Which day I lose weight

I could swear it is weekend's.
But making a 'seasonal' plot, thus aggregating all data for each weekday, showed I do not so good on weekends. Especially Sundays. I am supposed to do sport on sundays. But, hey we had really bad weather the whole July. And some social obligations too...

Is it my day?

Boxes and Wiskers Plot of weekdays: the horizontal line in the middle is the  median. Upper box border is the 75% quartile, lower border the 25% quartile,so that 50% of values are between 25-75%. Lines outside are the the next 2-98 percentiles. Dots are outliers. Forget the legend, 0.8 is only the opacity of the boxes.

So in hindsight my worst day is Sunday and my best is Wednesday. How does it relate to kcal left to base rate? How would a weekday regression look like?

A weak start
The regression tells that sunday and monday are fatty
The bigger the dots, the more calories left to base rate. 

I even cheated one sunday because of overnight stay in the mountains, including booze, I didn't record.
Disclaimer: You don't know what a mountain is, if you where not there. And I know the evidence is 'thin', five data-points per weekday is not what you should base a scientific law upon

More Quantitative Diet Analysis

Two Questions:

1. What is the correlation between calorie consumption and weight loss?
2. Is it happening the same day?

This Saturday, I skipped hiking up to the mountains to answer these naging questions my last diet analysis left over. To answer them, let me first present the data, carefully recorded over 35 days of dieting.

Weight-loss per day

Measured each morning before breakfast and after taking a crap, pardon my french.

How much did I lose on a regular day? 
Most of the time lost between  -0.07 and 0.5kg

The Percentiles are: 

Min.     1st Q. Median  Mean  3rd Q.  Max. 

-0.66kg  -0.07  0.16    0.2   0.5     1.5kg 

The 1.5 kg outlier draws the attention. Is it a measurement error?

Net caloric intake per day

This is the amount of calories I have eaten, minus the calories that I have burned doing sport.

When I say calories I mean the american metric which corresponds to the european kilo-calories (kcal).

Caloric Balance Sheet
How much calories did I take-in and consume in a day?
Most often 500 kcal to 960 kcal

  

The Percentiles are: 

Min.      1st Q  Median  Mean  3rd Q  Max. 

-1009kcal 490    660     630   960    1480 kcal 

My friend, the outlier, is here again. Seems reasonable: A day of heavy exercise and little eating... but 1.5 kg? That's a lot.

Caloric intake left to cover the daily base burn rate

Now its getting nasty. Our body consumes calories even if we lay in bed all day. This is the base rate. Whitout getting into details, it depends roughly on your body weight. When you take-in lesser calories than the base-rate (plus exercising) you lose fat. My formula for this spread goes like this:

kcal_left = base-rate - net_kcal

And the distribution of the not consumed calories is:

Distribution of calories-left
I normally underperform the base-rate by 250kcal - 730kcal.

   

   Min.   1st Q Median  Mean 3rd Q  Max. 

 -240kcal 250   520     570  730    2230kcal 

Median underperformance is 520kcal, roughly a spurned Pizza Magherita. Two times I've consumed slighty more than the base-rate. And the outlier from my sport weekend is here too!

Correlation between calories left and weight-loss

Back to question 1: What is the correlation between calorie consumption and weight loss?

Now I know that I have to maximize calories-left (to the sedentary base-rate) in order to lose weight.

What are the results of my effort?

Figuring a trend

The Linear regression line in blue 

shows there is a positive correlation
between calories-left and  weight loss.
The border of the darker region
is the mean deviation oft the data 

from the regression line,
a.k.a. the standard error.

If you are a genius you certainly have noticed that the outlier is away. It would have greatly influenced the regression and I felt that I want to answer what happened in normal days. Also the correlation is not high (R^2 = 0.3541857), there are other effects that influence the variables a lot and it's clear that grand part of them are measurement errors.

Coefficients of the regression line are:

(Intercept)   kCal_Left  

 0.1174047    0.0001555  

Basically this is the linear function:  

weightLoss = 0.1174047 +  0.0001555 * kCal_Left

For the median calorie underperformance of 520 kcal this means:

520 kcal/day * 0.0001555 kg/kcal + 0.1174 kg/day ~=  0.2 kg/day

Not bad at all, and its supported by the fact that really I lost 7kg in 34days. 7/34 = 0.20!

Do I lose weight the same day that I 'starve'?

Question 2 is remaining: Is it happening the same day?

Short answer: Yes. Long answer: Yes, but there might be a lag and prolonged effect for sport activities. The evidence in a picture:

Direct impact of 'fasting'
Size of points representing calories left to base-rate
The higher the line, the greater the weight-loss.
A calorie point sits on the weight-loss recorded the morning after.
That is: the loss-spike is caused by the calorie point it carries.

Often a bigger point sits on a higher spike, which leads to the satisfactory conclusion that indeed you lose the kilos the same day as you restrict your calorie intake. The big outlier we saw already before has a different behavior. Here, the big balls hang relatively low. Does sport have a weight loss lag? The mythical regeneration phase?

The days my sport activity burned more than 1000kcal: 

Day 12: 1587 kcal

Day 13: 1946 kcal

Day 29: 1099 kcal

This big outlier on day 12 and 13 could cause a after-burner effect, but the evidence is thin. 

More data needed!

Exponentially Smoothed Diet

Body weight prediction based on irregular measurements over five weeks.
Green is the predicted path in the next ten days.

Exponential smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an orderly, but noisy, process. Whereas in the simple moving average the past observations are weighted equally, exponential smoothing assigns exponentially decreasing weights over time.
[http://en.wikipedia.org/wiki/Exponential_smoothing]


I applied Exponential smoothing to the time series I obtained from my livestrong.com recordings. Of course I have the highest motivation to beware this noble technique from being wrong.
Find all the R code and data below.

Lies, Damn Lies and Diets

The simplest diet that works is to eat not more calories than you spend. Each day. I experimented with livestrong's myplate, a slick calorie counter.

You enter the food that you ate - "penne alla arrabiata - 100g". You enter the exercise or tasks - "computer work - 480 min" and you can instantly figure out your remaining calorie budget.
It's addicting!
Furthermore it's an effective example how a quantitative approach resolves a problem.

My strongest believe is that one should pay more attention to the genuine scientific question: "How much it is?" than to the genuine philosophical question: "What is it?". Size does matter. All diets are deeply 'philosophical' in this sense, they try to answer the question of what to eat instead of how much. Contrary to this approach you have to start with the amount of calories first, and then - in order to eat enough without spending too much of your calorie budget - you learn to choose food that is calorie-cheap. You eat the vegetable dish and not the pizza. When having a calorie rich plate, you simply eat less. Don't be afraid of throwing half of a Magnum Dark Chocolate Icecream away.

Do you see how big the correlation coefficient R must be here? Linear weight loss, sans famine.

Italy's self-financed debt?

If national debt is financed by its own households, according to common wisdom the exposure is not problematic. Italy has traditionally a high saving rate, and the national banks advertise government bonds appealingly.
Probably a good share of household savings go into BOT, BCT etc.
But the saving rate has diminished  from >16% to 7.4% in the last twenty years.
When experts bring up the high saving rates argument, I can't trust them.

http://www.gfmag.com/tools/global-database/economic-data/10396-household-saving-rates.html#axzz1RpkjkzTb