Advanced Linear Models for Data Science 2: Statistical Linear Models

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About this course: Welcome to the Advanced Linear Models for Data Science Class 2: Statistical Linear Models. This class is an introduction to least squares from a linear algebraic and mathematical perspective. Before beginning the class make sure that you have the following: - A basic understanding of linear algebra and multivariate calculus. - A basic understanding of statistics and regression models. - At least a little familiarity with proof based mathematics. - Basic knowledge of the R programming language. After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: Welcome to the Advanced Linear Models for Data Science Class 2: Statistical Linear Models. This class is an introduction to least squares from a linear algebraic and mathematical perspective. Before beginning the class make sure that you have the following: - A basic understanding of linear algebra and multivariate calculus. - A basic understanding of statistics and regression models. - At least a little familiarity with proof based mathematics. - Basic knowledge of the R programming language. After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general understanding of regression models.

Who is this class for: This class is for students who already have had a class in regression modeling and are familiar with the area who would like to see a more advanced treatment of the topic.

Created by:  Johns Hopkins University
  • Taught by:  Brian Caffo, PhD, Professor, Biostatistics

    Bloomberg School of Public Health
Level Advanced Commitment 6 weeks of study, 1-2 hours/week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Coursework

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Syllabus


WEEK 1


Introduction and expected values
In this module, we cover the basics of the course as well as the prerequisites. We then cover the basics of expected values for multivariate vectors. We conclude with the moment properties of the ordinary least squares estimates.


7 videos, 3 readings expand


  1. Video: Introductory video
  2. Reading: Welcome to the class
  3. Reading: Course textbook
  4. Reading: Introduction to expected values
  5. Video: Multivariate expected values, the basics
  6. Video: Expected values, matrix operations
  7. Video: Multivariate variances and covariances
  8. Video: Multivariate covariance and variance matrix operations
  9. Video: Expected values of quadratic forms
  10. Video: Expected value properties of least squares estimates

Graded: Expected Values

WEEK 2


The multivariate normal distribution
In this module, we build up the multivariate and singular normal distribution by starting with iid normals.


4 videos, 2 readings expand


  1. Reading: Introduction to the multivariate normal
  2. Video: Normals and multivariate normals
  3. Video: The singular normal distribution
  4. Video: Normal likelihoods
  5. Video: Normal conditional distributions
  6. Reading: A note on the last quiz question.

Graded: the multivariate normal

WEEK 3


Distributional results
In this module, we build the basic distributional results that we see in multivariable regression.


8 videos, 1 reading expand


  1. Reading: Distributional results
  2. Video: Chi squared results for quadratic forms
  3. Video: Confidence intervals for regression coefficients
  4. Video: F distribution
  5. Video: Coding example
  6. Video: Prediction intervals
  7. Video: Coding example
  8. Video: Confidence ellipsoids
  9. Video: Coding example

Graded: Distributional results

WEEK 4


Residuals
In this module we will revisit residuals and consider their distributional results. We also consider the so-called PRESS residuals and show how they can be calculated without re-fitting the model.


4 videos, 2 readings expand


  1. Reading: Residuals
  2. Video: Residuals distributional results
  3. Video: Code demonstration
  4. Video: Leave one out residuals
  5. Video: Press residuals
  6. Reading: Thanks for taking the course

Graded: Residuals
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