Probability, Statistical Inference and Regression Analysis

Overview

Welcome to Probability, Statistical Inference and Regression Analysis. This course is an introduction to statistical methods and thinking, focusing on modern applications. Some of the concepts will be familiar to those who have taken an elementary statistics course. However, some of the topics presented here extend those ideas into new and emerging applications. These contemporary applications include graphics and data visualization, big data, and newer analytical methods, such as bootstrapping. Acquiring a strong foundation in Regression Analysis is an objective of this course. There is a companion book available that was written by our instructors and would be an excellent companion guide for learners who'd like to further deepen their knowledge of these topics. Proceed to the first module for further details, and to begin learning about Descriptive Statistics.

Syllabus

Course Introduction and Descriptive Statistics

*This 4-course Specialization covers the use of statistical methods in today's business, industrial, and social environments, including several new methods and applications. Prof. Douglas Montgomery reflects: "H.G. Wells foresaw an era when the understanding of basic statistics would be as important for citizenship as the ability to read and write. Modern Statistics for Data-Driven Decision-Making teaches the basics of working with and interpreting data, skills necessary to succeed in Wells’s 'new great complex world' that we now inhabit." *In this course, learners will gain an ability to apply basic statistical methods for data description and visualization, inference, and decision-making. *In the first module, you will enter into Descriptive Statistics, and apply apply basic statistical methods for data description and visualization. We also invite you to orient yourself to the course design, read the instructor bios, and review the learning outcomes. Please begin when ready.

Probability Distributions

In Module 2, you will learn the probability foundations that support statistical modeling and data-driven decision-making. You will work with discrete and continuous probability distributions, compute probabilities and distribution summaries, and understand how probability models describe uncertainty in real-world contexts. Before starting, be sure to view the course introduction video and review the learning objectives.

Inferential Statistics

In Module 3, we explore the basic concepts of random sampling and the relationship between random sampling and inference. We also construct confidence intervals to estimate means and variances of one or two populations and hypotheses tests and confidence interval estimation on the mean of a population whose variance is known. Be sure to review the learning objectives before beginning work in this module.

Bootstrapping

In Module 4, we will review bootstrapping methods that can be used to solve a statistical problem. Be sure you review the learning objectives before beginning work in this module.

Big Data

In Module 5, we will review applications of big data in statistical methods and models. Be sure to view videos for this module, complete the readings, and any assignments. Begin by reviewing the learning objectives before beginning work in this module.

Regression Methods in Modern Statistics

Module 6 introduces core regression methods, including multiple linear regression, diagnostics, regularization, GLMs, and nonlinear regression. Assessments reinforce conceptual understanding and practical interpretation.