Uploaded August 2025 | Updated September 2026, 2 weeks ago
âïž ðŸð€ð£ð£ððð© ð¬ðð©ð ðªðš ð€ð£ ððŒððððð
patreon.com/socratica
Linear Regression is one of the most widely used tools in applied math and data analysis. It helps us make sense of noisy data by finding the best-fit lineâthe line that comes closest to all of our data points without favoring any single one. In this video, weâll explore what âbestâ really means, how we measure and minimize errors, and how calculus leads us to the formulas for slope and intercept.
Along the way, weâll work through examples by hand, then apply the method to real-world data from AI systems. Youâll also see when linear regression fails and why inspecting your data is a crucial step. By the end, youâll have a deep understanding of how linear regression works, and when itâs the right tool for the job.
âïž ðð€ðª ððð£ ððªð¢ð¥ ð©ð€ ðšððð©ðð€ð£ðš ð€ð ð©ðð ð«ðððð€ ððð§ð:
0:00 â Introduction to Linear Regression
0:39 â Why regression is needed
1:18 â Measuring error and least squares
2:19 â Calculating squared errors
3:16 â Minimizing error with calculus
4:22 â General formulas for slope & intercept
5:40 â Real-world AI example (prompt length vs. time)
7:07 â When linear regression fails (Inspect your Data!)
â¶ïž ððŒððŸð ðððð:
Covariance youtu.be/ATfDsdlze3E
ðœððð€ð¢ð ð€ðªð§ ððð©ð§ð€ð£ ð€ð£ ððð©ð§ðð€ð£:
patreon.com/socratica
ð ðð ð§ððð€ð¢ð¢ðð£ð (affiliate links):
The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow
amzn.to/4j9n0YP
The Art of Statistics: How to Learn from Data by David Spiegelhalter
amzn.to/3S9E46a
How to Be a Great Student (from Socratica!)
ebook: amzn.to/2Lh3XSP
paperback: amzn.to/3t5jeH3
ð¬ ðŸððð¿ððð:
Written & Produced by: Michael Harrison & Kimberly Hatch Harrison
Edited by: Alivia Brown and Megi Shuke
Music License from Soundstripe
Code: 6F6NQWRP2DBJBIQZ
ð ðŒðœððð ððð ðððððððŸðððð:
Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.
Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor.
Michael and Kimberly Harrison co-founded Socratica.
Their mission? To create the education of the future.
Ready to ð§ ðððŒðð ðððð with Socratica?
ðº ððªððšðð§ððð for SMART videos in Math, Science & Programming:
bit.ly/SocraticaSubscribe
â¶ïž ðððŒðððððð:
Study Tips bit.ly/StudyTipsPlaylist
Python bit.ly/PythonSocratica
Chemistry bit.ly/Chemistry_Playlist
Calculus bit.ly/CalculusSocratica
Geometry bit.ly/GeometrySocratica
#LinearRegression #math #bestfitline
âïž ðŸð€ð£ð£ððð© ð¬ðð©ð ðªðš ð€ð£ ððŒððððð
patreon.com/socratica
Linear Regression is one of the most widely used tools in applied math and data analysis. It helps us make sense of noisy data by finding the best-fit lineâthe line that comes closest to all of our data points without favoring any single one. In this video, weâll explore what âbestâ really means, how we measure and minimize errors, and how calculus leads us to the formulas for slope and intercept.
Along the way, weâll work through examples by hand, then apply the method to real-world data from AI systems. Youâll also see when linear regression fails and why inspecting your data is a crucial step. By the end, youâll have a deep understanding of how linear regression works, and when itâs the right tool for the job.
âïž ðð€ðª ððð£ ððªð¢ð¥ ð©ð€ ðšððð©ðð€ð£ðš ð€ð ð©ðð ð«ðððð€ ððð§ð:
0:00 â Introduction to Linear Regression
0:39 â Why regression is needed
1:18 â Measuring error and least squares
2:19 â Calculating squared errors
3:16 â Minimizing error with calculus
4:22 â General formulas for slope & intercept
5:40 â Real-world AI example (prompt length vs. time)
7:07 â When linear regression fails (Inspect your Data!)
â¶ïž ððŒððŸð ðððð:
Covariance youtu.be/ATfDsdlze3E
ðœððð€ð¢ð ð€ðªð§ ððð©ð§ð€ð£ ð€ð£ ððð©ð§ðð€ð£:
patreon.com/socratica
ð ðð ð§ððð€ð¢ð¢ðð£ð (affiliate links):
The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow
amzn.to/4j9n0YP
The Art of Statistics: How to Learn from Data by David Spiegelhalter
amzn.to/3S9E46a
How to Be a Great Student (from Socratica!)
ebook: amzn.to/2Lh3XSP
paperback: amzn.to/3t5jeH3
ð¬ ðŸððð¿ððð:
Written & Produced by: Michael Harrison & Kimberly Hatch Harrison
Edited by: Alivia Brown and Megi Shuke
Music License from Soundstripe
Code: 6F6NQWRP2DBJBIQZ
ð ðŒðœððð ððð ðððððððŸðððð:
Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.
Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor.
Michael and Kimberly Harrison co-founded Socratica.
Their mission? To create the education of the future.
Ready to ð§ ðððŒðð ðððð with Socratica?
ðº ððªððšðð§ððð for SMART videos in Math, Science & Programming:
bit.ly/SocraticaSubscribe
â¶ïž ðððŒðððððð:
Study Tips bit.ly/StudyTipsPlaylist
Python bit.ly/PythonSocratica
Chemistry bit.ly/Chemistry_Playlist
Calculus bit.ly/CalculusSocratica
Geometry bit.ly/GeometrySocratica
#LinearRegression #math #bestfitline
