导图Multiple Linear Regression

CFA 二级 思维导图 多元线性回归 包括假设、假设的违背、模型的设定、模型的不当设定、定性变量的分析。

Multiple Linear Regression

• Introduction
  • t-test
  • ANOVA
    • two types of uncertainty:
      • SEE(standard error of estimate):uncertainty in the regression model itself
      • b0,b1: uncertainty about the esti mates of the regression coefcients.
    • • 随着自变量Xi的数量的增加，R^2会增加，R^2的可靠性降低，此时要对照adjusted R^2来看
  • Dummy Variables
    • Dummy variables in a regression model can help analysts determine whether a particular qualitative independent variable explains the model’s dependent variable.一个定性的自变量能否解释因变量
    • 值(0,1)
    • 要在n个分类中确认，需要有n-1个虚拟变量
    • 截距表示被省略的分类X对应的Y平均值,斜率表示每个分类对Y的的增量效果（incremental effect ）
  • 与一个变量的线性回归类似
• Asumptions and Violations
  • Asumtions
    • A linear relation exists between the Xj and Y.
    • Xj are not random;no exact linear relation exists between Xj,Xk
    • E(ε)=0
    • Var(ε)=Var(Yi)
    • ε is uncorrelated across observations.
    • ε is normally distributed
  • Violations
    • heteroskedasticity
      • no conditional heteroskedasticity
      • conditional heteroskedasticity
      • Breusch–Pagan test
    • serial correlation
      • Positive serial correlation
        • 方差会减小
        • t-statistics：inflates
        • F-statistic：inflates
      • Durbin–Watson statistic （DW)
        • DW=2*(1-r)
          • DW的值介于0-4
        • 参考值:DW=2,
        • DW偏离DW=2太远，表明有序列相关问题
    • multicollinearity
      • 1个或多个自变量X存在高度相关性
        • 不是完美相关（not perfectly）
      • t-statistics：不显著 t值小
      • F-statistic：显著，F值大
      • 单个斜率系数的方差会增加，总体回访差减小
• Model Specification misSpecification
  • Model Specification
    • cogent economic reasoning
      • The model should be grounded in cogent economic reasoning
    • functional form .(LN,对数化)
      • The functional form chosen for the variables in the regression should be appropriate given the nature of the variables.(LN,对数化)
    • parsimonious（简约)
      • The model should be parsimonious（简约).
        • 小X，大Y，见微知著。
    • assumptions violations
      • be examined for violations of regression assumptions before being accepted.
    • useful out of sample
      • The model should be tested and be found useful out of sample before being accepted.
  • misSpecification
    • functional form
      • variables could be omitted
      • variables may need to be transformed
      • pools data from different samples
    • X correlated with the error term
      • estimated regression coefcients to be biased and inconsistent
    • time-series misspecifcation
      • lagged dependent variables as independent
      • including a function of dependent variable as an independent variable
      • independent variables that are measured with error
• qualitative dependent variable
  • Probit models
    • based on the normal distribution
  • logit models
    • based on the logistic distribution