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# Fundamentals of Statistics

Philippe Rigollet, Jan-Christian Hütter, and Karene Chu

Statistics is the science of turning data into insights and ultimately decisions. Behind recent advances in machine learning, data science and artificial intelligence are fundamental statistical principles. The purpose of this class is to develop and understand these core ideas on firm mathematical grounds starting from the construction of estimators and tests, as well as an analysis of their asymptotic performance.

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Statistics is the science of turning data into insights and ultimately decisions. Behind recent advances in machine learning, data science and artificial intelligence are fundamental statistical principles. The purpose of this class is to develop and understand these core ideas on firm mathematical grounds starting from the construction of estimators and tests, as well as an analysis of their asymptotic performance.

After developing basic tools to handle parametric models, we will explore how to answer more advanced questions, such as the following:

• How suitable is a given model for a particular dataset?
• How to select variables in linear regression?
• How to model nonlinear phenomena?
• How to visualize high-dimensional data?

Taking this class will allow you to expand your statistical knowledge to not only include a list of methods, but also the mathematical principles that link them together, equipping you with the tools you need to develop new ones.

This course is part of theMITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.

## What's inside

### Learning objectives

• Construct estimators using method of moments and maximum likelihood, and decide how to choose between them
• Quantify uncertainty using confidence intervals and hypothesis testing
• Choose between different models using goodness of fit test
• Make prediction using linear, nonlinear and generalized linear models
• Perform dimension reduction using principal component analysis (pca)

## Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Delves into advanced statistical questions, such as model suitability, variable selection, and nonlinear phenomena
Taught by seasoned instructors with expertise in statistics and machine learning
Provides a solid foundation for data science and machine learning applications
Requires a strong mathematical background, making it suitable for advanced learners

## Save this course

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## Reviews summary

### Challenging but rewarding statistics course

Learners say that this 5-star rated Fundamentals of Statistics course is challenging but rewarding. Reviewers mention that the course covers theoretical and mathematical topics in depth, but this in-depth coverage means that the course is difficult. Reviewers also note that the course is very well organized and that the staff and TAs are supportive.
This course is well organized and the staff is supportive.
"It's very well organized and teached you a lot."
"The course was also perfect."
"Staff team, teach assistants and fellow students was very supportive and always gave some additional clues about existed brainsmashing topics."
This course is challenging, but rewarding.
"It's tough and rigorous."
"This is a tough course, but very rewarding."
"It is one of the hardest classes I've ever taken."
This course covers theoretical and mathematical topics in depth.
"This is a tough course, but very rewarding."
"It covers some of the basics of estimation, such as maximum likelihood, but in a depth which most courses don't take."
"This course is fantastic for a rigorous, theoretical and mathematical tour of statistics."
This course requires a significant time commitment.
"You have to reserve at least 15 h/w"
"If you don't have any backgroud in Stat, you will easily need to spend over 15 hours a week"
"The class material can be divided up to two courses easily to make the material more friendly"

## Career center

Learners who complete Fundamentals of Statistics will develop knowledge and skills that may be useful to these careers:
Data Scientist
A Data Scientist designs, collects, analyzes, and interprets data to find trends and insights that inform decision-making. Knowledge of hypothesis testing and statistical principles from the course "Fundamentals of Statistics" is essential, as they provide the foundation for understanding how to collect, analyze, and interpret data accurately. By taking this course, you'll gain a deep mastery of the mathematical grounds of statistics, enabling you to better design and execute data-driven solutions as a Data Scientist.
Statistician
A Statistician applies statistical theory and methods to a wide range of fields, such as medicine, public health, and finance. The course "Fundamentals of Statistics" covers the core ideas of statistics, including how to construct estimators, perform hypothesis testing, and analyze the asymptotic performance of statistical models. By gaining a strong foundation in these principles, you'll be well-equipped to develop and apply statistical methods for solving real-world problems as a Statistician.
Quantitative Analyst
A Quantitative Analyst (Quant) uses mathematical and statistical models to analyze financial data and make investment decisions. The course "Fundamentals of Statistics" provides a strong foundation in statistical principles, including hypothesis testing and model selection, which are essential for developing and evaluating financial models. By taking this course, you'll gain the quantitative skills necessary to succeed in a career as a Quant.
Machine Learning Engineer
A Machine Learning Engineer designs, develops, and maintains machine learning models to solve business problems. The course "Fundamentals of Statistics" covers the foundations of statistical modeling, including how to choose between different models, make predictions, and perform dimension reduction. This knowledge is crucial for understanding the principles underlying machine learning algorithms and developing effective ML solutions.
Data Analyst
A Data Analyst collects, processes, and analyzes data to extract insights and inform decision-making. The course "Fundamentals of Statistics" provides a strong foundation in statistical principles and methods, including data visualization, hypothesis testing, and model selection. By developing these skills, you'll be well-prepared to perform data analysis and communicate insights effectively as a Data Analyst.
Financial Analyst
A Financial Analyst uses financial data and statistical models to evaluate investment opportunities and make recommendations. The course "Fundamentals of Statistics" covers the basics of statistical modeling, including how to construct estimators, perform hypothesis testing, and select between different models. By gaining this knowledge, you'll be able to analyze financial data, develop investment strategies, and provide informed advice as a Financial Analyst.
Business Analyst
A Business Analyst uses data analysis and statistical methods to solve business problems and improve organizational performance. The course "Fundamentals of Statistics" provides a foundation in statistical principles and techniques, including data visualization, hypothesis testing, and model selection. With this knowledge, you'll be able to leverage data to identify opportunities, develop solutions, and make better decisions as a Business Analyst.
Market Researcher
A Market Researcher conducts research to understand consumer behavior and market trends. The course "Fundamentals of Statistics" provides a strong foundation in statistical methods and data analysis techniques. By taking this course, you'll gain the skills necessary to design and execute market research studies, analyze data, and draw meaningful conclusions, which will help you succeed as a Market Researcher.
Data Engineer
A Data Engineer designs, builds, and maintains data infrastructure and systems to support data analysis and machine learning. The course "Fundamentals of Statistics" provides a foundation in statistical principles and data analysis techniques. By taking this course, you'll gain the knowledge necessary to understand the data landscape, design efficient data pipelines, and collaborate effectively with data scientists and other stakeholders as a Data Engineer.
Software Engineer
A Software Engineer designs, develops, and maintains software applications. While not directly related to statistics, the course "Fundamentals of Statistics" can provide a valuable foundation for Software Engineers who work on data-driven applications or who need to understand statistical concepts to develop more robust and efficient software solutions.
Product Manager
A Product Manager manages the development and launch of new products or features. The course "Fundamentals of Statistics" can provide a valuable foundation for Product Managers who need to understand statistical concepts to make informed decisions about product design, pricing, and marketing.
Operations Research Analyst
An Operations Research Analyst uses mathematical and statistical models to solve complex business problems. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to develop and analyze models to optimize processes, improve efficiency, and make better decisions as an Operations Research Analyst.
Risk Analyst
A Risk Analyst identifies, assesses, and manages risks to an organization. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to analyze data, develop risk models, and make informed decisions to mitigate risks effectively as a Risk Analyst.
Actuary
An Actuary uses mathematical and statistical models to assess and manage financial risks. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to develop and analyze models to evaluate insurance risks, set premiums, and make informed decisions as an Actuary.
Epidemiologist
An Epidemiologist investigates the causes and patterns of diseases in populations. The course "Fundamentals of Statistics" provides a foundation in statistical principles and data analysis techniques. By taking this course, you'll gain the skills necessary to design and conduct epidemiological studies, analyze data, and draw meaningful conclusions to inform public health policy and practice as an Epidemiologist.

## Reading list

We've selected seven books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Fundamentals of Statistics.
Provides a broad overview of statistical learning methods, including supervised and unsupervised learning, and is commonly used as a textbook for introductory courses in machine learning and data science.
Provides a more in-depth treatment of statistical learning methods, including advanced topics such as ensemble methods, support vector machines, and deep learning.
Provides a comprehensive introduction to statistical inference, covering topics such as point estimation, hypothesis testing, and confidence intervals.
Provides a strong foundation in mathematical statistics, covering topics such as probability theory, random variables, and statistical distributions.
Provides a comprehensive overview of statistics, covering topics such as descriptive statistics, inferential statistics, and Bayesian statistics.
Provides an introduction to statistical methods commonly used in psychology, covering topics such as descriptive statistics, inferential statistics, and research design.
Provides a gentle introduction to statistics, covering topics such as descriptive statistics, inferential statistics, and probability theory.

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