Hence our Q statistics is as follows: 0.052,44 4 1(444 1)185.66 220.127.116.112RESETQF 0.052,39185.66 138.41 39.138.412RESETQF0.052,396.66(3.23)RESETQFSince 6.66 is greater than 3.23, we can reject the null hypothesis that the coefficients of the added variables are jointly zero, allowing us to conclude that there is a specification error in Equation (5). 3. Information Criteria A. Theil’s Adjusted R2Criterion (2R)An important property of R2is that it is a non-decreasing function of the number of explanatory variables present in the model; as the
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected]Lecture Notes 10 number of explanatory variables increases, R2almost invariably increases and never decreases. Stated differently, an additional X variable will not decrease R2. In view of this, in comparing two regression models with the same dependent variable but differing number of X variables, one can choose the model with highest R2. To compare two R2terms, one must take into account the number of X variables present in the model. This can be done readily if we consider an alternative coefficient of determination, which is as follows: 222ˆ(1)1(1)ttuTkRyT (1) where k= the number of parameters in the model excluding the intercept term. The R2thus defined is known as the adjusted R2, denoted by 2R. B. Akaike Information Criterion (AIC) Imposing a penalty for adding explanatory variables to the model is the basis of the AIC criterion: