Modern Regression Analysis in R

Modern Regression Analysis in R

This course is part of Statistical Modeling for Data Science Applications Specialization

Instructor: Brian Zaharatos

8,606 already enrolled

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6 modules

Gain insight into a topic and learn the fundamentals.

36 reviews

Intermediate level

Recommended experience

Flexible schedule

5 weeks at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

6 modules

Gain insight into a topic and learn the fundamentals.

36 reviews

Intermediate level

Recommended experience

Flexible schedule

5 weeks at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

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.

Skills you'll gain

Tools you'll learn

R Programming

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

2 quizzes, 9 assignments

Taught in English

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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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Earn a shareable career certificate

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 readings1 quiz1 assignment2 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

1 quiz Total 30 minutes

The Linear Regression Model 30 minutes

1 assignment Total 30 minutes

Introduction to Statistical Modeling 30 minutes

2 programming assignments Total 180 minutes

Optional Introduction to Jupyter and R 60 minutes
Module 1 Autograded 120 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 videos1 quiz1 assignment1 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

1 quiz Total 30 minutes

Diagnostics I: Linearity and Independence 30 minutes

1 assignment Total 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

(14 ratings)

Brian Zaharatos

University of Colorado Boulder

4 Courses 14,947 learners

Offered by

University of Colorado Boulder

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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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Frequently asked questions

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.