You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. What is the most likely cause of these results?

 

　　A     Incorrect standard errors.

 

　　B     Heteroskedasticity.

 

　　C     Serial correlation.

 

　　D     Multicollinearity.

 

　　解析：

 

　　Answer: D

 

　　Explanation: Age and experience are highly correlated and would lead to multicollinearity. In fact, low t-statistics but a high R2 do suggest this problem also.

 

　　知識點：

 

　　Multicollinearity

 

　　Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related.

 

　　l  Perfect multicollinearity arises when one of the regressors is a perfect linear combination of the other regressors.

 

　　l  Imperfect multicollinearity arises when one of the regressors is very highly correlated – but not perfectly correlated – with the other regressors. When conducting regression analysis, we need to be cognizant of imperfect multicollinearity since OLS estimators will be computed, but the resulting coefficients may be improperly estimated. The most common way to detect multicollinearity is the situation where t-tests indicate that none of the individual coefficients is significantly different than zero, while the R2 is high.