1. REGRESSION DIAGNOSTICS1

2. Problems Influentials and outliers Heteroscedasticity Autocorrelation
Multicollinearity – relationship of independent variables

3. EXCURSUS - RESIDUALS 3

4. Residuals - review Unstandardized residuals H = hat matrix
Predicted residuals

5. Residuals - review
Standardized residuals
Jackknife residuals

6. I. Influentials
If omitted from computation big change in regression coeffs can be found.
Goal: to find and exclude

7. Influentials -diagnosis
DFBETA(-i)=b-b(-i)
Rule of thumb: Problem if NDFBETA>2/√n
Note : NDFFIT problem if NDFFIT>2/√(n/p)

8. II. Heteroscedasticity
Assumption for regression: variance of error is the same for all values of indep. variable
Checking: Charts for residuals vs. ind. vars
Consequence: big standard errors of coeffs, t-tests statistically insig.
Tests - Glejser, Goldfeld-Quandt tests
Analytical solution: weighted LS (WLS)

9. Glejser’s test
Model for residuals on ind. vars :

10. III. Multicollinearity
Estimate:
Strong relationship between ind. variables:
X´X is singular matrix or nearly singular Consequence: standard errors of coeffs are inflated, t-test statistically insignificant, estimates are not stable

11. Multicollinearity
Diagnosis: Correlation of ind. vars – cor. coeff>0,8
Other options:
a) Tolerance (1-R2j)
b) VIF = 1/(1-R2j) VIF diagonál cells R-1
c) Conditon index: square root of ratio: max lambda/min lambda ROT* > 30 → problem
*ROT=Rules of thumb

12. Multicollinearity Solution Ignore  Leave out variable Get more data
Use factor analysis (see later)
Ridge regression Biased estimates but smaller standard erorrs (slight change in diagonal’s elements)

13. IV. Autocorrelation
Assumption for regression: variance of error is independent for individual observations
Checking: Charts for residuals vs. time
Consequence: big standard errors of coeffs, t-tests statistically insig.
Tests - Durbin-Watson
Solution: weighted LS
Autocorrelation is present in time series (usually not used in social sciences)