Selected Regression Problems   
ProblemIdentified byCausesEffect of ProblemSolution 
Autocorrelation.1
Serial Correlation Random Tracking (error terms are correlated) 

1. Durbin-Watson Statistic

2. Von Neumann Statistic

3. Elements off of the main diagonal of the variance- covariance matrix are non-zero.

4. Plot of residuals or residuals squared shows a pattern. 

1. Inertia in time series

2. Omitted variable

3. Incorrect functional form

4. Cobweb pattern

5. Lags in time series

6. Manipulations of data such as moving averages or exponential smoothing

1. Estimators are still linear and unbiased and consistent.

2. Residuals variance underestimates the true variance.

3. R squared may be overestimated.

4. Standard errors of regression coefficients underestimated.

5. t and F tests are no longer valid.

1. Respecify model

2. Use first differences

3. Maximum liklihood method

4. Generalized least squares (GLS). There are several procedures used to estimate r in GLS. Durbin-Watson procedure; Cochrane-Orcutt; Theil-Nagar modification; non-linear least squares.

 
Heteroschedasticity (error term variance is not constant)2

1. Plot of residuals squared against estimated Y.

2. White test

3. Park Test

4. Glejser test

5. Goldfield-Quandt ratio

6. Spearman's rank correlation test

7. Breusch-Pagan test

8. Bartlett test

9. Szroeter's tests 

1. Improvement in data collection techniques may reduce error.

2. As people learn their errors of behavior may decrease.

3. Errors are percentages.

4. Omitted variable.

5. Misspecified model.

1. Coefficients are linear and unbiased and consistent.

2. Standard errors of coeffeicients underestimated.

3. T tests unreliable. 

1. Weighted least squares (WLS).

2. Maximum likelihood method.

3. Transform the data and perform regression again.

4. Include other variables.

5. Different functional form. 

 
Multicollinearity (significant correlation among independent variables.)

1. High R squared but few significant t ratios.

2. Significant correlation between independent variables.

3. Auxilliary regressions.

4. Eigenvalues and condi-tional index.

5. Tolerance coefficient.

6. Higher correlation between indepedent variables than with dependent variable. 

1. Poor design of model

1. Coefficient standard errors are unreliable.

2. T tests unreliable.

3. F test reliable. 

1. Proxies

2. Combine variables

3. Transform variables

4. Ridge regression

5. Principal component regression

6. Stein-like estimators

7. Large number of observations. 

 
      
1See Brown, 163-92; Gujarati, 353-92; Judge, Griffiths, Hill, Lutkepohl, and Lee, 275-332.     
2See Brown, 193-216; Gujarati, 316-42; Judge, Griffiths, Hill, Lutkephohl, and Lee, 419-55.     
3See Brown, 110-16; Gujarati, 283-309; Judge, Griffiths, Hill, Lutkepohl, and Lee, 896-930.