Advanced Linear Models for Data Science 2: Statistical Linear Models
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Advanced Linear Models for Data Science 2: Statistical Linear Models
This course is part of Advanced Statistics for Data Science Specialization
Instructor: Brian Caffo, PhD
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There are 4 modules in 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.
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.
What's included
7 videos3 readings1 assignment
7 videos•Total 38 minutes
- Introductory video•2 minutes
- Multivariate expected values, the basics•5 minutes
- Expected values, matrix operations•3 minutes
- Multivariate variances and covariances•6 minutes
- Multivariate covariance and variance matrix operations•6 minutes
- Expected values of quadratic forms•4 minutes
- Expected value properties of least squares estimates•14 minutes
3 readings•Total 30 minutes
- Welcome to the class•10 minutes
- Course textbook•10 minutes
- Introduction to expected values•10 minutes
1 assignment•Total 30 minutes
- Expected Values•30 minutes
In this module, we build up the multivariate and singular normal distribution by starting with iid normals.
What's included
4 videos2 readings1 assignment
4 videos•Total 31 minutes
- Normals and multivariate normals•9 minutes
- The singular normal distribution•8 minutes
- Normal likelihoods•5 minutes
- Normal conditional distributions•9 minutes
2 readings•Total 20 minutes
- Introduction to the multivariate normal•10 minutes
- A note on the last quiz question.•10 minutes
1 assignment•Total 20 minutes
- the multivariate normal•20 minutes
In this module, we build the basic distributional results that we see in multivariable regression.
What's included
8 videos1 reading1 assignment
8 videos•Total 60 minutes
- Chi squared results for quadratic forms•11 minutes
- Confidence intervals for regression coefficients•7 minutes
- F distribution•5 minutes
- Coding example•8 minutes
- Prediction intervals•11 minutes
- Coding example•5 minutes
- Confidence ellipsoids•7 minutes
- Coding example•6 minutes
1 reading•Total 10 minutes
- Distributional results•10 minutes
1 assignment•Total 20 minutes
- Distributional results•20 minutes
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.
What's included
4 videos2 readings1 assignment
4 videos•Total 32 minutes
- Residuals distributional results•5 minutes
- Code demonstration•3 minutes
- Leave one out residuals•9 minutes
- Press residuals•15 minutes
2 readings•Total 20 minutes
- Residuals•10 minutes
- Thanks for taking the course•10 minutes
1 assignment•Total 30 minutes
- Residuals•30 minutes
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Reviewed on Jan 30, 2017
Good course on applied linear statistical modeling.
Reviewed on Oct 12, 2019
It is a very good course for any statistics to learn and have a sweet tastes of math and its behind functionality on data.
Reviewed on Aug 6, 2020
This course is very powerfull for statistical linear
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