L2R12 - Multiple Regression

• 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.

• - baised or inconsistent regression coefficients
• - unreliable hypothesis testing and inaccurate predictions

• 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 R²_resid
• 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