Master Computational Statistics with our comprehensive PDF course, designed for engineering students across India. Aligned with advanced statistical needs for engineering applications, this course covers key concepts in computational statistics, enriched with solved MAKAUT Previous Year Questions (PYQs) from the last 5 years (2020–2024) to ensure academic excellence and practical proficiency.

Why Choose This Course?

MAKAUT-Aligned Content: Tailored to meet the needs of engineering students, with PYQs for exam preparation.
Practical Focus: Emphasis on computational techniques using statistical software (e.g., R, Python).
Comprehensive PDF Format: Self-paced learning with detailed explanations, examples, and visualizations.
Expert-Crafted: Designed by faculty with expertise in computational statistics.
Hands-On Learning: Includes coding exercises and real-world case studies.

Module-Wise Syllabus

Module 1: Conditional Distribution and Regression Models

Conditional Distribution: Understanding conditional probability distributions and their role in regression.
Relation to Regression Models: How conditional distributions underpin regression analysis, estimating expected values of dependent variables.
Parameter Estimation: Techniques for estimating regression parameters (e.g., least squares, maximum likelihood).

Module 2: Multiple Linear Regression

Standard Models: Building and interpreting multiple linear regression models.
Diagnostics: Detection of collinearity (Variance Inflation Factor), outliers (standardized residuals), non-normality (Q-Q plots), and autocorrelation (Durbin-Watson test).
Model Validation: Assessing assumptions (linearity, homoscedasticity, independence) using diagnostic plots and statistical tests.

Module 3: Multivariate Regression

Assumptions: Multivariate normality, homogeneity of variance-covariance matrices, absence of multicollinearity.
Parameter Estimation: Estimating coefficients for multiple dependent variables.
Multivariate Analysis of Variance and Covariance (MANOVA/MANCOVA): Analyzing multiple dependent variables simultaneously.

Module 4: Discriminant Analysis

Statistical Background: Principles of discriminant analysis for classification.
Linear Discriminant Function Analysis (LDA): Constructing linear discriminant functions to separate classes; Fisher’s discriminant.
Estimating Functions: Properties and computation of discriminant functions, including eigenvalue-based solutions.

Module 5: Principal Component Analysis (PCA)

Principal Components: Creating orthogonal variables to capture data variance.
Algorithm for PCA: Steps for conducting PCA, including eigenvalue decomposition.
Choosing Components: Deciding how many principal components to retain (e.g., scree plot, variance explained).
H-Plot: Visualizing principal components.

Module 6: Factor Analysis

Factor Analysis Model: Understanding latent factors and their relation to observed variables.
Extracting Common Factors: Methods like principal axis factoring and maximum likelihood.
Number of Factors: Determining factors using eigenvalue criteria and scree plots.
Transformations and Factor Scores: Rotating factors and computing scores for interpretation.

Module 7: Cluster Analysis

Introduction: Types of clustering (partitioning, hierarchical, overlapping).
Correlations and Distances: Measuring similarity/dissimilarity in data.
Clustering Methods: K-Means clustering, hierarchical clustering, profiling, and interpreting clusters.