Multivariate Non-Graphical Exploratory Data Analysis (EDA) :

Multivariate Non-Graphical Exploratory Data Analysis (EDA) :

Multivariate Non-Graphical EDA focuses on analyzing relationships among two or more variables using numerical/statistical methods, without using plots or charts.
It is a critical step in Data Science, AI & ML, especially before modelling.

1️⃣ What is Multivariate Data?

Multivariate data involves more than one variable measured on each observation.

Example:

Student Maths Science English A 80 75 70 B 90 85 88

Here, 3 variables are analyzed together → Multivariate data

What is Multivariate Non-Graphical EDA?

Multivariate Non-Graphical Exploratory Data Analysis (EDA) is the process of analyzing two or more variables together using numerical and statistical methods, without using graphs or plots, in order to understand relationships, dependencies, and structure within the data.

🔍 Simple Definition

Multivariate Non-Graphical EDA examines how multiple variables interact with each other using numbers and statistical measures instead of visualizations.

🧠 Breakdown of the Term

Multivariate → More than one variableNon-Graphical → No charts (no scatter plots, heatmaps, etc.)EDA → Exploring data to understand patterns before modeling

📌 Example

A dataset with:

AgeIncomeEducation levelSpending score

Analyzing how income and education together affect spending using correlation or covariance values is multivariate non-graphical EDA.

🧮 Common Techniques Used

CovarianceCorrelationCovariance MatrixCorrelation MatrixCross-tabulation (for categorical variables)Multidisciplinary checksPCA (numerical results like eigenvalues)

🎯 Purpose

Understand relationships between variablesDetect strong or weak associationsIdentify redundant featuresPrepare data for Machine Learning models

📘 One-Line Definition (Exam-Ready)

Multivariate Non-Graphical EDA is the statistical analysis of relationships among multiple variables using numerical methods without graphical visualization.

2️⃣ What is Multivariate Non-Graphical EDA?

🔹 It is the numerical examination of relationships and dependencies between multiple variables
🔹 Uses statistical summaries, matrices, and numerical measures
🔹 Helps identify patterns, strength of relationships, and structure in data

📌 No charts like scatter plots, heatmaps, etc.

3️⃣ Why Multivariate Non-Graphical EDA is Important?

✔ Understand relationships between features
✔ Detect multicollinearity
✔ Identify important predictors
✔ Improve feature selection
✔ Essential for regression, classification & clustering

4️⃣ Types of Multivariate Non-Graphical EDA Techniques

🔹 1. Covariance

Definition:

Covariance measures how two variables change together.

Formula:

Cov(X,Y)=1n−1∑(Xi−Xˉ)(Yi−Yˉ)Cov(X,Y) = \frac{1}{n-1}\sum (X_i - \bar X)(Y_i - \bar Y)Cov(X,Y)=n−11​∑(Xi​−Xˉ)(Yi​−Yˉ)

Interpretation:

CovarianceMeaningPositiveVariables increase togetherNegativeOne increases, other decreasesZeroNo linear relationship

⚠ Covariance does not show strength clearly due to units.

🔹 2. Covariance Matrix

A matrix showing covariance between all variable pairs.

Example:

XYZXVar(X)Cov(X,Y)Cov(X,Z)YCov(Y,X)Var(Y)Cov(Y,Z)ZCov(Z,X)Cov(Z,Y)Var(Z)

📌 Used in PCA, ML pre-processing

🔹 3. Correlation

Definition:

Correlation measures strength and direction of linear relationship.

Formula:

r=Cov(X,Y)σXσYr = \frac{Cov(X,Y)}{\sigma_X \sigma_Y}r=σX​σY​Cov(X,Y)​

Range:

ValueInterpretation+1Perfect positive0No relationship-1Perfect negative

✔ Unit-free
✔ Easy to interpret

🔹 4. Correlation Matrix

A table of correlations among all variables.

📌 Helps detect:

Redundant featuresMulti collinearityFeature importance

🔹 5. Multiple Summary Statistics

Used to compare variables together:MeasureMeaningMean VectorAverage of all variablesVarianceSpread of each variableStd DeviationConsistencySkewnessAsymmetryKurtosisTail behavior

🔹 6. Cross Tabulation (Contingency Table)

Used when variables are categorical.

Example:

GenderPassFailMale4010Female455

📌 Helps analyze association between categories

🔹 7. Multicollinearity Analysis

Occurs when independent variables are highly correlated.

Problems:

❌ Redundant features
❌ Unstable ML models

Detection:

✔ High correlation coefficients
✔ Variance Inflation Factor (VIF)

🔹 8. Principal Component Analysis (PCA) – (Numerical Aspect)

PCA reduces multiple variables into fewer components using variance and covariance values.

📌 Non-graphical part includes:

Eigenvalues Explained variance ratio Component loadings

5️⃣ Multivariate Non-Graphical vs Graphical EDA

AspectNon-GraphicalGraphicalOutputNumbersPlotsAccuracyHighVisual intuitionComputationFastInterpretativeUse CaseML prepPattern spotting

6️⃣ Real-World Example (Data Science)

📌 House Price Prediction
Variables:

AreaBedroomsLocationPrice

Multivariate Non-Graphical EDA:
✔ Correlation between area & price
✔ Covariance matrix
✔ PCA to reduce dimensions
✔ Detect redundant features

7️⃣ Summary

✅ Multivariate Non-Graphical EDA analyzes relationships among multiple variables using statistics
✅ Uses covariance, correlation, matrices, PCA, cross-tabs
✅ Essential before ML modeling
✅ Improves accuracy, interpretability, and efficiency

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