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Quantified Nutrition: Regression and Correlation Between Calories and Weight

2025-09-15

If you love data, biohacking and nerding out, you are in for a treat!

Today, I tried to find the statistical connection between calories consumed and my body weight.

I already know Pearson's Correlation and I thought I can learn linear regression this way, which will very likely help me with my PhD.

Even though I have a big dataset of my weight, but the calories data is limited. But, still, I went ahead with the analysis.

My data
Date Calories (c) Weight (w) Weight (after 1 day) (w+1) Weight (after 2 days) (w+2)
2025-09-04 3,107 88.80 88.30 88.00
2025-09-05 1,557 88.30 88.00 88.00
2025-09-06 1,865 88.00 88.00 87.90
2025-09-07 1,881 88.00 87.90 88.05
2025-09-08 2,738 87.90 88.05 88.90
2025-09-09 2,348 88.05 88.90 88.60
2025-09-10 2,314 88.90 88.60 89.10
2025-09-11 2,110 88.60 89.10 88.60
2025-09-12 2,525 89.10 88.60 88.10
2025-09-13 2,119 88.60 88.10 88.90
2025-09-14 2,610 88.10 88.90
2025-09-15 88.90

Pearson's Correlation
Coefficient (r) Significance (p)
c, w 0.27 0.43
c, w+1 0.31 0.35
c, w+2 0.21 0.56

The r value shows how strong the relationship between the variables is (-1.00 is perfectly negative, +1.00 is perfectly positive and 0 is no relation).

Significance is the statistical significance, which refers how the probability that the variation in data is due to chance. It should be less than a threshold, 0.05 in our case.

Linear Regression
R^2 Slope Significance of slope (f)
c, w 0.071 0.000253 0.42
c, w+1 0.096 0.0003 0.35
c, w+2 0.043 0.0002 0.56

R^2 shows how well calories predict the weight.

Slope shows how much weight increases per calorie consumed.

Interpretation

The results were weak, because our dataset was very small and the number of variables are limited.

For example, I haven't yet taken into account:

  • TDEE (Total Daily Energy Expenditure) which is the number of calories burned every day
  • BMR (Basal Metabolic Rate) which is the number of calories my body burns just for survival
  • Calories burned through exercise

The graph shown in the featured image above shows the scatter plot for the data points.

Interesting thing I found

As I expected, the correlation and regression is (relatively) strongest for c vs w+1, i.e., if I consume more calories today, the next day's weight will be higher. r=0.31, p=0.35, R^2=0.096. But note that these results are still weak overall.

The slope of the regression shows that 20-30g weight increases / 100 cal consumed, which is quite off from the 12.9 fat / 100 cal, as derived from the scientific understanding that a pound of fat relates to 3500 calories.

Conclusion and Future Plans

From the perspective of statistics and research, this endeavor was not rigorous. But it was supposed to be a fun activity, which I guess it was!

To make this analysis robust, I need to collect a huge amount of data for these variables.

References:

Tools I used: