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Welcome to Session 1 of the Concept to Combat series on TAAI. Today, we begin our Machine Learning module with Linear Regression, progressing from basic theory to tackling challenging questions for GATE DA 2026. What you'll learn: Mastering Linear Regression and Regularization through extensive practice. Identifying traps in difficult questions to build a winner’s mindset. 📘 Click the link below to download all session PDFs: https://drive.google.com/drive/folder... Join our Communities for Notes: Telegram: https://t.me/ManojGateDA Discord: / discord ML Module Schedule: Jan 20 – Feb 1. Subscribe to TAAI- Manoj Kumar to join the combat live! Jump to Topics: [00:00] Introduction [00:45] Concept to Combat Series: Goals & Strategy [02:47] ML Module Schedule & Phase 1 Timeline [07:20] The Function Approximation Logic [11:15] Practical Example: Hiring Decision Logic in ML [12:31] Real-world Case: House Price Prediction Logic [15:48] Terminology: Features, Labels, Independent vs. Dependent Variables [19:13] Supervised vs. Unsupervised Learning Overview [22:17] Regression vs. Classification: Output types & Differences [24:50] Regression as a Curve Fitting Problem [30:40] Linear Regression Deep Dive: Ice Cream Sales Example [33:32] The Loss Function: Why Sum of Squared Errors (SSE)? [38:41] Derivation: Partial Derivatives for Intercept and Slope [41:41] The Normal Equations (Scalar Form) [44:03] Statistical Approach: Covariance & Beta coefficients [51:05] Tricky Concept: Weighted Linear Regression Derivation [01:05:49] Exam Trap: Regression without Intercept [01:13:37] Solving GATE 2025 PYQ on Linear Regression [01:16:08] Effect of Data Transformation (Scaling/Shifting) on Weights [01:22:47] Impact of Data Duplication on Model Parameters [01:31:17] Vector Calculus for ML: Linear and Quadratic Forms [01:36:50] Multiple Linear Regression: Matrix Formulation [01:40:42] Vectorized Loss Function Derivation [01:45:57] Final Normal Equation [01:52:14] Tricky MCQ: Design Matrix Dimensions & Properties [02:04:27] Feature Scaling & Weight Invariance Theory [02:14:36] Time Complexity Breakdown [02:18:27] Gradient Descent (GD) Start: Intuition & Derivatives [02:28:53] Gradient Ascent vs. Descent: Moving towards Optima [02:31:50] Visualizing Loss: Level Curves, Contours, and Convexity [02:36:30] Parameter Update Rule for Linear Regression [02:43:11] Numerical Practice: Two Iterations of GD [02:56:32] GD Drawbacks: Local Minima & Saddle Points (Non-convex) [03:21:29] Types of GD: Batch vs. Mini-batch vs. Stochastic GD (SGD) [03:31:54] Closing Remarks & Specail tips #GATEDA #MachineLearning #LinearRegression #TAAI #ConceptToCombat GATE DA 2026 GATE Data Science AI GATE 2026 preparation GATE DA free course GATE DA practice questions GATE DA MCQ MSQ NAT GATE DA strategy GATE DA toppers preparation GATE DA machine learning Linear algebra for GATE DA Probability for GATE DA GATE DA exam tips GATE DA concepts and questions GATE DA next level preparation TAAI GATE Tomorrow's Architect of AI GATE DA rank-oriented GATE DA 2026 full syllabus GATE DA beyond concepts To check out the course- https://www.taai.live/ Join our complete course to boost your GATE DA preparation. 🔹About the complete course: ✅ Complete syllabus coverage for GATE DA. ✅ Concept-focused lectures + regular doubt sessions. ✅ Question bank + tests. ✅ Subject-specific doubt channels. ✅ Expert guidance from our faculty (Manoj Sir, AIR-13 and Sahitya Sir). This course is for anyone who wishes to crack GATE DA, whether you're an absolute beginner or a pro. Join our community: 📌 Website: https://www.taai.live 📌 Telegram: https://t.me/Manoj_Gate_DSAI 📌 Discord: / discord 📌LinkedIn: https://www.linkedin.com/company/taai... 🔔 Subscribe to our channel and hit the bell icon to get more updates.