Linear Regression analysis – Inner Resilience, Detachment, Equanimity, Modern Yoga, Inner Equipoise and well-being
Description
Interpreting the Graphs and Statistics: A Dive into Mathematical Portraits 1. Inner Resilience: • Graph: A sinuous wave gracefully oscillates, embodying inner resilience. It reflects the strength to endure challenges. • Statistics: The mean is around 0, indicating a balance in the sine curve. The skewness is close to 0, suggesting a symmetric distribution. The kurtosis is negative, revealing slightly flattened peaks. 2. Detachment from Outcomes: • Graph: A sharp V-shaped curve symbolises detachment, a visual detachment from predefined outcomes. • Statistics: The mean is around 0.5, the midpoint of the V. The skewness is 0, showcasing symmetry. The kurtosis is negative, emphasising the V's sharpness. 3. Embracing Equanimity: • Graph: A cos wave brings a sense of equilibrium, capturing the essence of equanimity in its rhythmic highs and lows. • Statistics: The mean hovers around 0, signifying balance. The skewness is 0, indicating symmetry. A negative kurtosis highlights a gentle peak. 4. Modern Application of Yoga: • Graph: A more intricate sin curve suggests a modern interpretation of yoga, blending complexity and balance. • Statistics: The mean aligns with 0, reflecting balance. The skewness is close to 0, showing symmetry. Negative kurtosis hints at a smoother curve. 5. Navigating Work and Life: • Graph: A straight line illustrates navigating work and life with equipoise, a visual guide for maintaining balance. • Statistics: The mean and median are linearly increasing, depicting a balanced progression. The skewness is 0, signifying symmetry. 6. Stress Reduction and Well-being: • Graph: An exponential decay curve embodies stress reduction, descending into a serene well-being space. • Statistics: The mean is around 0.5, showcasing central tendency. The skewness is negative, emphasising a longer tail on the left. Negative kurtosis denotes a flatter curve.
Files
Steps to reproduce
import numpy as np import matplotlib.pyplot as plt from scipy.stats import describe, skew, kurtosis # Create a range for the x-axis x = np.linspace(0, 1, 100) # Function to represent Inner Resilience in Action inner_resilience = np.sin(2 * np.pi * x) # Function to represent Detachment from Outcomes detachment = 1 - np.abs(2 * x - 1) # Function to represent Embracing Equanimity equanimity = np.cos(2 * np.pi * x) # Function to represent Modern Application of Yoga modern_yoga = np.sin(4 * np.pi * x) # Function to represent Navigating Work and Life inner_equipoise = 0.5 * x + 0.25 # Function to represent Stress Reduction and Well-being well_being = np.exp(-8 * (x - 0.5)**2) # List of functions and labels functions = [inner_resilience, detachment, equanimity, modern_yoga, inner_equipoise, well_being] labels = ['Inner Resilience', 'Detachment', 'Equanimity', 'Modern Yoga', 'Inner Equipoise', 'Well-being'] # Plotting and Statistical Analysis plt.figure(figsize=(14, 16)) for i in range(6): plt.subplot(3, 2, i + 1) plt.plot(x, functions[i], label=labels[i]) plt.title(labels[i]) # Statistical analysis stat_desc = describe(functions[i]) mean, std_dev, skewness, kurt = stat_desc.mean, np.sqrt(stat_desc.variance), skew(functions[i]), kurtosis(functions[i]) minimum, maximum = np.min(functions[i]), np.max(functions[i]) plt.text(0.5, 0.1, f'Mean: {mean:.2f}\nStd Dev: {std_dev:.2f}\nSkewness: {skewness:.2f}\nKurtosis: {kurt:.2f}\n' f'Min: {minimum:.2f}\nMax: {maximum:.2f}', transform=plt.gca().transAxes, fontsize=10, verticalalignment='bottom', horizontalalignment='center') plt.tight_layout() plt.show()