L2R12 - Multiple Regression
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- 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.
Effects of Model Misspecification
- - baised or inconsistent regression coefficients
- - unreliable hypothesis testing and inaccurate predictions
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))
- 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
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
- 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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