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Advanced Linear Models for Data Science 1: Least Squares
  • Level Expert
  • Duration 9 hours
  • Course by Johns Hopkins University
  • Offered by

About

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.

Modules

Welcome

    • 1 Videos
    • 3 Readings
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1 Videos

  • Introduction

3 Readings

  • Welcome to the class
  • Course textbook
  • Grading

Relevant matrix results

    • 2 Videos
    • 1 Readings
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2 Videos

  • Matrix derivatives
  • Coding example

1 Readings

  • In this module

Centering and means

    • 2 Videos
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2 Videos

  • Centering by matrix multiplication
  • Coding example

Variance

    • 2 Videos
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2 Videos

  • Variance via matrix multiplication
  • Coding example

Quiz

    • 1 Assignment
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1 Assignment

  • Background Quiz

Single parameter basics

    • 3 Videos
    • 1 Readings
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3 Videos

  • Regression through the origin
  • Centering first
  • Coding example

1 Readings

  • Before you begin

Linear regression

    • 3 Videos
    • 1 Readings
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3 Videos

  • Connection with linear regression
  • Coding example
  • Fitted values and residuals

1 Readings

  • Before you begin

Quiz

    • 1 Assignment
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1 Assignment

  • One Parameter Regression Quiz

Least squares for linear regression

    • 2 Videos
    • 1 Readings
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2 Videos

  • Least squares
  • Coding example

1 Readings

  • Before you begin

Prediction

    • 2 Videos
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2 Videos

  • Prediction
  • Coding example

Residuals

    • 2 Videos
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2 Videos

  • Residuals
  • Coding example

Generalizations

    • 2 Videos
    • 1 Readings
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2 Videos

  • Generalizations
  • Generalizations example

1 Readings

  • Generalizations

Quiz

    • 1 Assignment
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1 Assignment

  • Linear Regression Quiz

Least squares

    • 3 Videos
    • 1 Readings
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3 Videos

  • Least squares
  • Coding example
  • Second derivation of least squares

1 Readings

  • Before you begin

Projections

    • 1 Videos
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1 Videos

  • Projections

Least squares, third derivation

    • 2 Videos
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2 Videos

  • Third derivation of least squares
  • Coding example

Quiz

    • 1 Assignment
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1 Assignment

  • General Least Squares Quiz

Examples

    • 4 Videos
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4 Videos

  • Basic examples of design matrices and fits
  • Group effects
  • Change of parameterization
  • ANCOVA

Quiz

    • 1 Assignment
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1 Assignment

  • Least Squares Examples Quiz

Bases

    • 4 Videos
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4 Videos

  • Bases, introduction
  • Bases 2, Fourier
  • Bases 3, SVDs
  • Bases, coding example

Quiz

    • 1 Assignment
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1 Assignment

  • Bases Quiz

Residuals

    • 2 Videos
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2 Videos

  • Introduction to residuals
  • Partitioning variability

Quiz

    • 1 Assignment
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1 Assignment

  • Residuals Quiz

Auto Summary

Elevate your data science skills with the "Advanced Linear Models for Data Science 1: Least Squares" course. This expert-level program delves into the intricacies of least squares through a rigorous linear algebraic and mathematical lens. Ideal for those with a foundational grasp of linear algebra, multivariate calculus, statistics, regression models, and basic R programming, this course enhances your understanding of regression modeling from a theoretical standpoint. Led by Coursera, this intensive 540-minute course is designed to solidify your grasp of linear algebraic approaches to regression, thereby enriching your capabilities as an applied data scientist. Flexible subscription options, including Starter and Professional plans, make it accessible for dedicated learners aiming to deepen their expertise in maths and statistics. Whether you're a seasoned data scientist or an advanced learner seeking to specialize further, this course offers the comprehensive knowledge you need to excel.

Brian Caffo, PhD
Instructor

Brian Caffo, PhD