Why Start With Linear Regression?
Every machine learning journey should begin with linear regression. Not because it is the most powerful model, but because it introduces every concept you will need: cost functions, optimization, gradient descent, regularization, and the bias-variance tradeoff. Understanding linear regression deeply means understanding the DNA of machine learning itself.
The Normal Equation vs Gradient Descent
Linear regression is unique among ML algorithms because it has a closed-form solution. The normal equation gives you the optimal weights in one computation. Yet we still teach gradient descent with it - because gradient descent is the universal optimization tool that scales to neural networks, where closed-form solutions do not exist. Learning it here, where you can verify the answer, builds intuition for when you cannot.
Assumptions Matter More Than You Think
The most common mistake beginners make is fitting a linear model without checking assumptions. Linearity, independence, homoscedasticity, and normality of residuals are not just theoretical requirements - violating them leads to biased estimates, wrong confidence intervals, and misleading predictions. A residual plot takes seconds and can save hours of debugging.
Regularization: Your First Defense Against Overfitting
Ridge and Lasso regression are not just extensions of linear regression - they introduce the fundamental concept of regularization that applies to every model in machine learning. L2 regularization shrinks weights, L1 performs feature selection, and Elastic Net combines both. Understanding why they work here makes understanding dropout, weight decay, and other techniques natural.
From Linear to Everything
Logistic regression is linear regression with a sigmoid. A neural network is stacked logistic units. SVMs find optimal linear separators. Even decision trees can be viewed as piecewise linear models. The thread of linearity runs through all of machine learning, and it starts here.