Multiple Regression Flashcards
A good regression should have these features
the explanatory variables should have a strong theoretical support
the sign of the estimated coefficients are consistent with theory
the estimated coefficients are significant
the regression has a high R squared
Homoscedasticity
n statistics, if all observations have the same variance, i.e. var(Xi) is the same for all i, Xi is said to be homoscedastic
effect of homo / hetero cedasticity
f residuals are homoscedastic, the t stats and hypothesis tests are valid.
If residuals are heteroscedastic, the estimated coefficients are still unbiased.
But the standard errors (needed for t-tests and confidence intervals) are now biased
Heteroscedasticity: Remedial Measures
Take logarithm transformations of the dependent and some of the independent variables
Calculate robust standard errors
Multicollinearity
multicollinearity may occur when two or more independent variables are highly correlated
leaving us unable to identify which variable is important
Detecting Multicollinearity
A sign of possible multicollinearity:
Insignificant t-stats for individual coefficients but significant F-stat for the regression
Detecting Multicollinearity by using the
Variance inflation factor:
This captures high correlations across more than two variables
Cross-sectional Data and Regression
Cross-sectional data are collected for the same period across different subjects.
spurious regressions are?
Significant regressions without valid economic relationships
Stationarity
A stationary series is one where the mean and variance of the data are constant over time
Autocorrelation
Correlation measures the strength of the relationship between two different variables
With time-series data, autocorrelation is the
correlation of a variable with its own past
