Multiple Linear Regression and Its Assumptions

Multiple linear regression explained: many input features, what each weight means, and the assumptions of linear regression. One input gave us a line. With two inputs the model becomes a plane, and with twenty it is still the same equation: one weight for every column. This video shows that picture, explains what a weight really means, fits a small example with scikit-learn, and then goes through the five assumptions of linear regression with one picture each, and how to check them. You will learn: How the line becomes a plane, and why "one weight per column" works for any number of columns What a weight means: the change in the prediction for one unit of its column, with the others held fixed A worked example: six students, marks = 3 x study + 2 x sleep + 1, fitted with scikit-learn That a direct formula (the normal equation) gives the weights, without derivation The five assumptions: a linear relation, independent errors, constant spread (the funnel), roughly normal errors (needed for intervals and tests, not for the fit), and no twin columns (multicollinearity) Why two nearly identical columns make the weights unstable, shown with two fits that differ by one mark A checklist: what to look for in a residual plot Chapters 0:00 More than one input 0:33 From a line to a plane 1:12 One weight per column 1:45 A small example, fitted with scikit-learn 2:22 What a weight means 2:59 The residual plot; assumption 1: linear 3:36 Assumption 2: independent errors 4:01 Assumption 3: constant spread 4:24 Assumption 4: roughly normal errors 4:47 Assumption 5: no twin columns (a question) 5:22 Why twin columns make weights unstable 6:19 Checklist, recap + try it yourself Try it yourself: with marks = 3 x study + 2 x sleep + 1, predict the marks of a student who studies 2 hours and sleeps 8. Then give this student one more hour of sleep and predict again. By how much did it change? Animations made with Manim Community Edition. The narration is a synthetic voice. #MachineLearning #LinearRegression #AIEngineer More from Harban AI Labs: https://harban-ai-labs.vercel.app/