### Cost Function

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__Cost Function :-__

A cost function is plotted based on the following equation,**J(θ0,θ1)**

=2m1i=1∑m(hθ(xi)−yi)2

=2m1i=1∑m(hθ(xi)−yi)2

J(θ0,θ1) - Cost Function

m - No.of input values

hθ(xi) - Value of Hypothesis function on iᵗʰ input.

yi - Actual value on iᵗʰ input.

It is basically the average(mean) of differences between squares of hypothesis value and actual values. As the value of cost function reduces the accuracy will be better.

So we will be trying to keep J(θ₁,θ၀) minimum. (0 in ideal case).

The cost function plot will be a 3D figure with,

θ၀ - x axis

θ₁ - y axis

J(θ₁,θ၀) - z axis

The graph will look like a set of concave dips and the minimum height of the graph will provide best value of

**θ₁**and

**θ၀**.

For convenience, we are skipping θ၀ for now and plots

**θ₁ vs J(θ₁)**

Here, h(θ) = xθ₁ and best value for θ₁ is marked in red. One more concept

**gradient descent**will help us to find the minimum value of Cost function.

On Next - Gradient Descent

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