Apprendre Multivariate Analysis

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Multivariate analysis allows you to examine the interactions among three or more variables simultaneously, offering a deeper understanding of complex data relationships that cannot be uncovered with univariate or bivariate techniques alone. By exploring how multiple features relate to each other, you can detect patterns, clusters, and dependencies that are critical for building robust models and drawing meaningful insights from your data. This approach is particularly valuable when working with real-world datasets, where variables rarely act in isolation.


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import pandas as pd

# Sample DataFrame with multiple variables
data = {
    "age": [25, 32, 47, 51, 62],
    "income": [50000, 64000, 120000, 110000, 150000],
    "score": [88, 92, 95, 70, 65],
    "spending": [200, 250, 400, 150, 100]
}
df = pd.DataFrame(data)

# Select multiple columns for multivariate analysis
selected_columns = ["age", "income", "score", "spending"]
df_selected = df[selected_columns]

print(df_selected)


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import seaborn as sns
import matplotlib.pyplot as plt

# Create a pair plot to visualize relationships among selected variables
sns.pairplot(df_selected)
plt.show()

Pair plots visualize the pairwise relationships between variables in a dataset by displaying scatter plots for every combination of features, along with their univariate distributions on the diagonal. When you look at a pair plot, pay attention to the shape and direction of the scatter plots: linear trends suggest correlation, while clusters or groupings may indicate the presence of subgroups or hidden patterns. Outliers and unusual distributions also become more apparent. By scanning the grid, you can quickly spot variables that are strongly related or those that might contribute to multicollinearity.


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# Compute the correlation matrix
corr_matrix = df_selected.corr()

# Visualize the correlation matrix as a heatmap
sns.heatmap(corr_matrix, annot=True, cmap="coolwarm")
plt.show()

A correlation heatmap provides a color-coded summary of the linear relationships between variables. Strong positive or negative values, shown by intense colors, indicate variables that move together or in opposite directions. When you see high correlations (close to 1 or -1) between two or more predictors, it suggests multicollinearity, which can affect the performance and interpretability of machine learning models. Use the heatmap to identify redundant variables and guide feature selection or engineering, ensuring your analysis and models remain robust and insightful.

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Section 1. Chapitre 23

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Section 1. Chapitre 23