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ECON301_Handout_13_1213_02

# Hence our q statistics is as follows 005 244 4 1 44 4

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Hence our Q statistics is as follows: 0.05 2,44 4 1 (44 4 1) 185.66 138.41 . 138.41 2 RESET Q F   0.05 2,39 185.66 138.41 39 . 138.41 2 RESET Q F 0.05 2,39 6.66 ( 3.23) RESET Q F Since 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 R 2 Criterion ( 2 R ) An important property of R 2 is 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: Lecture Notes 10 number of explanatory variables increases, R 2 almost invariably increases and never decreases. Stated differently, an additional X variable will not decrease R 2 . 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 R 2 . To compare two R 2 terms, 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: 2 2 2 ˆ ( 1) 1 ( 1) t t u T k R y T   (1) where k = the number of parameters in the model excluding the intercept term. The R 2 thus defined is known as the adjusted R 2 , denoted by 2 R . B. Akaike Information Criterion (AIC) Imposing a penalty for adding explanatory variables to the model is the basis of the AIC criterion: