# Correlation between emotional support and positive response

## Description

The provided Python code illustrates the relationship between emotional support provided to students and their positive response over time. The code utilizes Gaussian functions to model the dynamics of emotional support and positive response, with adjustable parameters such as amplitude, mean time, and standard deviation. First, the code defines parameters for the Gaussian functions representing emotional support and positive response, including their amplitudes, mean times, and standard deviations. These parameters allow for customization of the shape and magnitude of the curves. Next, the code calculates the emotional support provided and positive response over a specified time range using the integrals of the respective Gaussian functions. By integrating the functions over time, the cumulative emotional support and positive response are obtained. Subsequently, the code plots the emotional support provided and positive response over time on a graph, with time on the x-axis and magnitude on the y-axis. This visualization allows for a clear understanding of how emotional support and positive response evolve over the specified time period. Finally, the code computes the correlation coefficient between emotional support and positive response, providing a quantitative measure of their relationship. The correlation coefficient indicates the strength and direction of the linear relationship between the two variables, with values closer to 1 indicating a strong positive correlation. Overall, the code facilitates the analysis of how emotional support influences students' positive response and provides insights into the nature of their relationship. By adjusting the parameters of the Gaussian functions, researchers and educators can explore different scenarios and assess the impact of emotional support on student outcomes.

## Files

## Steps to reproduce

import numpy as np import matplotlib.pyplot as plt # Define parameters for emotional support Gaussian function A_support = 1.5 # Amplitude of emotional support mu_support = 10 # Mean time for emotional support sigma_support = 2 # Standard deviation of emotional support # Define parameters for positive response Gaussian function A_response = 1 # Amplitude of positive response mu_response = 10 # Mean time for positive response (same as emotional support for simplicity) sigma_response = 2 # Standard deviation of positive response (can be adjusted) # Define the Gaussian functions for emotional support and positive response def gaussian_support(x): return A_support * np.exp(-0.5 * ((x - mu_support) / sigma_support) ** 2) def gaussian_response(x): return A_response * np.exp(-0.5 * ((x - mu_response) / sigma_response) ** 2) # Define the time range t = np.linspace(0, 20, 1000) # Time from 0 to 20 units # Calculate emotional support provided over time using the integral of the emotional support Gaussian function emotional_support = np.zeros_like(t) for i in range(len(t)): emotional_support[i] = np.trapz(gaussian_support(t[:i+1]), t[:i+1]) # Calculate positive response over time using the integral of the positive response Gaussian function positive_response = np.zeros_like(t) for i in range(len(t)): positive_response[i] = np.trapz(gaussian_response(t[:i+1]), t[:i+1]) # Calculate the correlation between emotional support provided and positive response correlation = np.corrcoef(emotional_support, positive_response)[0, 1] # Plotting emotional support provided and positive response over time plt.figure(figsize=(10, 6)) plt.plot(t, emotional_support, color='blue', label='Emotional Support') plt.plot(t, positive_response, color='red', label='Positive Response') plt.title('Emotional Support and Positive Response Over Time') plt.xlabel('Time') plt.ylabel('Magnitude') plt.legend() plt.grid(True) plt.show() # Output correlation coefficient print("Correlation between emotional support and positive response:", correlation)