Supervised learning - regression model
- Linear Regression Model
- Linear Regression (linear regression) is a linear model, it is assumed that there is a linear relationship between the input variables x and output variables y single
- In particular, the use of a linear regression model, X can be from a set of input variables linear combination, calculates the output variable y
Solving linear equations
Suppose we have a following linear equations:
y = ax + b
We know the two sets of data: x = l when, y = 3, i.e., (1,3)
When x = 2, y = 5, i.e., (2,5)
The data input in the equation, we obtain:
a + b = 3
2a + b = 5
Solutions obtained: a = 2, b = 1
That equation: 2x + 1 = y
When we have any x, the equation input, can be obtained the corresponding y
For example, when x = 5, y = 11.
Linear regression models
• d has a given attribute (feature) described in Example x = (x1; x2; ...; xd), where xi is the value of x in the i-th attribute (feature) of
Linear model (linear model) by trying to learn a property (characteristic) function to perform a linear combination of prediction, namely:
• - as a vector written in the form:
• assumed linear characteristics and the results are satisfying, i.e., not more than one side.
After • w and b learn, the model is determined.
• Many more powerful foundation of nonlinear model can be a linear model based on high-dimensional map obtained by introducing a hierarchy or.
Least squares method
• The method of minimizing the mean square error is resolved based on the model called "least squares method" (least square method)
• Its main idea is to choose the unknown parameters so that the difference between the square and the minimum theoretical and observed values.
- We assume that the number of input attributes (features) is only one:
- linear regression, the least squares method is to try to find a straight line, so that all the samples to the sum of the minimum Euclidean distance on a straight line.
• Solution B and w, so that the 
minimization process, called a linear regression model of the "least squares parameter estimation"
• the 
respective derivative of w and b can be obtained
• make partial derivatives are zero, you can get
--among them:
