Probability, Statistical Inference and Regression Analysis
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Probability, Statistical Inference and Regression Analysis
This course is part of Modern Statistics for Data-Driven Decision-Making Specialization
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What you'll learn
Learners will apply basic statistical methods for data description and visualization, inference, and decision-making.
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January 2026
9 assignments
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There are 6 modules in this course
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.
*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 Wellsβs '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.
What's included
6 videos5 readings1 assignment
6 videosβ’Total 31 minutes
- Specialization Introductionβ’2 minutes
- Course Introductionβ’9 minutes
- Segment 1: Introduction and Understanding Variabilityβ’4 minutes
- Segment 2: Methods of Data Collection and Inferential Statisticsβ’4 minutes
- Segment 3: Hypothesis Testing and Numerical Summariesβ’3 minutes
- Segment 4: Measures of Central Tendency and Variabilityβ’10 minutes
5 readingsβ’Total 40 minutes
- Course Resources and Peer Reviewsβ’5 minutes
- Meet Your Instructorsβ’5 minutes
- Chapter 1: The Role of Statistics in Engineeringβ’10 minutes
- Introduction to Statistics and Sampling Lecture - Video Segment Overviewβ’10 minutes
- Chapter 6: Descriptive Statisticsβ’10 minutes
1 assignmentβ’Total 30 minutes
- Practice Assignment for Descriptive Statistics and Probability Distributionsβ’30 minutes
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.
What's included
11 videos3 readings
11 videosβ’Total 39 minutes
- Segment 1: Definition of Random Variables β’2 minutes
- Segment 2: Describing Data Transmission Error Over a Digital Channel β’2 minutes
- Segment 3: Cumulative Distribution Function - Discrete β’4 minutes
- Segment 4: Mean and Variance of a Discrete Random Variable β’6 minutes
- Segment 5: Common Discrete Probability Distributions β’3 minutes
- Segment 6: Binomial Distribution Example β’3 minutes
- Segment 1: Continuous Probability Distributions and Probability Density Functions β’5 minutes
- Segment 2: Cumulative Distribution Functions β’3 minutes
- Segment 3: Mean and Variance of a Continuous Random Variable β’2 minutes
- Segment 4: Normal (Gaussian) Distribution β’3 minutes
- Segment 5: Common Continuous Distributionsβ’6 minutes
3 readingsβ’Total 30 minutes
- Basic Probability, Part 1 Lecture - Video Segment Overviewβ’10 minutes
- Basic Probability, Part 2 Lecture - Video Segment Overviewβ’10 minutes
- Chapter 2: Probabilityβ’10 minutes
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.
What's included
17 videos5 readings1 assignment
17 videosβ’Total 95 minutes
- Segment 1: Introduction to Estimation of Parameters and Point Estimation β’5 minutes
- Segment 2: Central Limit Theorem and Unbiased Estimators β’5 minutes
- Segment 3: Variance of a Point Estimator and Standard Error β’5 minutes
- Segment 4: Bootstrap Standard Error and Methods of Point Estimationβ’6 minutes
- Segment 1: Introduction and Development of Confidence Intervals β’7 minutes
- Segment 2: Choice of Sample Size and One-Sided Confidence Bounds β’6 minutes
- Segment 3: Large-Sample Approximate Confidence Interval and Confidence Interval on the Mean, Variance Unknown β’5 minutes
- Segment 1: Introduction to Hypothesis Testing and Decisions in Hypothesis Testing β’5 minutes
- Segment 2: Computing the Probability of Type I and Type II Error β’3 minutes
- Segment 3: Examples and Practical Applications β’6 minutes
- Segment 4: General Procedure for Hypothesis Tests β’7 minutes
- Segment 5: Type II Error and Choice of Sample Size and Large Sample Size β’6 minutes
- Segment 6: Summary for One-Sample t-test with Example β’5 minutes
- Segment 1: Introduction, Inference, and Hypothesis Tests on the Difference in Means, Variances Knownβ’8 minutes
- Segment 2: Confidence Interval on the Difference in Means, Variances Known β’3 minutes
- Segment 3: Hypothesis Tests on the Difference in Means, Variances Unknown, and Examplesβ’12 minutes
- Segment 4: Confidence Interval on the Difference in Means, Variances Unknown, and Example: Cement Hydration β’3 minutes
5 readingsβ’Total 130 minutes
- Estimation of Parameters Lecture - Video Segment Overviewβ’10 minutes
- Confidence Intervals Lecture - Video Segment Overviewβ’10 minutes
- Hypothesis Testing Lecture - Video Segment Overviewβ’10 minutes
- Statistical Inference for Two Samples Lecture - Video Segment Overviewβ’10 minutes
- Chapters 7 - 9 of Applied Statistics and Probability for Engineersβ’90 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Basic Statisticsβ’30 minutes
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.
What's included
2 videos1 reading1 assignment
2 videosβ’Total 17 minutes
- Basic Concept of Bootstrappingβ’10 minutes
- Application of Bootstrappingβ’7 minutes
1 readingβ’Total 10 minutes
- Section 8.6 of Chapter 8: Statistical Intervals for a Single Sampleβ’10 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Bootstrappingβ’30 minutes
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.
What's included
2 videos1 assignment
2 videosβ’Total 17 minutes
- What Is Big Data?β’6 minutes
- How Big Data Impacts Statisticsβ’11 minutes
1 assignmentβ’Total 30 minutes
- Practice Quiz for Big Dataβ’30 minutes
Module 6 introduces core regression methods, including multiple linear regression, diagnostics, regularization, GLMs, and nonlinear regression. Assessments reinforce conceptual understanding and practical interpretation.
What's included
24 videos5 readings5 assignments1 peer review
24 videosβ’Total 92 minutes
- Segment 1: Intro. to Multiple Linear Regression Modelβ’2 minutes
- Segment 2: Method for Least Squares Estimation of Parametersβ’2 minutes
- Segment 3: Wire Bond Strength Example 1β’2 minutes
- Segment 4: Matrix Approach to Multiple Linear Regressionβ’3 minutes
- Segment 5: Wire Bond Strength Example 2β’6 minutes
- Segment 6: Closing: The Importance and Wide Application of Regression Analysisβ’1 minute
- Segment 1: Review of Standard Regression Assumptions and Common Problemsβ’2 minutes
- Segment 2: Solving for Unequal Variance: Tactics and Examplesβ’5 minutes
- Segment 3: Understanding Multicollinearity: Sources and Effectsβ’11 minutes
- Segment 4: Methods for Dealing with Multicollinearityβ’5 minutes
- Segment 1: Rationale for Generalized Ridge Regression, Lasso and Elastic Net Techniquesβ’4 minutes
- Segment 2: Generalized Regression Examples: Analyzing Acetylene Dataset with JMP Softwareβ’4 minutes
- Segment 3: Using Principal Component Regression to Manage Multicollinearityβ’7 minutes
- Segment 1: Introduction to Generalized Linear Modelsβ’3 minutes
- Segment 2: Applications of Binary Response Variablesβ’4 minutes
- Segment 3: Using Logistic Regression to Model Binary Response Variablesβ’3 minutes
- Segment 4: How the Generalized Linear Model Works: The Role of Link Functions β’3 minutes
- Segment 5: Generalized Linear Model Example: Cycles to Failure - Yarnβ’4 minutes
- Segment 6: Summary of Generalized Linear Model Benefitsβ’1 minute
- Segment 1: Linear Versus Nonlinear Regressionβ’3 minutes
- Segment 2: Nonlinear Least Squares and Maximum Likelihood Estimation Methodsβ’4 minutes
- Segment 3: Transformation to Linear Model Example (Puromycin Data)β’4 minutes
- Segment 4: Linearization Methodβ’4 minutes
- Segment 5: Linearization Example (Puromycin Data)β’4 minutes
5 readingsβ’Total 50 minutes
- Regression Analysis Lecture - Video Segment Overviewβ’10 minutes
- Complications to Standard Regression Lecture - Video Segment Overviewβ’10 minutes
- Generalized Regression Techniques Lecture - Video Segment Overviewβ’10 minutes
- Generalized Linear Models, Lecture - Video Segment Overviewβ’10 minutes
- Nonlinear Regression Lecture - Video Segment Overviewβ’10 minutes
5 assignmentsβ’Total 150 minutes
- Practice Quiz for Regression Analysisβ’30 minutes
- Practice Quiz for Complications to Standard Regressionβ’30 minutes
- Practice Quiz for Generalized Regression Techniquesβ’30 minutes
- Practice Quiz for Generalized Linear Modelsβ’30 minutes
- Practice Quiz for Nonlinear Regression β’30 minutes
1 peer reviewβ’Total 60 minutes
- Mini-project for Modern Statistics for Data-Driven Decision-Makingβ’60 minutes
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