Coursera Machine learning:regression Multiple regression

Multivariate regression

Review simple linear regression: A feature, two correlation coefficients

　　

The actual application is much more complicated than this, such as

1, house prices and housing area is not just a simple linear relationship.

2, there are many factors affecting the price, not only the size of the house, but also many other factors.

　　　　

Now, in the first case, the price and the housing area are not simply linear, and may be two or polynomial:

Two times function:

　　

Polynomial functions:

　　

Polynomial regression:

　　

The characteristics are obtained by the self-variable of the housing area.

　　

　　

In the second case, the factors that affect house prices are not just the size of the house, which adds to the number of bedrooms. This is the multivariate linear regression.

　　

General Expressions:

　　

In multivariate linear regression, the correlation coefficients are understood:

Analyzing the correlation coefficients of a characteristic x[j] WJ, first fixing the values of other features, so that the correlation coefficients of the features can be analyzed in a plane.

　　

In polynomial regression, it is not possible to analyze the correlation coefficients of features by fixing other characteristics.

　　

Coursera Machine learning:regression Multiple regression