理解patsy||Design Matrices

• patsy

  patsy is a Python package for describing statistical models and building design matrices.

• Design Matrices

  In statistics, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects.

  Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object.

  The design matrix is used in certain statistical models, e.g., the general linear model. It can contain indicator variables (ones and zeros) that indicate group membership in an ANOVA, or it can contain values of continuouse variables.

  The design matrix contains data on the independent variables (also called explanatory variables) in statistical models which attempt to explain observed data on a response variable (often called a dependent variables) in terms of the explanatory variables.

  $X_{i,j}$ represents the value of the $j^{th}$ variable associated with the $j^{th}$ object.
  $$y=X\beta$$
  $X$ is the design matrix;

  $\beta$ is the vector of the model’s coefficients.