Introduction to Linear Regression: Cost Function

Cost Function (Method I)

For calculating the cost in linear regression, typically we use Sum of Squared Error method(SSE)

$\ J(\theta) = \frac{1}{2m}\sum_{i=1}^m{(h(x^{(i)})-{y^{(i)}})^2}$

The goal is to minimize $\ J(\theta)$ and figure out $\ \theta$ values corresponding to the minimum cost. There are several optimization algorithms used to achieve this.

Introduction to Linear Regression: Polynomial Regression

Polynomial Regression

This form of regression is used to fit more complex functions and this is a general concept not restricted to linear regression, but also used commonly in classification algorithms such as Logistic Regression and Neural Networks as well. I hope to talk about it in detail in a future post. For now take a look at the following scatter plot.

Introduction to Linear Regression: A Machine Learning Approach

Supervised Learning is a form of learning in which we use known data with actual outputs from past experiences to model a relationship and this model is used to predict future outcomes. The known data used to build up the model is called 'training data'.

To build a supervised learning model we need,

1. Training Data
2. Hypothesis
3. Cost Function
4. Optimization method for Minimization