The Comprehensive Statistics & R Programming course is a detailed, academic-focused program designed to provide learners with a deep understanding of statistical theory, methods, and practical applications. This course is ideal for students, BBA/graduate learners, and professionals aiming to master statistics, R programming, and data analysis techniques for research, academics, or professional use.

Delivered online, the program combines theoretical explanations with hands-on exercises, case studies, and real-world examples to help learners gain confidence in statistical reasoning, data analysis, and reporting. Students will explore topics ranging from basic descriptive statistics to advanced statistical theories, linear algebra, probability, and biostatistics.

What Students Will Learn

R Statistics

• Introduction to R and RStudio

• Data types and variables in R

• Vectors, matrices, arrays, lists

• Data frames

• Importing and exporting data

• Data manipulation (dplyr, tidyverse basics)

• Data visualization (ggplot2 basics)

• Descriptive statistics in R

• Hypothesis testing in R

• Regression analysis in R

BBA Statistics

• Introduction to statistics in business

• Data collection and classification

• Measures of central tendency

• Measures of dispersion

• Correlation and regression

• Index numbers

• Time series analysis

• Probability basics

• Decision making under uncertainty

Advanced Linear Algebra

• Vector spaces and subspaces

• Linear independence and basis

• Linear transformations

• Matrix algebra

• Eigenvalues and eigenvectors

• Diagonalization

• Inner product spaces

• Orthogonality

• Singular Value Decomposition

• Applications in statistics

Advanced Statistical Theory

• Random variables and distributions

• Joint and conditional distributions

• Expectation and variance

• Moment generating functions

• Estimation theory

• Maximum likelihood estimation

• Method of moments

• Sufficiency and completeness

• Consistency and efficiency

• Bayesian estimation

Biostatistics and Epidemiology

• Measures of disease frequency

• Incidence and prevalence

• Mortality and morbidity rates

• Study designs (cohort, case-control, cross-sectional)

• Risk ratio and odds ratio

• Survival analysis basics

• Logistic regression

• Clinical trials basics

Measure-Theoretic Probability

• Sigma algebra

• Measurable space

• Probability measure

• Random variables as measurable functions

• Lebesgue integration

• Convergence concepts

• Law of large numbers

• Central limit theorem

Advanced Nonparametric Statistics

• Rank-based tests

• Sign test

• Wilcoxon test

• Mann-Whitney test

• Kruskal-Wallis test

• Kolmogorov-Smirnov test

• Kernel density estimation

• Bootstrap methods

SRS (Simple Random Sampling)

• Definition of SRS

• With and without replacement

• Sampling distribution of mean

• Estimation under SRS

• Variance estimation

• Advantages and limitations

Statistical Analysis

• Data cleaning and preprocessing

• Exploratory data analysis

• Model selection

• Assumption checking

• Interpretation of results

• Reporting statistical findings

Hypothesis Testing

• Null and alternative hypothesis

• Type I and Type II errors

• Level of significance

• p-value concept

• One-tailed and two-tailed tests

• Z-test

• T-test

• Chi-square test

• ANOVA

Statistics and Probability

• Descriptive statistics

• Probability rules

• Conditional probability

• Bayes theorem

• Random variables

• Discrete and continuous distributions

• Expectation and variance

• Central limit theorem

Teaching Method

The course is conducted through interactive online sessions, combining lectures, practical exercises, and real-world examples. The methodology includes:

• Step-by-step guidance on R programming and statistical concepts
• Hands-on exercises and data analysis projects
• Case studies and application-based learning for business and research contexts
• Personalized doubt-solving and progress tracking
• Emphasis on applied statistics for academic, professional, and research purposes

Why This Course

This program offers a complete, structured curriculum spanning basic to advanced statistics, applied business analytics, R programming, and data analysis techniques. It prepares learners for academic research, business analytics, or professional roles requiring strong statistical and analytical skills.

Benefits and Outcomes

By completing this course, students will:

• Master statistics from foundational to advanced concepts
• Gain proficiency in R programming for data analysis and visualization
• Understand linear algebra, probability theory, and advanced statistical methods
• Apply statistical techniques in business, research, and biostatistics contexts
• Conduct hypothesis testing, data analysis, and report generation
• Develop confidence in interpreting and presenting statistical findings

This course equips learners with both theoretical understanding and practical skills, ensuring readiness for academic, research, and professional applications.