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Modern Regression Analysis in R
  • Level Professional
  • Duration 45 hours
  • Course by University of Colorado Boulder
  • Offered by

About

This course will provide a set of foundational statistical modeling tools for data science. In particular, students will be introduced to methods, theory, and applications of linear statistical models, covering the topics of parameter estimation, residual diagnostics, goodness of fit, and various strategies for variable selection and model comparison. Attention will also be given to the misuse of statistical models and ethical implications of such misuse. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Logo adapted from photo by Vincent Ledvina on Unsplash

Modules

Optional Introduction to R and Jupyter

    • 1 Programming
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1 Programming

  • Optional Introduction to Jupyter and R

Introduction to Statistical Modeling

    • 2 Videos
    • 3 Readings
    • 1 Discussion
    • 1 Quiz
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1 Discussions

  • Introduce Yourself

2 Videos

  • Frameworks and Goals of Statistical Modeling
  • The Assumption of Concept Validity

3 Readings

  • Earn Academic Credit for your Work!
  • Course Support
  • Assessment Expectations

1 Quiz

  • Introduction to Statistical Modeling

The Linear Regression Model

    • 6 Videos
    • 1 Quiz
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6 Videos

  • The Linear Regression Model
  • Matrix Representation of the Linear Regression Model
  • Assumptions of Linear Regression
  • The Appropriateness of Linear Regression
  • Interpreting the Linear Regression Model I
  • Interpreting the Linear Regression Model II

1 Quiz

  • The Linear Regression Model

Assignments: Linear Regression and Standardization

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 1 Autograded

1 Peer Review

  • Module 1 Peer Review Submission

1 Labs

  • Module 1: Peer Reviewed Lab

Least Squares

    • 5 Videos
    • 1 Quiz
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5 Videos

  • Introduction to Least Squares
  • Linear Algebra for Least Squares
  • Deriving the Least Squares Solution
  • Regression Modeling in R: a First Pass
  • Justifying Least Squares: the Gauss-Markov Theorem and Maximum Likelihood Estimation

1 Quiz

  • Least Squares

Variability and Identifiability in Regression Models

    • 4 Videos
    • 1 Quiz
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4 Videos

  • Sums of Squares and Estimating the Error Variance
  • The Coefficient of Determination
  • The Problem of Non-identifiabiliity
  • Regression Modeling in R: a Second Pass

1 Quiz

  • Variability and Identifiability in Regression Models

Assignments: Least Squares, Parameter Estimation and Interpreting SLR Models

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 2 Autograded Assignment

1 Peer Review

  • Module 2 Peer Review Submission

1 Labs

  • Module 2 Peer Reviewed Lab

Statistical Inference: Introduction and t-tests

    • 4 Videos
    • 1 Quiz
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4 Videos

  • Motivating Statistical Inference in the Linear Regression Context
  • The Sampling Distribution of the Least Squares Estimator
  • T-Tests for Individual Regression Parameters
  • T-Tests in R

1 Quiz

  • Statistical Inference: Intro and T-Tests

Statistical Inference: the F-tests and Confidence Intervals

    • 4 Videos
    • 1 Quiz
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4 Videos

  • Motivating the F-Test: Multiple Statistical Comparisons
  • The F-Test
  • The F-Test in R
  • Confidence Intervals in the Regression ContextConfidence Intervals in the Regression Context

1 Quiz

  • Statistical Inference: the F-tests and Confidence Intervals

Ethics in Statistical Practice

    • 1 Readings
    • 1 PeerReview
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1 Peer Review

  • Ethics in Statistical Practice and Communication: Five Recommendations

1 Readings

  • Ethics in Statistical Practice and Communication: Five Recommendations

Assignments: Coefficient Importance and Confidence Intervals

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 3 Autograded Assignment

1 Peer Review

  • Module 3 Peer Review Submission

1 Labs

  • Module 3 Peer Reviewed Lab

Prediction

    • 5 Videos
    • 1 Quiz
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5 Videos

  • Differentiating Prediction and Explanation
  • Point Estimates for Prediction
  • Interval Estimates for Prediction
  • Making Predictions Using Real Data in R
  • When Prediction Goes Wrong

1 Quiz

  • Prediction

Explanation

    • 1 Videos
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1 Videos

  • Defining Causality

Assignments: Predictive Models, Prediction Intervals and Experimental Design

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 4 Autograded Assignment

1 Peer Review

  • Module 4 Peer Review Submission

1 Labs

  • Module 4 Peer Review Lab

Diagnostics I: Linearity and Independence

    • 3 Videos
    • 1 Quiz
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3 Videos

  • Linear Regression Diagnostic Methods
  • Violations of the Linearity Assumption
  • Violations of the Independence Assumption

1 Quiz

  • Diagnostics I: Linearity and Independence

Diagnostics II: Constant Variance and Normality

    • 3 Videos
    • 1 Quiz
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3 Videos

  • Violations of the Constant Variance Assumption
  • Violations of the Normality Assumption
  • Diagnostics in R

1 Quiz

  • Diagnostics II: Constant Variance and Normality

Assignments: Regression Assumptions and Diagnostics

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 5 Autograded Assignment

1 Peer Review

  • Module 5 Peer Review Submission

1 Labs

  • Module 5 Peer Review Assignment

Model Selection I: Testing-based Procedures

    • 2 Videos
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2 Videos

  • Motivating Model Selection Methods
  • Testing-Based Procedures and their Shortfalls

Model Selection II: Criterion-based Procedures

    • 5 Videos
    • 1 Quiz
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5 Videos

  • Criterion-Based Procedures: AIC
  • Criterion-Based Procedures: BIC
  • Criterion-Based Procedures: Adjusted R-Squared
  • The Mean Squared Prediction Error as a Model Selection Method
  • Model Selection in R

1 Quiz

  • Model Selection II: Criterion-based Procedures

Multicollinearity

    • 3 Videos
    • 1 Quiz
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3 Videos

  • The Problem of Collinearity
  • Diagnosing Multicollinearity
  • The Problem of Multicollinearity: Solutions and R Implementation

1 Quiz

  • Multicollinearity

Assignments: Model Selection, Information Criterion and Multicollinearity

    • 1 PeerReview
    • 1 Lab
    • 1 Programming
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1 Programming

  • Module 6 Autograded Assignment

1 Peer Review

  • Module 6 Peer Review Submission

1 Labs

  • Module 6 Peer Review Lab

Auto Summary

"Modern Regression Analysis in R" is a professional course focused on foundational statistical modeling tools for data science, particularly linear models. Offered by CU Boulder, this course covers parameter estimation, residual diagnostics, and model comparison, while addressing ethical implications. It is part of the MS-DS degree on Coursera, featuring interdisciplinary faculty and performance-based admissions. The course duration is approximately 2700 minutes, with starter and professional subscription options. Ideal for learners with a background in computer science, information science, mathematics, and statistics.

Brian Zaharatos
Instructor

Brian Zaharatos