關於此課程：Welcome to the Advanced Linear Models for Data Science Class 1: Least Squares. 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.
此課程適用人群：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.
製作方： Johns Hopkins University
教學方： Brian Caffo, PhD, Professor, Biostatistics
Bloomberg School of Public Health
| 級別 | 高級設置 |
| 承諾學習時間 | 6 weeks of study, 1-2 hours/week |
| 語言 | 英語（English） |
| 如何通過 | 通過所有計分作業以完成課程。 |
| 用戶評分 |
授課大綱
第 1 週
Background
We cover some basic matrix algebra results that we will need throughout the class. This includes some basic vector derivatives. In addition, we cover some some basic uses of matrices to create summary statistics from data. This includes calculating and subtracting means from observations (centering) as well as calculating the variance.
7 個視頻, 4 個閱讀材料
- Reading: Welcome to the class
- Reading: Course textbook
- Reading: Grading
- Reading: In this module
- 視頻: Matrix derivatives
- 視頻: Coding example
- 視頻: Centering by matrix multiplication
- 視頻: Coding example
- 視頻: Variance via matrix multiplication
- 視頻: Coding example
已評分: Background Quiz
第 2 週
One and two parameter regression
In this module, we cover the basics of regression through the origin and linear regression. Regression through the origin is an interesting case, as one can build up all of multivariate regression with it.
6 個視頻, 2 個閱讀材料
- Reading: Before you begin
- 視頻: Centering first
- 視頻: Coding example
- Reading: Before you begin
- 視頻: Connection with linear regression
- 視頻: Coding example
- 視頻: Fitted values and residuals
已評分: One Parameter Regression Quiz
第 3 週
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 個視頻, 2 個閱讀材料
- Reading: Before you begin
- 視頻: Coding example
- 視頻: Prediction
- 視頻: Coding example
- 視頻: Residuals
- 視頻: Coding example
- Reading: Generalizations
- 視頻: Generalizations
- 視頻: Generalizations example
已評分: Linear Regression Quiz
第 4 週
General least squares
We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.
6 個視頻, 1 個閱讀材料
- Reading: Before you begin
- 視頻: Coding example
- 視頻: Second derivation of least squares
- 視頻: Projections
- 視頻: Third derivation of least squares
- 視頻: Coding example
已評分: General Least Squares Quiz
第 5 週
Least squares examples
Here we give some canonical examples of linear models to relate them to techniques that you may already be using.
4 個視頻
- 視頻: Group effects
- 視頻: Change of parameterization
- 視頻: ANCOVA
已評分: Least Squares Examples Quiz
第 6 週
Bases and residuals
Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
6 個視頻
- 視頻: Bases 2, Fourier
- 視頻: Bases 3, SVDs
- 視頻: Bases, coding example
- 視頻: Introduction to residuals
- 視頻: Partitioning variability
已評分: Bases Quiz
已評分: Residuals Quiz
常見問題解答
運作方式
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製作方
Johns Hopkins University
The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.
評分和審閱
Very thorough and rigorous. A great review for me.
Great, detailed walk-through of least squares. Linear Algebra is a must for this course. To follow the last part requires knowledge of matrix (eigen?)decomposition, which derailed me somewhat.
Great Course
CL
Very good