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.
教学大纲 - 您将从这门课程中学到什么
周
1完成时间为 1 小时
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 个视频 （总计 28 分钟）, 4 个阅读材料, 1 个测验
7 个视频
Introduction2分钟
Matrix derivatives5分钟
Coding example2分钟
Centering by matrix multiplication6分钟
Coding example2分钟
Variance via matrix multiplication6分钟
Coding example2分钟
4 个阅读材料
Welcome to the class10分钟
Course textbook10分钟
Grading10分钟
In this module10分钟
1 个练习
Background Quiz12分钟
周
2完成时间为 1 小时
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 个视频 （总计 29 分钟）, 2 个阅读材料, 1 个测验
6 个视频
Centering first8分钟
Coding example1分钟
Connection with linear regression7分钟
Coding example1分钟
Fitted values and residuals4分钟
2 个阅读材料
Before you begin10分钟
Before you begin10分钟
1 个练习
One Parameter Regression Quiz10分钟
周
3完成时间为 1 小时
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 个视频 （总计 23 分钟）, 2 个阅读材料, 1 个测验
8 个视频
Coding example1分钟
Prediction2分钟
Coding example2分钟
Residuals2分钟
Coding example1分钟
Generalizations6分钟
Generalizations example2分钟
2 个阅读材料
Before you begin10分钟
Generalizations10分钟
1 个练习
Linear Regression Quiz12分钟
周
4完成时间为 1 小时
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 个视频 （总计 39 分钟）, 1 个阅读材料, 1 个测验
6 个视频
Coding example3分钟
Second derivation of least squares4分钟
Projections9分钟
Third derivation of least squares12分钟
Coding example4分钟
1 个阅读材料
Before you begin10分钟
1 个练习
General Least Squares Quiz20分钟
4.4
22 个审阅热门审阅
We need more advanced, theoretical courses on Coursera, like this one, in order to deeply understand the more general courses like Regression Models and Linear Models.
Good mathematical rigour for the analysis of linear models. Builds some good intuition for the geometry of least squares which helps in model result interpretation.
讲师
Brian Caffo, PhD
Professor, BiostatisticsBloomberg School of Public Health
关于 约翰霍普金斯大学
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.
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