coursera机器学习公开课笔记4: linear-regression-with-multiple-variables

Multiple Features

Note: [7:25 - $θ^T$ is a 1 by (n+1) matrix and not an (n+1) by 1 matrix]

Linear regression with multiple variables is also known as “multivariate linear regression”.

We now introduce notation for equations where we can have any number of input variables.

$$begin{align*}x_j^{(i)} &= text{value of feature } j text{ in the }i^{th}text{ training example} \ x^{(i)}& = text{the input (features) of the }i^{th}text{ training example} \ m &= text{the number of training examples} \ n &= text{the number of features} end{align*}$$
The multivariable form of the hypothesis function accommodating these multiple features is as follows:
$$h_theta (x) = theta_0 + theta_1 x_1 + theta_2 x_2 + theta_3 x_3 + cdots + theta_n x_n$$
In order to develop intuition about this function, we can think about $θ_0$ as the basic price of a house, $θ_1$ as the price per square meter, $θ_2$ as the price per floor, etc. $x_1$ will be the number of square meters in the house, $x_2$ the number of floors, etc.

Using the definition of matrix multiplication, our multivariable hypothesis function can be concisely represented as :

最后

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