---
title: "How I Overfit My Waistline in Python"
author: "Wade K. Copeland"
date: last-modified
date-format: "MMMM DD, YYYY"
output-file: index.html
bibliography: references.bib
format:
html:
embed-resources: true
code-overflow: wrap
page-layout: full
toc: true
toc-location: left
toc-depth: 4
toc-expand: 4
html-math-method: mathjax
code-fold: true
code-tools:
toggle: false
source: true
caption: "Source Code"
number-sections: false
appendix-style: plain
engine: knitr
knitr:
opts_knit:
root.dir: "./"
---
```{r}
#| echo: false
library("reticulate")
use_virtualenv("./.venv")
```
# Introduction
My wife and I are pursuing a mutual reduction in gravitational pull, and as a certified try-hard sweat lord, I naturally wrote a Python program to monitor our descent into svelteness.
Daily fluctuations are misleading (empirical evidence: a single urination event produced a -2 lb delta), so I employed statistical learning to reveal the true signal beneath the noise. Future weight loss now arrives with 95% confidence and 0% chill.
```{python introduction}
###########
# Imports #
###########
import pandas as pd
import numpy as np
import seaborn as sns
from numbers_parser import Document
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf
import math
import session_info
##############
# Data setup #
##############
def setup_data():
doc = Document("Waimee’s Weight.numbers")
sheets = doc.sheets
tables = sheets[0].tables
data = tables[0].rows(values_only=True)
data = pd.DataFrame(data[1:], columns=data[0])
data = pd.melt(data, id_vars='Day', var_name='Person', value_name='Weight')
data['Day'] = data['Day'].astype('int')
data['Person'] = data['Person'].astype('category')
data['Weight'] = data['Weight'].astype('float')
return data
d = setup_data()
```
# Results
```{python results}
##################################
# Linear Model to Predict Weight #
##################################
model = smf.ols('Weight ~ Day + Person + Day:Person', data = d)
# Coefficients
intercept = model.fit().params.iloc[0]
person = model.fit().params.iloc[1]
day = model.fit().params.iloc[2]
day_person = model.fit().params.iloc[3]
####################
# Weight Loss Plot #
####################
days = np.linspace(d['Day'].min(), d['Day'].max(), 100)
predicted_data = pd.DataFrame({
'Day': np.tile(days, 2),
'Person': ['Person L']*len(days) + ['Person R']*len(days)
})
predicted = model.fit().predict(predicted_data)
predicted_data['Weight'] = predicted
def weight_plot(data, pdata):
plt.figure(figsize = (10, 6))
for person in pdata['Person'].unique():
person_pred = pdata[pdata['Person'] == person]
sns.lineplot(x = 'Day', y = 'Weight', color = 'black', data = person_pred, linewidth = 2, alpha = 0.4)
sns.lineplot(x = 'Day', y = 'Weight', hue = 'Person', data = data)
plt.xlabel('Day')
plt.ylabel('Weight')
plt.legend(title='Person')
plt.grid(True)
plt.savefig('weight_fig.png')
#########################
# Expectation Functions #
#########################
def predicted_weight(model, person, day):
model_fit = model.fit()
weight = model_fit.params.iloc[0] + model_fit.params.iloc[1]*person + model_fit.params.iloc[2]*day + model_fit.params.iloc[3]*person*day
return weight
def predicted_day(model, person, weight):
model_fit = model.fit()
day = (weight - model_fit.params.iloc[0] - model_fit.params.iloc[1]*person)/(model_fit.params.iloc[2] + model_fit.params.iloc[3]*person)
return day
def delta_weight_day(model, person):
model_fit = model.fit()
dweight = model_fit.params.iloc[2] + model_fit.params.iloc[3]*person
return dweight
cruise_days = (pd.to_datetime('6-21-2026') - pd.Timestamp.now().normalize()).days
summary = {
'Expected Weight<br>Loss Per Day (lbs/day)': {
'Person R': round(delta_weight_day(model, 1), 2),
'Person L': round(delta_weight_day(model, 0), 2)
},
'Expected Weight<br>Loss Per Week (lbs/week)': {
'Person R': round(delta_weight_day(model, 1)*7, 2),
'Person L': round(delta_weight_day(model, 0)*7, 2)
},
'Weight at Time of Cruise (lbs)': {
'Person R': round(predicted_weight(model, 1, cruise_days), 2),
'Person L': round(predicted_weight(model, 0, cruise_days), 2)
},
'Days to 200 lbs': {
'Person R': math.ceil(predicted_day(model, 1, 200))-d['Day'].max(),
'Person L': math.ceil(predicted_day(model, 0, 200))-d['Day'].max()
}
}
```
```{python weight_plot}
#| echo: false
#| label: weight-fig
#| fig-cap: "Lineplot of daily weight with predicted values."
weight_plot(d, predicted_data)
```
```{python summary_stats}
#| echo: false
summary = pd.DataFrame(summary)
summary.style.format("{:.2f}")
```
# Statistical Methods {#sec-stat-methods}
Ordinary least-squares regression was used to fit the model [@fox2015applied].
```{python model_summary}
#| echo: false
############################
# Regression Model Summary #
############################
model.fit().summary()
```
<br/>
@eq-weight-model can be used to predict weight given the person and number of days since the diet started.
$$
\begin{equation}
\begin{split}
E[\text{Weight}|\text{Person}, \text{Day}] = `r round(py$intercept, 2)` + `r round(py$person, 2)`*\text{Person} + `r round(py$day, 2)`*\text{Day} + `r round(py$day_person, 2)`*\text{Person}*\text{Day} \\ \text{ where Person = 1 if Person R and 0 otherwise}
\end{split}
\end{equation}
$$ {#eq-weight-model}
@eq-day-model can be used to predict the day a given weight will be achieved by either person.
$$
\begin{equation}
\begin{split}
E[\text{Day}|\text{Weight}, \text{Person}] = \frac{\text{Weight} - `r round(py$intercept, 2)` - `r round(py$person, 2)`*\text{Person}}{`r round(py$day, 2)` + `r round(py$day_person, 2)`*\text{Person}} \\ \text{ where Person = 1 if Person R and 0 otherwise}
\end{split}
\end{equation}
$$ {#eq-day-model}
@eq-day-rate can be used to determined the expected average weight loss per day.
$$
\begin{equation}
\begin{split}
\frac{d(E[\text{Weight}|\text{Person}, \text{Day}])}{d(Day)} = `r round(py$day, 2)` + `r round(py$day_person, 2)`*\text{Person} \\ \text{ where Person = 1 if Person R and 0 otherwise}
\end{split}
\end{equation}
$$ {#eq-day-rate}
# Python Session Information
All of the files needed to reproduce these results can be downloaded from the Git repository <https://github.com/wkingc/weighme-py>.
```{python session_info}
#| echo: false
session_info.show()
```
