L2R12 - Multiple Regression

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  1. Model Misspecifications
    • 1- The functional form can be misspecified
    • - Important variables can be omitted.
    • - variable should be transformed.
    • - data is improperly pooled.
    • 2- Explanatory variables are correlated with the error term in time series models.
    • - a lagged dependent variable is used an an independent variable.
    • - a function of the dependent variable is used as an independent variable.
    • - independent variable are measured with error.
    • 3- Other time-series misspecifications that result in non-stationary.
  2. Effects of Model Misspecification
    • - baised or inconsistent regression coefficients
    • - unreliable hypothesis testing and inaccurate predictions
  3. Qualitative Independent Variables (Dummy Variables)
    • Idea: calculate Prob. (Independent variable = 1)
    • - capture the effect of a binary independent variables
    • - use one less dummy variable than the number of categories
    • - required methods other than ordianry least squares (e.g. probit, logit (using max. likelihood), or discriminant analysis (using a linear function similar to ordinary least squares))
  4. Conditional Heteroskedasticity
    • What is it? Residual variance related to the level of independent variable
    • What it does? Too many Type I errors
    • How to detect? Breusch-Pagan Chi Square Test BP = n x R2resid
    • How to Fix: Used White-corrected (robust) standard errors
  5. Serial Correlation
    Can be positive or negative (+ive S.C. is more common)

    • What is it? Residuals are correlated
    • What it does? Too many Type I errors (too many type II errors for -ive S.C.)
    • How to detect? Durbin Watson Test = 2(1-r)
    • How to Fix: Use Hansen method to adjust standard errors

    If C.H. and +ive S.C. are present together, use Hansen method to adjust standard errors
  6. Multicollinearity
    • What is it? Two or more independent variables are correlated
    • What it does? Too many Type II errors
    • How to detect? t-Test implies insignificance of individual variables but F-Test implies significance
    • How to Fix: remove one of the correlated variables

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L2R12 - Multiple Regression
2010-05-07 23:16:05

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