Emotional State analysis with Yoga Practice
Description
Statistical analysis for the visual representation involves examining the trends and relationships within the data. Here, we're dealing with a conceptual model rather than real-world data, so the analysis is more qualitative. However, we can perform some basic analysis and provide interpretations: 1. Decay Constant (k): • The decay constant affects the rate at which emotional state decreases over time. Higher values of k will result in faster emotional decay. 2. Yoga Effect (alpha): • The yoga effect is a linear term that represents the positive impact of yoga practice on emotional well-being. A higher alpha implies a more significant positive effect of yoga. 3. Time (independent variable): • Time is the independent variable representing the duration of the emotional evolution. 4. Emotional Evolution (dependent variable): • Emotional Evolution is the dependent variable representing the emotional state over time. Analysis: • The plot shows an initial exponential decay in emotional state, representing a natural decline over time. • The positive linear term (alpha * yoga_effect * time) introduces a positive impact of yoga. As time progresses, the effect of yoga becomes more prominent, contributing to an increase in emotional well-being. • Key points (Start Yoga, Determination, Equanimity) are highlighted, emphasizing the potential positive milestones in the emotional well-being journey through yoga practice. Interpretation: • The model suggests that the emotional state naturally declines over time, but this decline is mitigated and even reversed by the positive impact of yoga. • The effectiveness of yoga is demonstrated by the increasing emotional state as time elapses, especially during key periods like the initiation of yoga practice, determination to continue, and achieving equanimity.
Files
Steps to reproduce
import numpy as np import matplotlib.pyplot as plt # Parameters k = 0.1 # decay constant alpha = 0.33 # coefficient for yoga effect time = np.linspace(0, 10, 100) # time points # Emotional evolution model (exponential decay with yoga effect) emotional_state = 1.0 # initial emotional state yoga_effect = 1 # binary variable (0 or 1) for yoga practice emotional_evolution = emotional_state * np.exp(-k * time) + alpha * yoga_effect * time # Plot emotional evolution over time plt.plot(time, emotional_evolution, label='Emotional State') plt.axhline(0, color='black', linestyle='--', label='Zero Emotional State') # Highlight key points plt.scatter([2, 5, 8], [emotional_state, 0.5 * emotional_state, 0], color='red', zorder=5) plt.text(2, emotional_state, 'Start Yoga', fontsize=10, color='red', verticalalignment='bottom') plt.text(5, 0.5 * emotional_state, 'Determination', fontsize=10, color='red', verticalalignment='bottom') plt.text(8, 0, 'Equanimity', fontsize=10, color='red', verticalalignment='bottom') # Labeling and legend plt.title('Emotional Evolution with Yoga Practice') plt.xlabel('Time') plt.ylabel('Emotional State') plt.legend() plt.grid(True) # Show the plot plt.show()