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.
教學大綱 - 您將從這門課程中學到什麼
週
1完成時間為 1 小時
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 （總計 28 分鐘）, 4 個閱讀材料, 1 個測驗
7 個視頻
Introduction2分鐘
Matrix derivatives5分鐘
Coding example2分鐘
Centering by matrix multiplication6分鐘
Coding example2分鐘
Variance via matrix multiplication6分鐘
Coding example2分鐘
4 個閱讀材料
Welcome to the class10分鐘
Course textbook10分鐘
Grading10分鐘
In this module10分鐘
1 個練習
Background Quiz12分鐘
週
2完成時間為 1 小時
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 （總計 29 分鐘）, 2 個閱讀材料, 1 個測驗
6 個視頻
Centering first8分鐘
Coding example1分鐘
Connection with linear regression7分鐘
Coding example1分鐘
Fitted values and residuals4分鐘
2 個閱讀材料
Before you begin10分鐘
Before you begin10分鐘
1 個練習
One Parameter Regression Quiz10分鐘
週
3完成時間為 1 小時
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 個視頻 （總計 23 分鐘）, 2 個閱讀材料, 1 個測驗
8 個視頻
Coding example1分鐘
Prediction2分鐘
Coding example2分鐘
Residuals2分鐘
Coding example1分鐘
Generalizations6分鐘
Generalizations example2分鐘
2 個閱讀材料
Before you begin10分鐘
Generalizations10分鐘
1 個練習
Linear Regression Quiz12分鐘
週
4完成時間為 1 小時
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 （總計 39 分鐘）, 1 個閱讀材料, 1 個測驗
6 個視頻
Coding example3分鐘
Second derivation of least squares4分鐘
Projections9分鐘
Third derivation of least squares12分鐘
Coding example4分鐘
1 個閱讀材料
Before you begin10分鐘
1 個練習
General Least Squares Quiz20分鐘
週
5完成時間為 1 小時
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 （總計 44 分鐘）, 1 個測驗
4 個視頻
Group effects4分鐘
Change of parameterization4分鐘
ANCOVA10分鐘
1 個練習
Least Squares Examples Quiz12分鐘
週
6完成時間為 1 小時
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 （總計 44 分鐘）, 2 個測驗
6 個視頻
Bases 2, Fourier5分鐘
Bases 3, SVDs8分鐘
Bases, coding example9分鐘
Introduction to residuals5分鐘
Partitioning variability10分鐘
2 個練習
Bases Quiz8分鐘
Residuals Quiz10分鐘
4.4
22 個審閱熱門審閱
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.
講師
Brian Caffo, PhD
Professor, BiostatisticsBloomberg School of Public Health
關於 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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