文档介绍：Chapter 15
Multiple Linear
Regression Analysis
Multiple linear regression
Choice of independent variable
Application
Content
Goal:construct the multiple linear regression model to assess the relationship between one dependant variable and a set of independent variables.
Data:the dependant variable is quantitative data; the independent variables are all or most quantitative data. If there are some qualitative data or ranked data ,we must change them.
Application :explain and prediction.
significance:Since the things are influenced by many facts, the change of dependent variable may influenced by many others independent variables. For example, the change of diabetes’ blood sugar may affected by many biochemical criterions such as insulin, glycosylated hemoglobin, total cholesterol of serum, triglyceride and so on.
§  1
Multiple linear regression
variable:one dependant variable, a set of independent . together m+1 。
Sample size:n
Data form in Table 15-1
General model of the regression equation:
1、 Multiple linear regression model
In the above model, the dependent variable y can be denoted the linear function of independent variables(x1,x2,•••xm) approximately.
ß0 is the constant, ß 1, ß2, •••ßm are partial regression coefficient, denote that when other dependent variable holds the line, xj increase or decrease one unit that mean variation of y. The residual e is random error that excludes m entries independent variable influence to y.
Table 15-1 Data form of multiple regression
Qualification
(1)There is linear relationship between y and x1,x2,•••xm.
(2)The measured value yi(i=1,2, •••,n) of each case is independent.
(3) The residual e is independent and normally distributed with mean 0 and variance σ2, it equates to that for any independent variables x1,x2,•••xm the dependent variable y has the same variance, and obey to normal distribution.
General process
construct regression equation
(2) test and evaluate regression equation, the effect of each i