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Exploring Temperature, Voltage, and Conductivity Data in Sheet1

Analysis the data

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The dataset from DATA 2.xlsx contains a single sheet named Sheet1. It includes measurements across three columns:

Temperature (°C): The temperature in degrees Celsius.
Voltage (V): The voltage in volts.
Conductivity (S/m): The electrical conductivity in Siemens per meter.

The data appears to be structured for analysis of how temperature and voltage affect conductivity.

Answer the research question, how do temperature and voltage affect the conductivity of a semiconductor material?

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The analysis of how temperature and voltage affect the conductivity of a semiconductor material reveals the following observations from the plotted graphs:

Temperature vs Conductivity: There is a visible trend indicating that as the temperature increases, the conductivity of the semiconductor material also increases. This suggests a positive correlation between temperature and conductivity.
Voltage vs Conductivity: Similarly, the graph shows that as the voltage increases, the conductivity of the semiconductor material increases, indicating a positive correlation between voltage and conductivity.

These findings suggest that both temperature and voltage positively affect the conductivity of a semiconductor material, with increases in either parameter leading to an increase in conductivity.

Test the null hypothesis which state that There is no significant relationship between temperature, voltage, and the conductivity of a semiconductor material.

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It seems there was an issue with the syntax used in defining the model for our hypothesis testing. The correct approach involves using the column names directly without backticks or additional functions. Let's correct this and proceed with the hypothesis testing.

from statsmodels.formula.api import ols
import statsmodels.api as sm

df = data['Sheet1']

Correctly defining the model

model = ols('Conductivity ~ Temperature + Voltage', data=df.rename(columns={'Conductivity (S/m)': 'Conductivity', 'Temperature (°C)': 'Temperature', 'Voltage (V)': 'Voltage'})).fit()

Summary of the model to check p-values

summary = model.summary()
print(summary)

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The hypothesis testing results, based on the OLS regression model, indicate that:

Temperature: The p-value associated with temperature is less than 0.05, suggesting that temperature has a statistically significant relationship with conductivity.
Voltage: Similarly, the p-value for voltage is less than 0.05, indicating that voltage also has a statistically significant relationship with conductivity.

These findings lead us to reject the null hypothesis, which stated that there is no significant relationship between temperature, voltage, and the conductivity of a semiconductor material. Instead, both temperature and voltage have significant effects on the conductivity.

Investigate the interaction effect between temperature and voltage on conductivity

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The investigation into the interaction effect between temperature and voltage on conductivity, using an OLS regression model with an interaction term, reveals that:

Temperature and Voltage Interaction: The p-value for the interaction term between temperature and voltage is less than 0.05, indicating a statistically significant interaction effect on conductivity.

This result suggests that the effect of temperature on conductivity is not constant across different levels of voltage, and vice versa. The interaction between temperature and voltage significantly influences the conductivity of a semiconductor material, beyond the individual effects of temperature and voltage.

Visualize this for me

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The 3D scatter plot visualizes the interaction effect between temperature, voltage, and conductivity in a semiconductor material. Key observations include:

Temperature and Voltage: Both factors vary along their respective axes.
Conductivity: Represented on the z-axis, showing how it changes with temperature and voltage.
Color Scale: Indicates the level of conductivity, with the color gradient providing a visual cue to the conductivity values.

This visualization underscores the significant interaction between temperature and voltage on conductivity, highlighting that the relationship is not merely additive but involves complex interplay affecting conductivity.