Linear Regression - Key Tool in Data Analysis

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⏭️ 𝘾𝙤𝙣𝙣𝙚𝙘𝙩 𝙬𝙞𝙩𝙝 𝙪𝙨 𝙤𝙣 𝙋𝘼𝙏𝙍𝙀𝙊𝙉 https://www.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 line—the line that comes closest to all of our data points without favoring any single one. In this video, we’ll explore what “best” really means, how we measure and minimize errors, and how calculus leads us to the formulas for slope and intercept. Along the way, we’ll work through examples by hand, then apply the method to real-world data from AI systems. You’ll also see when linear regression fails and why inspecting your data is a crucial step. By the end, you’ll have a deep understanding of how linear regression works, and when it’s the right tool for the job. ⏭️ 𝙔𝙤𝙪 𝙘𝙖𝙣 𝙟𝙪𝙢𝙥 𝙩𝙤 𝙨𝙚𝙘𝙩𝙞𝙤𝙣𝙨 𝙤𝙛 𝙩𝙝𝙚 𝙫𝙞𝙙𝙚𝙤 𝙝𝙚𝙧𝙚: 0:00 – Introduction to Linear Regression 0:39 – Why regression is needed 1:18 – Measuring error and least squares 2:19 – Calculating squared errors 3:16 – Minimizing error with calculus 4:22 – General formulas for slope & intercept 5:40 – Real-world AI example (prompt length vs. time) 7:07 – When linear regression fails (Inspect your Data!) ▶️ 𝙒𝘼𝙏𝘾𝙃 𝙉𝙀𝙓𝙏: Covariance https://youtu.be/ATfDsdlze3E 𝘽𝙚𝙘𝙤𝙢𝙚 𝙤𝙪𝙧 𝙋𝙖𝙩𝙧𝙤𝙣 𝙤𝙣 𝙋𝙖𝙩𝙧𝙚𝙤𝙣: https://www.patreon.com/socratica 📚 𝙒𝙚 𝙧𝙚𝙘𝙤𝙢𝙢𝙚𝙣𝙙 (affiliate links): The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow https://amzn.to/4j9n0YP The Art of Statistics: How to Learn from Data by David Spiegelhalter https://amzn.to/3S9E46a How to Be a Great Student (from Socratica!) ebook: https://amzn.to/2Lh3XSP paperback: https://amzn.to/3t5jeH3 🎬 𝘾𝙍𝙀𝘿𝙄𝙏𝙎: Written & Produced by: Michael Harrison & Kimberly Hatch Harrison Edited by: Alivia Brown and Megi Shuke Music License from Soundstripe Code: 6F6NQWRP2DBJBIQZ 🎓 𝘼𝘽𝙊𝙐𝙏 𝙊𝙐𝙍 𝙄𝙉𝙎𝙏𝙍𝙐𝘾𝙏𝙊𝙍𝙎: Michael earned his BS in Math from C

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