Correlation and Trend Analysis
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Understanding the relationship between two variables is a key part of engineering analysis. Correlation is a statistical measure that describes how closely two variables move together. For example, in many engineering systems, you might want to know if there is a relationship between temperature and pressure readings in a closed vessel. If temperature increases, does pressure also increase? Quantifying this relationship helps you make informed decisions and diagnose system behavior.
12345678910import numpy as np # Example temperature (in Celsius) and pressure (in kPa) readings from a system temperature = [20, 22, 25, 27, 30, 32, 35] pressure = [101, 104, 108, 110, 115, 118, 121] # Calculate the Pearson correlation coefficient corr_matrix = np.corrcoef(temperature, pressure) correlation_coefficient = corr_matrix[0, 1] print(f"Correlation coefficient: {correlation_coefficient:.2f}")
The output from the previous calculation gives you a correlation coefficient, which always ranges from -1 to 1. A value close to 1 means a strong positive relationship: as temperature increases, pressure tends to increase as well. If the coefficient is close to -1, it indicates a strong negative relationship: as one variable increases, the other decreases. A coefficient near 0 means there is little or no linear relationship between the variables. In the temperature and pressure example, a coefficient near 1 suggests that increases in temperature are closely linked to increases in pressure, which is consistent with the behavior of gases in closed systems.
1234567891011import matplotlib.pyplot as plt temperature = [20, 22, 25, 27, 30, 32, 35] pressure = [101, 104, 108, 110, 115, 118, 121] plt.scatter(temperature, pressure, color="blue") plt.title("Temperature vs. Pressure") plt.xlabel("Temperature (°C)") plt.ylabel("Pressure (kPa)") plt.grid(True) plt.show()
1. What does a correlation coefficient close to 1 indicate?
2. How can engineers use correlation analysis in system diagnostics?
3. Which numpy function computes the correlation coefficient?
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