Cost Function

Cost Function

Given a training set (set of sizes and selling prices), hypothesis: h(x) = a₀ + a₁x, how to choose a₀ and a₁? Choose a₀ and a₁ so that h(x) is close to y for our training examples (x, y).

There are many ways to make sure h(x) is as close to y as possible. Minimize Square error function (or Mean squared error) works well with regression problems:

Important:

• h(x) for fixed a₀ and a₁ is a function of x, a₀ and a₁ are constants
• J(a₀, a₁) is a function of a₀ and a₁, x is constant

Below is the graph of h(x) vs. graph of J(a₁) (let a₀ = 0 for simplicity). Each color of h(x) line corresponds to a point of J(a₁) graph

Since our objective is to minimize cost function J, from the graph above, we can achieve our goal by setting a₁ = 1

Resource:

- https://www.coursera.org/learn/machine-learning/supplement/nhzyF/cost-function
- https://www.coursera.org/learn/machine-learning/supplement/u3qF5/cost-function-intuition-i