7. A researcher is trying to determine the explanatory variables of hourly earnings of 104 workers in Korea. These are the variables the re- searcher is using in his experiment: E is hourly earnings in KRW, S is years of schooling, SCR is a score on literacy test, and MAT is a score on a typical math test. SCR and MAT have a total score of 100, and the correlation between them is 0.81. Researcher decided to take log on the hourly earnings and created a variable InE and hypothesized that there are 3 possible models and fitted the data accordingly. (Standard errors stated in parenthesis) (1) In E = 2.02 +0.063S+0.0044SCR+0.0026M AT RSS = 2,000 (1.81) (0.007) (0.0011) 0.0010 In E = 1.72 +0.050S+0.0068 AV ER RSS = 2,045 (2) (1.78) (0.005) (0.0010) In E = 2.02 +0.063S+0.0088AV ER-0.0018M AT RSS = 2,000 (1.81) (0.007) (0.0022) 0.0012 (3) where AVER = SCR+MAT (a) Show that the model(2) is a restricted version of the model (1). State the restriction. (b) Perform F test of the restriction. (c) Show that model (3) is a reparametrized version of the model (1). Perform t test of the restriction of the model (2). (d) Perform a test of hypothesis that MAT has a greater effect on earnings than the SCR. 7. A researcher is trying to determine the explanatory variables of hourly earnings of 104 workers in Korea. These are the variables the re- searcher is using in his experiment: E is hourly earnings in KRW, S is years of schooling, SCR is a score on literacy test, and MAT is a score on a typical math test. SCR and MAT have a total score of 100, and the correlation between them is 0.81. Researcher decided to take log on the hourly earnings and created a variable InE and hypothesized that there are 3 possible models and fitted the data accordingly. (Standard errors stated in parenthesis) (1) In E = 2.02 +0.063S+0.0044SCR+0.0026M AT RSS = 2,000 (1.81) (0.007) (0.0011) 0.0010 In E = 1.72 +0.050S+0.0068 AV ER RSS = 2,045 (2) (1.78) (0.005) (0.0010) In E = 2.02 +0.063S+0.0088AV ER-0.0018M AT RSS = 2,000 (1.81) (0.007) (0.0022) 0.0012 (3) where AVER = SCR+MAT (a) Show that the model(2) is a restricted version of the model (1). State the restriction. (b) Perform F test of the restriction. (c) Show that model (3) is a reparametrized version of the model (1). Perform t test of the restriction of the model (2). (d) Perform a test of hypothesis that MAT has a greater effect on earnings than the SCR