Comprehensive Statistics Course

Offered by DelftX

Course Description

This comprehensive Statistics course, offered by DelftX, is designed to provide a solid foundation in mathematics and statistics, crucial for success in science and engineering disciplines. It's an intermediate-level course that serves as an excellent refresher for those preparing for a master's degree, advancing their professional skills, or looking to solidify their knowledge in statistics and data analysis.

The course covers a wide range of topics, from descriptive statistics to advanced concepts like linear regression and bootstrapping. It uniquely combines theoretical knowledge with practical application using the R programming language, making it ideal for those interested in machine learning, data science, and other data-driven fields.

What Students Will Learn

  • Create and interpret numerical and graphical summaries of datasets
  • Apply various techniques to find and compare estimators for unknown parameters
  • Construct and interpret confidence intervals
  • Perform hypothesis testing in different scenarios
  • Conduct simple and multiple linear regression on quantitative and categorical variables
  • Apply resampling, bootstrapping, and non-parametric approaches in non-standard situations
  • Utilize the R software package for statistical analysis and data visualization

Prerequisites

This is a review course, so students are expected to have prior knowledge of the material covered. Basic calculus and familiarity with probability theory concepts such as expectation, variance, central limit theorem, and Bayes' theorem are required. Some experience with basic statistical concepts is also expected.

Course Coverage

  • Descriptive statistics and data visualization
  • Estimator theory and quality assessment
  • Hypothesis testing in various settings
  • Confidence interval construction and interpretation
  • Simple and multiple linear regression analysis
  • Categorical variable analysis in regression
  • Bootstrap and resampling techniques
  • Parametric and non-parametric approaches
  • Application of statistical concepts using R programming

Who This Course Is For

  • Students preparing for engineering or science master's programs
  • Professionals looking to enhance their statistical skills for career advancement
  • Data scientists and analysts seeking to refresh their knowledge
  • Anyone interested in deepening their understanding of statistics and its applications

Real-World Applications

  1. Data analysis and interpretation in various industries
  2. Informed decision-making based on statistical evidence
  3. Predictive modeling and machine learning projects
  4. Quality control and process improvement in manufacturing
  5. Market research and consumer behavior analysis
  6. Scientific research and hypothesis testing
  7. Financial forecasting and risk assessment
  8. Healthcare data analysis and epidemiological studies

Syllabus

Week 1: Descriptive statistics

  • Graphical summaries of datasets
  • Numerical summaries of datasets
  • Connection with probability theory

Week 2: Estimator theory

  • Quality of estimators
  • Methods to obtain estimators

Week 3: Hypothesis testing

  • Concepts
  • How to perform a test in various settings

Week 4: Confidence intervals (CI)

  • Motivation
  • How to construct a CI in various settings

Week 5: Linear regression

  • Simple and multiple linear regression
  • Categorical variables
  • Interpreting output

Week 6: Bootstrap and resampling

  • Parametric and non-parametric approach
  • How to deal with non-standard situations

This course offers a unique opportunity to master statistics and probability, providing a strong mathematics foundation essential for success in engineering, data science, and machine learning. By combining theoretical knowledge with practical application using R, students will develop valuable data analysis skills applicable in various professional contexts. Whether you're aiming to excel in your engineering master's program or enhance your career prospects in data-driven fields, this statistics course will equip you with the tools and knowledge needed to succeed in today's data-centric world.