Andrew ng machine learning of two single variable linear regression __ machine learning

Model Representation

NG Video has an example of a house price, a data set between the House area X and the price y:

area (x)	Price (y)
2104	460
1416	232
1534	315
852	178
...	...

Here is defined:

m: Number of training samples, M = 4 visible in the table above
x (i) x^{(i)} : I i input variables/features, in multiple input variables x (i) x^{(i)} represents a set of inputs, such as X (1) =1416 x^{(1)}=1416 in the previous table.
y (i) y^{(i)} : output, such as Y (1) =232 y^{(1) In the previous table}=232

The process of introducing a hypothetical function (hypothesis function) hθ (x) H_\theta (x) in the original text is shown in figure:

That is, to seek a mapping function from x x to Y y, which is what the learning algorithm ultimately obtains by learning the contents of a dataset. So how do you find this hypothetical function? Obviously this is a regression problem (which distinguishes between classification and regression in the previous article), if only the univariate linear regression is discussed, then the form of the assumed function can be written as hθ (x) =θ0+θ1x H_\theta (x) =\theta_0+\theta_1x, in order to hθ (x) H_\theta (x) for analysis, we introduce the loss function . loss functions (cost function)

The introduction of the loss function is derived from the evaluation of the assumption function.
Assuming we've got a hypothetical function hθ (x) =θ0+θ1x H_\theta (x) =\theta_0+\theta_1x, now we need to evaluate the mapping capabilities of this function, and how to do it. One approach is to obtain the variance of the hθ (x (i)) H_\theta (x^{(i)}) and Y (i) y^{(i)} based on the assumed function for x (i) x^{(i)}, as follows:
　　
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