calorie counting tool.

This leads naturally to the question: Can we use our proxy measurements to control our calorie intake? If we measure Pertinacity's fist-sized portions every day and adhere to the suggested limit, will our consumption of calories decrease? The following analysis suggests the answer is "Yes".

# Controlling Calories via Proxy

Data were collected from 28 Turkers on Amazon's Mechanical Turk. Two Turkers gave incorrect data, so there were N=26 usable data sets. Each consisted of seven days of daily records of food item descriptions along with calorie estimates and fist-size portion estimates.

These summary variables were calculated from the data for each of the 26 data sets:

```
F = mean of fists-sized portions consumed over the first six days
C = mean of database calories consumed over the first six days
f = number of fists-sized portions consumed on the seventh day
c = number of database calories consumed on the seventh day
```

We regress

```
(c-C) = beta1*(f-F) + eps
```

and find that beta1 = 129 Calories/fist (t-stat = 5) and correlation(f-F, c-C) = .58.

In terms of percentage changes:

```
(c/C-1) = beta2*(f/F-1) + eps
```

we find beta2 = .67 (t-stat = 5), and correlation(f/F-1, c/C-1) = .59.

In each case models regressed with constant terms showed statistically insignificant constant terms, so constants were omitted from the final models.

The first regression says that a change in consumption of one fist from the trailing 6-day average is equivalent to a change in consumption of 126 Calories from the trailing 6-day average. The second says that a 10% change in fists, f, from the trailing 6-day average, F, results in a 6.7% change in calories, c, from the trailing 6-day average, C.

In other words, changes in "fists" consumed effect changes in calories consumed. For the users in the data set above, a reduction of one fist/day in consumption would be equivalent to a reduction of 129 Calories/day.

The calorie proxy isn't as precise as a calorie database lookup (as discussed previously), and we see that imprecision in the second regression. If there were no loss of precision in the use of the proxy the second regression would give beta2 = 1.0, meaning any percentage change in the calorie proxy would give the same percentage change in database calories. The fact that beta2 = .67 means that if we set a fixed calorie reduction target we would only achieve .67 of that target if we measured with fists. In the data set above a one-fist reduction with beta2 = .67 is equivalent to 129 Calories/day. If beta2 were equal to 1.0 -- perfect precision -- a one-fist reduction would be equivalent to 195 Calories/day.

# Designed for Ease-of-Use

Pertinacity's approach is to tune the system not to a specific calorie reduction target but, rather, to an "ease-of-use target". Pertinacity is concerned with making ongoing calorie reduction achievable rather than hitting a certain target weight on a certain date. Studies show that making a calorie counting tool easier to use improves adherence and that adherence improves results. Research doesn't seem to indicate that setting a more or less aggressive weight goal for a given date has any impact on weight loss success so Pertinacity doesn't do that.

Without a weight+date goal, what matters primarily is that calorie intake over time decreases, and the results above indicate that reducing fist-sized-portion intake reduces calorie intake.

# Conclusion

Reducing calorie intake as estimated by Pertinacity's proxy -- fist-sized portions -- results in a reduction of calorie intake as measured by a calorie database.

The advantage of Pertinacity's proxy is that it is very easy to use. Ease-of-use improves adherence, and adherence improves results.