Linear Regression From Scratch | Complete Hand-Solved Walkthrough

Описание: This lecture presents a from-zero, fully hand-worked explanation of linear regression, designed for undergraduate students.

Starting from raw data, the lecture walks step by step through the classical statistical process used to build a linear regression model without software or shortcuts.

You will see how data is centered using mean values, how deviations and are computed, and how squared terms and cross-products are used to measure spread and joint variation. Using this, the Pearson correlation coefficient is calculated and interpreted, followed by the derivation of the least-squares regression line.

The lecture concludes with writing the final regression equation and using it for prediction, exactly as required in undergraduate exams and board-based teaching.

This session focuses on conceptual clarity, manual calculation, and statistical reasoning, forming a strong foundation for data analysis and machine-learning regression models.

This video provides a hand-solved, step-by-step explanation of linear regression (0:08) for undergraduate students, demonstrating how to build a linear regression model without software.

The lecture covers:
Introduction to Linear Regression: The video begins by explaining the concept of linear regression and its importance in finding relationships and trends between correlated variables (0:17-0:42).
Data Setup and Mean Calculation: The speaker uses an example of student study hours (X) and their corresponding marks (Y) to illustrate the process. It shows how to calculate the mean of X (x̄) and mean of Y (ȳ) from a given dataset (0:45-4:35).
Calculating Deviations from the Mean: The video demonstrates how to compute the deviations of each data point from their respective means, i.e., (X - x̄) and (Y - ȳ) (6:23-7:29).
Calculating Squared Deviations and Cross-Products: It then explains the importance of calculating the squared deviations, (X - x̄)² and (Y - ȳ)², and the cross-product of deviations, (X - x̄)(Y - ȳ), to measure spread and joint variation (8:25-11:21).
Pearson Correlation Coefficient: The video explains how to calculate the Pearson correlation coefficient (r) using the derived values, interpreting its significance in terms of the strength and direction of the correlation (11:21-13:27).
Deriving the Least-Squares Regression Line: The lecturer proceeds to derive the equation of the least-squares regression line (y = bx + a), explaining how to calculate the slope (b) and the intercept (a) (13:29-16:32).
Using the Regression Equation for Prediction: Finally, the video concludes by showing how to use the derived regression equation to predict outcomes for new data points within the observed range, highlighting the practical utility of the model (17:08-19:01)

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