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Modern Regression Analysis in R

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Modern Regression Analysis in R

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Gain insight into a topic and learn the fundamentals.
4.3

37 reviews

Intermediate level

Recommended experience

Flexible schedule
5 weeks at 10 hours a week
Learn at your own pace
Build toward a degree
Gain insight into a topic and learn the fundamentals.
4.3

37 reviews

Intermediate level

Recommended experience

Flexible schedule
5 weeks at 10 hours a week
Learn at your own pace
Build toward a degree

What you'll learn

  • Articulate some recommended practices for ethical behavior and communication in statistics and data science.

  • Interpret important components of the MLR model, including the “systematic” and “random” components of the model.

  • Describe and implement testing-based procedures for model selections and select a “best” model based on a given procedure.

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Assessments

11 assignments

Taught in English

Build your subject-matter expertise

This course is part of the Statistical Modeling for Data Science Applications Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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There are 6 modules in this course

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

In this module, we will introduce the basic conceptual framework for statistical modeling in general, and for linear regression models in particular.

What's included

8 videos4 readings2 assignments2 programming assignments1 peer review1 discussion prompt1 ungraded lab

8 videos•Total 82 minutes
  • Frameworks and Goals of Statistical Modeling•15 minutes
  • The Assumption of Concept Validity•8 minutes
  • The Linear Regression Model•12 minutes
  • Matrix Representation of the Linear Regression Model•15 minutes
  • Assumptions of Linear Regression•9 minutes
  • The Appropriateness of Linear Regression•11 minutes
  • Interpreting the Linear Regression Model I•7 minutes
  • Interpreting the Linear Regression Model II•5 minutes
4 readings•Total 31 minutes
  • Course Updates and Accessibility Support•1 minute
  • Earn Academic Credit for your Work!•10 minutes
  • Course Support•10 minutes
  • Assessment Expectations•10 minutes
2 assignments•Total 60 minutes
  • Introduction to Statistical Modeling•30 minutes
  • The Linear Regression Model•30 minutes
2 programming assignments•Total 180 minutes
  • Module 1 Autograded•120 minutes
  • Optional Introduction to Jupyter and R•60 minutes
1 peer review•Total 60 minutes
  • Module 1 Peer Review Submission•60 minutes
1 discussion prompt•Total 10 minutes
  • Introduce Yourself•10 minutes
1 ungraded lab•Total 60 minutes
  • Module 1: Peer Reviewed Lab•60 minutes

In this module, we will learn how to fit linear regression models with least squares. We will also study the properties of least squares, and describe some goodness of fit metrics for linear regression models.

What's included

9 videos2 assignments1 programming assignment1 peer review1 ungraded lab

9 videos•Total 134 minutes
  • Introduction to Least Squares•12 minutes
  • Linear Algebra for Least Squares•10 minutes
  • Deriving the Least Squares Solution•20 minutes
  • Regression Modeling in R: a First Pass•20 minutes
  • Justifying Least Squares: the Gauss-Markov Theorem and Maximum Likelihood Estimation•14 minutes
  • Sums of Squares and Estimating the Error Variance•19 minutes
  • The Coefficient of Determination•9 minutes
  • The Problem of Non-identifiabiliity•7 minutes
  • Regression Modeling in R: a Second Pass•22 minutes
2 assignments•Total 60 minutes
  • Least Squares•30 minutes
  • Variability and Identifiability in Regression Models•30 minutes
1 programming assignment•Total 120 minutes
  • Module 2 Autograded Assignment•120 minutes
1 peer review•Total 60 minutes
  • Module 2 Peer Review Submission•60 minutes
1 ungraded lab•Total 120 minutes
  • Module 2 Peer Reviewed Lab•120 minutes

In this module, we will study the uses of linear regression modeling for justifying inferences from samples to populations.

What's included

8 videos1 reading2 assignments1 programming assignment2 peer reviews1 ungraded lab

8 videos•Total 121 minutes
  • Motivating Statistical Inference in the Linear Regression Context•10 minutes
  • The Sampling Distribution of the Least Squares Estimator•24 minutes
  • T-Tests for Individual Regression Parameters•14 minutes
  • T-Tests in R•20 minutes
  • Motivating the F-Test: Multiple Statistical Comparisons•8 minutes
  • The F-Test•23 minutes
  • The F-Test in R•10 minutes
  • Confidence Intervals in the Regression ContextConfidence Intervals in the Regression Context•11 minutes
1 reading•Total 30 minutes
  • Ethics in Statistical Practice and Communication: Five Recommendations•30 minutes
2 assignments•Total 60 minutes
  • Statistical Inference: Intro and T-Tests•30 minutes
  • Statistical Inference: the F-tests and Confidence Intervals•30 minutes
1 programming assignment•Total 120 minutes
  • Module 3 Autograded Assignment•120 minutes
2 peer reviews•Total 120 minutes
  • Ethics in Statistical Practice and Communication: Five Recommendations•60 minutes
  • Module 3 Peer Review Submission•60 minutes
1 ungraded lab•Total 60 minutes
  • Module 3 Peer Reviewed Lab•60 minutes

In this module, we will identify how models can predict future values, as well as construct interval estimates for those values. We will also explore the relationship between statistical modelling and causal explanations.

What's included

6 videos1 assignment1 programming assignment1 peer review1 ungraded lab

6 videos•Total 82 minutes
  • Differentiating Prediction and Explanation•12 minutes
  • Point Estimates for Prediction•11 minutes
  • Interval Estimates for Prediction•10 minutes
  • Making Predictions Using Real Data in R•19 minutes
  • When Prediction Goes Wrong•8 minutes
  • Defining Causality•22 minutes
1 assignment•Total 30 minutes
  • Prediction•30 minutes
1 programming assignment•Total 120 minutes
  • Module 4 Autograded Assignment•120 minutes
1 peer review•Total 60 minutes
  • Module 4 Peer Review Submission•60 minutes
1 ungraded lab•Total 60 minutes
  • Module 4 Peer Review Lab•60 minutes

In this module, we will learn how to diagnose issues with the fit of a linear regression model. In particular, we will use formal tests and visualizations to decide whether a linear model is appropriate for the data at hand.

What's included

6 videos2 assignments1 programming assignment1 peer review1 ungraded lab

6 videos•Total 72 minutes
  • Linear Regression Diagnostic Methods•9 minutes
  • Violations of the Linearity Assumption•13 minutes
  • Violations of the Independence Assumption•15 minutes
  • Violations of the Constant Variance Assumption•11 minutes
  • Violations of the Normality Assumption•10 minutes
  • Diagnostics in R•15 minutes
2 assignments•Total 60 minutes
  • Diagnostics I: Linearity and Independence•30 minutes
  • Diagnostics II: Constant Variance and Normality•30 minutes
1 programming assignment•Total 120 minutes
  • Module 5 Autograded Assignment•120 minutes
1 peer review•Total 60 minutes
  • Module 5 Peer Review Submission•60 minutes
1 ungraded lab•Total 120 minutes
  • Module 5 Peer Review Assignment•120 minutes

In this module, we will study methods for model selection and model improvement.. In particular, we will learn when and how to apply model selection techniques such as forward selection and backward selection, criterion-based methods, and will learn about the problem of multicollinearity (also called collinearity).

What's included

10 videos2 assignments1 programming assignment1 peer review1 ungraded lab

10 videos•Total 96 minutes
  • Motivating Model Selection Methods•10 minutes
  • Testing-Based Procedures and their Shortfalls•8 minutes
  • Criterion-Based Procedures: AIC•15 minutes
  • Criterion-Based Procedures: BIC•8 minutes
  • Criterion-Based Procedures: Adjusted R-Squared•8 minutes
  • The Mean Squared Prediction Error as a Model Selection Method •4 minutes
  • Model Selection in R•14 minutes
  • The Problem of Collinearity•8 minutes
  • Diagnosing Multicollinearity •12 minutes
  • The Problem of Multicollinearity: Solutions and R Implementation •8 minutes
2 assignments•Total 60 minutes
  • Model Selection II: Criterion-based Procedures•30 minutes
  • Multicollinearity•30 minutes
1 programming assignment•Total 180 minutes
  • Module 6 Autograded Assignment•180 minutes
1 peer review•Total 60 minutes
  • Module 6 Peer Review Submission•60 minutes
1 ungraded lab•Total 60 minutes
  • Module 6 Peer Review Lab•60 minutes

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Build toward a degree

This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

Instructor

Instructor ratings
4.4 (14 ratings)
University of Colorado Boulder
4 Courses•15,320 learners

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DK
·

Reviewed on Apr 29, 2024

A lot of work with several peer reviews, but it get you into R for Regression Analysis. Well laid out course. need knowledge of Linear algrebra for this course.

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