Linear Regression with multiple Variables

In previous blog(Linear Regression with one variable) linear regression that we developed, we have a single feature x, the size of the house, and we wanted to use that to predict why the price of the house and this was our form of our hypothesis. But now imagine, what if we had not only the size of the house as a feature or as a variable of which to try to predict the price, but that we also knew the number of bedrooms, the number of house and the age of the home and years.
It seems like this would give us a lot more information with which to predict the price.
Lets start with example of multiple variables :

In this input feature will be not only House Size like as one variable regression but also Number of Bed Rooms,Number of Floor, Age of House also will be the feature.

Hypothesis function will change from h(x) = Θ₀ +  Θ₁ x  to h(x) = Θ₀ +  Θ₁X₁   +  Θ₂ X₂ +  Θ₃ X₃ ...+  Θ_n X_n

For convenience of notation we define X₀₌₁  and hypothesis function h(x) becomes as

h(x) = Θ₀X₀ +  Θ₁X₁   +  Θ₂ X₂ +  Θ₃ X₃ ...+  Θ_n X_n

We represents each x and Θ value as vector X and Θ as

h(x) = Θ^T x

This hypothesis function h(x) is multivariate linear regression.

Cost function for multiple variables represents as :

Gradient Descent 

Previously in Linear Regression with one variable(n=1)

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Linear Regression with multiple variable(n > 1)

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