Selected Regression Problems | |||||
Problem | Identified by | Causes | Effect of Problem | Solution | |
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 t and F tests are no longer valid.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.)3 | 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. |