Your parents would like to find out more about the effects of education on wage rates (in case they want to reclaim costs of raising you!). The data set "Q1_wages.xlsx" contains information on wages ($/hour), education and years of experience for 1,000 workers.
(a)i) Your parents ask you to use Excel to estimate the following model:
where Wage=earnings per hour, Educ = years of education and Exper = years of experience and Exper2 is the squared years of experience.Interpret the estimated regression coefficient of Educ. Is the sign of the coefficient what you would expect? Make sure to copy and paste your Excel regression output here.
ii) Test the null hypothesis that against the alternative that at the level of significance. Clearly state your conclusion and interpret what this tells us about the relationship between education and wages
Now consider the estimated coefficients of Exper and Exper2 and explain whether Exper and Exper2 should be included as explanatory variables, justifying your answer using some of the values reported in the regression output.
Can you think of any other variables that you parents have not controlled for (i.e. not included in the regression model) that may be related to both educational attainment and earnings? What does this imply about how they should interpret their estimate of the relation between wages and education.
(a)i) Now, estimate the following model:
where Migrant = 1 for workers born overseas; 0 otherwise andFemale=1 for female workers;
0 for male workers. Copy and paste your Excel output below
ii)Interpret the estimated coefficients on the dummy variables for Female and Migrant, and for each one test the null hypothesis that the coefficient on the dummy variable equals zero
iii)Explain what would be the economic rationale to include the interaction term between migrant and female.
iv)Compared with non-migrant males, by how much are wages higher or lower for migrant males, for migrant females and for non-migrant females (show working).
Carry out a joint test that the three dummy variables have coefficients that all equal zero at the a=0.05 level. What do you conclude? Make sure to show working and clearly state your hypotheses
Are the explanatory variables as a whole statistically significant? (i.e. R2=0)?Explain
(a)Report an appropriate statistic from the "Regression Statistics" table for each of the two models to compare their predictive performance. Which model do you consider to better and why?
wage 18.7 11.5 15.04 25.95 24.03 20 53.84 25 28.85 16.83 14.8 43.25 19.23 14 8 57.7 20 20.83 22 68.75 10.5 9.88 10.96 8.25 14.86 8.75 15.3 12.7 10.75 17.33 7.5 18.5 9 51.29 20.53 12.68 7.25 18.28 21.63 19.23 25 16.83 10.53 16.35 5.2 50 10 9 13 educ exper 16 12 16 14 12 12 16 12 16 13 12 16 12 14 12 21 12 18 11 14 12 13 12 13 18 12 12 12 13 12 10 12 13 21 14 18 12 14 16 14 12 16 12 13 13 13 13 12 14 39 16 13 11 51 30 30 34 31 31 45 33 33 15 23 41 50 24 27 41 27 25 22 11 3 45 34 40 6 15 27 19 30 25 38 42 16 23 7 34 25 38 15 44 5 18 28 32 29 exper2 female 1521 256 169 121 2601 900 900 1156 961 961 2025 1089 1089 225 529 1681 2500 576 729 1681 729 625 484 121 9 2025 1156 1600 36 225 729 361 900 625 1444 1764 256 529 49 1156 625 1444 225 1936 25 324 784 1024 841 migrant 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 18.25 36.05 11.3 11 7.5 7.5 25.63 25.95 19.23 25 28 9 29.75 8.75 15.55 25.63 17.19 10.5 12.7 9.46 28.85 47.13 9 72.13 30.77 28.84 26.93 8 8 18.75 13 34.62 39.9 10.25 15.37 19.23 13.45 27.5 10 13.03 7.88 8 16.83 13.8 10.3 11.5 12 35.89 28.85 16.95 12 16 12 10 12 16 12 18 16 13 14 3 12 3 12 14 18 12 14 12 18 16 14 12 21 16 14 12 13 13 13 21 13 16 12 12 12 13 14 12 12 6 16 12 13 14 16 18 16 12 13 20 29 12 29 4 23 26 37 34 27 33 22 19 34 24 47 9 29 35 12 17 25 27 29 16 32 7 7 44 35 12 32 18 33 29 42 20 18 31 40 14 13 36 56 28 29 21 34 35 169 400 841 144 841 16 529 676 1369 1156 729 1089 484 361 1156 576 2209 81 841 1225 144 289 625 729 841 256 1024 49 49 1936 1225 144 1024 324 1089 841 1764 400 324 961 1600 196 169 1296 3136 784 841 441 1156 1225 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 17 8 40.38 20 19.23 10 35.71 39.06 9 13.5 31.25 19.23 29.91 13.5 15 32.68 29.08 27.83 14.25 38.47 18.28 20 9 12 12 25.63 22.05 10.5 6.76 6.5 9.32 10.58 24.03 18 18.03 39.23 18.52 24.05 28.85 9.57 14.95 15.65 25 27.88 15.4 19.23 38 15.38 28.85 15.88 14 14 16 13 13 16 16 14 18 12 18 12 16 12 16 13 16 14 12 16 12 16 14 12 16 18 13 16 9 10 13 12 16 12 14 18 12 16 13 10 13 13 18 21 13 14 16 12 13 13 29 3 17 26 17 32 16 18 43 7 22 21 33 23 6 24 12 6 46 47 13 34 19 65 13 21 12 37 20 63 34 46 42 27 16 43 21 24 27 11 33 39 20 15 32 4 33 35 48 17 841 9 289 676 289 1024 256 324 1849 49 484 441 1089 529 36 576 144 36 2116 2209 169 1156 361 4225 169 441 144 1369 400 3969 1156 2116 1764 729 256 1849 441 576 729 121 1089 1521 400 225 1024 16 1089 1225 2304 289 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 25 11.35 15.38 30.76 18.75 72.13 13.75 24.05 17.5 43.25 9.93 24.63 36.3 30.9 11 12.5 28.85 10 25.35 12.31 21.27 17.49 23 36.05 9 27.3 21.63 17 14.29 35.1 16 7 21.63 9.25 15.43 21.25 34.63 10 15.38 45.23 12 10 14 31.25 50.95 37.5 15.88 23.08 8.52 10 16 14 12 16 12 16 12 13 12 18 12 16 13 16 14 12 13 12 16 13 12 12 13 18 12 13 16 13 16 18 12 12 12 14 12 16 12 16 16 14 16 12 13 12 18 21 13 12 0 14 9 38 51 19 29 28 32 30 39 8 32 38 44 35 15 29 39 9 22 23 38 30 37 37 27 31 24 19 4 35 24 14 34 39 18 36 37 17 38 42 9 35 10 40 22 36 44 27 44 37 81 1444 2601 361 841 784 1024 900 1521 64 1024 1444 1936 1225 225 841 1521 81 484 529 1444 900 1369 1369 729 961 576 361 16 1225 576 196 1156 1521 324 1296 1369 289 1444 1764 81 1225 100 1600 484 1296 1936 729 1936 1369 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 18 31.73 20 28 7.25 14.4 21.63 24.05 21 24.29 6 12.5 19.23 15.53 7.25 35.49 19.24 22.7 30.7 10 72.13 72.13 19.23 9.9 15 6.5 28.72 34.63 12.03 9 30 3.75 16.83 12.08 43.8 8.25 19.55 21.54 14.5 10.5 11.3 35 19.55 10.94 13.33 18 9.5 18 15 13 14 13 16 18 9 16 12 13 13 16 14 12 12 12 11 18 18 18 18 13 16 16 14 13 8 13 12 18 13 14 16 16 14 12 21 13 14 16 12 8 13 12 14 12 12 12 12 12 18 12 37 19 10 7 16 17 22 29 9 28 6 16 15 27 12 9 8 29 25 13 11 22 44 9 43 57 14 19 9 8 16 31 10 24 33 7 32 19 34 37 21 51 28 10 50 21 10 24 17 15 1369 361 100 49 256 289 484 841 81 784 36 256 225 729 144 81 64 841 625 169 121 484 1936 81 1849 3249 196 361 81 64 256 961 100 576 1089 49 1024 361 1156 1369 441 2601 784 100 2500 441 100 576 289 225 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 19.2 11.5 36.52 10 20.04 24.03 31.25 13.04 16 31.25 16.88 29.8 7.6 11 16.28 17.57 24.33 16.24 22 25 20 43 40.38 11.5 19.23 7.5 19.23 21.5 26 16.08 14 23.06 13.25 61.11 11.25 16.83 8 8.63 18.75 30.33 40.46 27.63 11 7.5 17.88 8 18.3 28.83 13 25.32 14 12 16 12 13 16 14 13 12 12 16 13 12 13 16 13 16 16 16 12 13 12 16 13 13 13 16 12 14 18 16 16 12 18 13 16 13 12 14 18 13 16 16 13 16 13 12 13 12 12 39 21 30 39 30 4 35 15 44 44 36 42 47 35 35 50 18 36 9 32 22 29 39 17 42 44 19 35 28 36 7 33 20 22 10 35 5 36 14 34 32 42 3 6 15 27 33 34 28 35 1521 441 900 1521 900 16 1225 225 1936 1936 1296 1764 2209 1225 1225 2500 324 1296 81 1024 484 841 1521 289 1764 1936 361 1225 784 1296 49 1089 400 484 100 1225 25 1296 196 1156 1024 1764 9 36 225 729 1089 1156 784 1225 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 18.9 17.86 9.26 18.49 14.43 24.05 6.87 19.24 24.05 20.09 26 21.15 27.4 38.45 12.86 10.3 11 15.13 24.05 13 20.2 7.5 8 7.25 11.5 24.05 24.05 13.73 7.93 8.75 13.2 15 15.39 8 35.25 14.68 12.4 12.5 10 21.67 20 13.08 7 19.23 15 6.5 8.5 6.35 19.24 20.63 12 12 12 12 12 18 16 18 18 16 12 16 13 16 12 12 16 12 14 12 16 11 13 8 13 13 12 13 13 16 10 12 12 12 16 18 12 13 12 18 12 14 12 16 14 12 12 12 14 13 38 45 43 39 26 30 9 24 10 9 53 14 36 33 34 14 43 32 45 13 17 9 5 18 64 35 55 26 27 35 25 38 41 19 25 12 37 12 36 26 30 16 36 14 28 24 14 17 7 34 1444 2025 1849 1521 676 900 81 576 100 81 2809 196 1296 1089 1156 196 1849 1024 2025 169 289 81 25 324 4096 1225 3025 676 729 1225 625 1444 1681 361 625 144 1369 144 1296 676 900 256 1296 196 784 576 196 289 49 1156 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24.05 48.55 13.16 12.75 19.57 8.53 10 24.33 11 33.65 14.91 14.16 10.78 21.36 38.23 36.71 6.25 27.1 10 8 7.5 10.38 13.73 54.05 17.3 20.3 7.14 25 31.15 9.5 8.1 8.5 25.96 13.75 12.5 9 57.69 72.13 36.05 19.79 50 7.49 16 40.38 33.65 38.45 52.88 13 24.05 8.75 3 18 16 12 16 13 13 12 14 18 16 12 13 16 12 13 18 16 12 16 12 13 16 16 12 14 12 16 14 12 12 12 14 16 14 12 16 14 16 12 18 12 12 21 16 18 16 12 12 16 36 42 4 28 13 5 6 40 41 34 38 6 44 33 36 19 15 29 21 29 18 6 22 31 42 6 18 14 28 8 10 9 14 9 30 20 43 32 6 46 15 40 33 31 32 32 43 50 17 8 1296 1764 16 784 169 25 36 1600 1681 1156 1444 36 1936 1089 1296 361 225 841 441 841 324 36 484 961 1764 36 324 196 784 64 100 81 196 81 900 400 1849 1024 36 2116 225 1600 1089 961 1024 1024 1849 2500 289 64 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 40.38 8.8 15.56 10 9.34 10.5 18 6.93 17.5 24.05 12.31 32.7 9.5 17.5 25 14.43 9.33 17.48 12.5 8 17.3 15.38 6.5 44.43 15.85 14.4 7.29 19.7 21 11 16.57 48.55 12 40.15 22.4 11.5 28.85 24.23 24.05 7.5 11.25 19.23 12.98 16.56 23 12 53.57 8.85 47.8 20 18 12 16 12 11 12 12 12 6 16 12 12 12 16 16 13 13 12 12 12 12 12 8 16 14 12 14 18 14 12 14 16 12 16 12 13 12 14 16 9 13 16 13 13 12 12 18 11 16 14 8 24 15 24 20 21 30 54 33 27 49 25 32 3 5 41 6 39 7 33 11 27 44 32 47 9 47 22 24 28 29 38 12 28 28 45 38 6 27 23 7 36 31 26 24 39 38 14 36 7 64 576 225 576 400 441 900 2916 1089 729 2401 625 1024 9 25 1681 36 1521 49 1089 121 729 1936 1024 2209 81 2209 484 576 784 841 1444 144 784 784 2025 1444 36 729 529 49 1296 961 676 576 1521 1444 196 1296 49 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1.97 10.51 9 9.73 38.45 28 27.23 13.03 30 10.1 16.25 15.25 35 57.68 50 9.63 10 15.23 10.5 10 20.1 8 17 35.17 9 12.9 12.75 24.05 10.19 38.45 14.25 12.03 19.23 8.75 29.1 33.65 16 13.88 25 15 25.18 17.5 36.8 32.68 28.83 25.25 16 18 14.5 41.35 18 12 13 14 16 16 12 12 16 14 12 12 13 21 16 12 14 12 12 16 12 12 13 18 13 16 9 18 12 14 12 6 13 14 13 16 12 3 12 13 13 12 18 18 16 13 10 12 12 18 51 38 11 13 39 17 40 27 26 18 14 43 10 16 43 42 29 44 37 4 40 49 9 26 54 11 28 25 38 33 35 21 27 33 39 31 20 64 42 8 25 34 10 17 33 34 11 18 21 44 2601 1444 121 169 1521 289 1600 729 676 324 196 1849 100 256 1849 1764 841 1936 1369 16 1600 2401 81 676 2916 121 784 625 1444 1089 1225 441 729 1089 1521 961 400 4096 1764 64 625 1156 100 289 1089 1156 121 324 441 1936 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 16.25 9 17.71 15.45 23.08 8 13.75 8.76 8.78 7.75 28.85 20.2 9.23 14 25 21.48 12.97 27 37.5 21.15 2.88 9.75 16 13 48.08 7.7 22.6 5.73 14.4 33.5 18.82 17.5 11 9.35 16.25 9.5 76.39 36.67 9 51.52 15 38.75 15.38 43.28 17.3 33.65 2.5 16.25 14.6 12.5 14 13 13 14 12 13 12 9 13 6 16 16 12 16 12 12 13 12 12 14 13 11 12 12 21 12 18 6 12 12 11 12 16 16 6 13 14 18 18 13 21 18 16 21 16 16 12 12 12 16 29 8 28 35 34 6 43 40 16 32 28 35 38 5 36 23 6 23 25 26 12 40 15 32 30 38 18 45 42 13 42 11 20 40 39 46 20 25 44 14 18 23 7 12 17 20 46 35 28 4 841 64 784 1225 1156 36 1849 1600 256 1024 784 1225 1444 25 1296 529 36 529 625 676 144 1600 225 1024 900 1444 324 2025 1764 169 1764 121 400 1600 1521 2116 400 625 1936 196 324 529 49 144 289 400 2116 1225 784 16 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 36.05 19.23 9.24 9.15 36.05 16.25 14.55 29.4 50.03 28 28.83 72.13 13 6.14 36.33 18.06 22.64 15 42.11 13.8 55 10.4 24.03 20.63 12.5 24.95 23.49 28 9.5 34.63 48.55 8.06 17.36 28.44 35.75 13.95 9 21 20 8.33 65.98 13 21.33 15 8.1 15 15 18.75 9.78 9.83 21 12 12 13 16 12 12 21 13 16 16 16 16 11 16 12 14 14 16 13 16 13 16 16 16 13 16 14 13 14 16 13 13 14 14 14 12 13 12 13 21 12 12 16 11 9 12 18 12 12 31 31 34 8 32 10 19 31 39 30 11 41 37 51 24 35 33 20 44 41 30 18 35 30 49 19 10 36 35 31 14 13 36 42 27 20 16 41 12 5 37 42 20 38 47 23 34 11 6 27 961 961 1156 64 1024 100 361 961 1521 900 121 1681 1369 2601 576 1225 1089 400 1936 1681 900 324 1225 900 2401 361 100 1296 1225 961 196 169 1296 1764 729 400 256 1681 144 25 1369 1764 400 1444 2209 529 1156 121 36 729 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 12.5 30.44 12.5 13.45 29.8 26.78 10 21.52 12.87 22.5 15 24.79 6.66 10.73 10.5 13.16 9.75 17 36.05 41.54 34.18 50 6.73 6.38 20.6 6.75 10 26.78 72.13 21.63 44.23 17.35 25.73 50 20 8 34.63 9.5 7.7 9 16 8.75 11 13.82 13.1 19.23 18.45 14.43 21.93 12 12 16 13 12 13 16 18 18 12 16 12 12 12 14 12 10 12 12 14 16 12 18 12 18 16 12 13 12 18 16 18 13 14 16 14 12 14 13 3 16 13 12 12 16 12 14 12 13 16 23 36 2 8 14 42 5 11 22 48 32 40 32 21 48 33 40 8 31 23 22 42 33 14 37 26 14 8 39 38 38 27 33 29 9 13 25 19 53 19 3 38 20 28 37 17 35 32 48 17 529 1296 4 64 196 1764 25 121 484 2304 1024 1600 1024 441 2304 1089 1600 64 961 529 484 1764 1089 196 1369 676 196 64 1521 1444 1444 729 1089 841 81 169 625 361 2809 361 9 1444 400 784 1369 289 1225 1024 2304 289 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 16.1 14.5 15.71 28.18 28.85 57.7 28.85 23.08 25.25 15 23.08 21.88 8.26 12.03 8.5 40 30 28 9.5 23.07 22.3 7.52 38.45 18.75 2.52 26.14 36.06 12 15.38 16.23 31.25 20 10.38 9.48 25 10.49 11.5 8 14.5 38.45 11.5 45.65 14 5.33 12.9 23.63 30.3 20.2 31.25 26.44 14 13 16 12 14 16 18 13 18 12 16 13 12 16 12 16 6 21 12 16 16 12 18 8 12 12 13 16 14 12 16 14 13 12 13 14 12 12 16 18 11 8 12 12 16 16 16 16 18 13 29 32 38 6 27 28 39 37 27 33 20 37 9 20 27 22 18 14 15 8 24 6 41 22 22 39 34 19 30 12 15 24 24 15 11 14 9 60 9 21 20 31 30 62 9 20 33 14 18 8 841 1024 1444 36 729 784 1521 1369 729 1089 400 1369 81 400 729 484 324 196 225 64 576 36 1681 484 484 1521 1156 361 900 144 225 576 576 225 121 196 81 3600 81 441 400 961 900 3844 81 400 1089 196 324 64 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 23 32.68 18.25 20.2 22.6 7.45 13 8 26.1 46.16 8 16 8.76 33.65 11.78 47.62 24.45 34.18 31.73 18.45 34.62 21.36 38.46 2.3 22.65 4.33 31.25 8.5 22.76 19.55 17.96 24.04 44.24 31.88 28.83 39.9 61.82 25.38 12 8.65 38.45 38.45 7.2 7.5 25 18.48 61.54 15.8 39.43 10 12 14 13 12 12 10 12 12 12 16 12 12 16 12 13 18 12 16 16 12 13 12 18 16 13 8 18 14 13 12 14 12 12 14 21 14 18 16 16 16 16 10 12 13 14 16 18 12 12 12 39 40 27 13 32 28 56 49 10 18 13 38 32 22 39 42 36 28 21 45 32 38 23 41 34 20 10 4 43 28 29 16 42 39 39 28 39 8 39 14 33 53 9 6 24 31 26 24 32 46 1521 1600 729 169 1024 784 3136 2401 100 324 169 1444 1024 484 1521 1764 1296 784 441 2025 1024 1444 529 1681 1156 400 100 16 1849 784 841 256 1764 1521 1521 784 1521 64 1521 196 1089 2809 81 36 576 961 676 576 1024 2116 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 6.25 28.85 15.33 23.3 9 21.8 15.33 10 20.17 25.64 10.5 10.38 16.83 15.75 19.24 8.65 10.85 18.7 16.22 9 12 6.77 20.13 15 10 12 17.96 37.6 14.43 42 41.52 23.08 24.53 9.52 12 13.8 42 10.55 10 12.75 8.75 28.85 25 25 25 9 72.13 21.03 35.23 9.4 21 18 12 18 12 13 12 12 16 16 13 13 16 12 14 12 16 13 11 9 12 12 14 13 12 12 16 16 13 16 13 16 16 13 16 12 13 12 13 14 12 16 16 18 16 12 18 16 16 12 11 34 31 40 9 28 22 11 45 15 41 44 24 39 34 28 26 47 26 24 13 23 35 22 26 38 19 31 9 28 30 25 13 30 28 48 21 7 10 35 40 12 4 26 11 29 43 22 42 61 121 1156 961 1600 81 784 484 121 2025 225 1681 1936 576 1521 1156 784 676 2209 676 576 169 529 1225 484 676 1444 361 961 81 784 900 625 169 900 784 2304 441 49 100 1225 1600 144 16 676 121 841 1849 484 1764 3721 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 12.5 37.5 6.5 52.5 7.5 31.25 25 10.48 17.75 13 5.97 25 18.5 11.55 44.87 7.4 11.85 24.17 7.2 18.18 14 36.05 13.61 34.63 17.3 14 29.9 15 16.14 38 7.98 24.03 23.51 22.43 15.75 11.5 21.63 45.45 35.63 19.05 30.63 16.35 12.4 31.25 14.1 24 27.49 7.9 11 16.83 13 14 12 13 14 16 18 12 12 13 12 21 13 11 16 8 12 16 14 13 12 13 12 16 16 14 18 13 18 16 12 18 21 21 13 13 18 18 12 9 13 14 12 12 14 14 16 12 12 12 7 56 54 27 17 10 11 40 22 37 43 27 37 19 24 16 50 23 15 18 20 19 22 8 10 58 44 11 7 15 19 23 31 20 41 51 32 42 22 38 28 35 11 21 38 28 30 40 15 38 49 3136 2916 729 289 100 121 1600 484 1369 1849 729 1369 361 576 256 2500 529 225 324 400 361 484 64 100 3364 1936 121 49 225 361 529 961 400 1681 2601 1024 1764 484 1444 784 1225 121 441 1444 784 900 1600 225 1444 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 57.68 11 6.4 16.83 19.58 28.52 12 21.15 14.9 14.26 8.15 32.3 7 22.5 30 24.14 72.13 11.8 60.1 19.23 12.82 15 21.25 11.51 28.83 25.64 12.26 10 8 25.48 52.88 19.22 19.23 15 19.23 23.58 4.58 9 15 25 29.8 64.11 19.23 27.4 21.63 10 11.55 38.45 17 64.11 16 16 12 14 11 12 12 13 12 12 11 16 12 12 13 16 18 14 18 12 16 16 14 6 12 21 16 12 12 16 21 16 18 12 16 13 12 12 12 13 18 18 14 12 12 12 13 16 12 16 35 5 27 23 36 24 30 23 36 28 46 29 12 22 35 14 36 23 31 10 7 11 10 16 20 19 23 23 8 34 39 44 14 32 37 35 38 31 14 36 37 21 24 23 26 32 25 10 8 32 1225 25 729 529 1296 576 900 529 1296 784 2116 841 144 484 1225 196 1296 529 961 100 49 121 100 256 400 361 529 529 64 1156 1521 1936 196 1024 1369 1225 1444 961 196 1296 1369 441 576 529 676 1024 625 100 64 1024 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 28.1 21.25 10.58 16.67 31.75 25.75 17.42 21.63 7.97 48.08 21.25 10 19.63 16 19.23 28.85 8.5 60 9.63 9 37.18 33.65 16.25 14.43 10 19.23 19.23 7 24.03 7.57 12.5 11.4 13 25 22.13 13.5 8 11.25 14.43 9.8 17.3 8 35.76 10 19.23 20 10.25 17.63 14.53 5.9 14 8 12 10 16 13 13 16 13 18 16 14 12 12 16 12 12 14 12 13 12 13 12 16 12 16 18 11 21 13 12 13 16 12 12 13 12 12 12 18 12 12 16 12 16 14 16 12 13 14 28 22 23 44 8 29 48 42 20 26 13 22 38 54 25 38 39 37 35 10 20 27 42 9 15 3 30 44 17 6 22 15 50 33 34 39 7 16 36 46 44 7 17 31 28 29 38 15 47 4 784 484 529 1936 64 841 2304 1764 400 676 169 484 1444 2916 625 1444 1521 1369 1225 100 400 729 1764 81 225 9 900 1936 289 36 484 225 2500 1089 1156 1521 49 256 1296 2116 1936 49 289 961 784 841 1444 225 2209 16 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 18.46 39.33 7.5 16 14.5 62.03 16.35 24.44 17 14.96 67.3 21 20.4 16 12.82 20 12 35.1 12.5 31.73 12.38 12.5 21 21.38 12.5 57.7 29.76 18 7.25 9 27.7 28 12 9.7 7 18.24 25.95 16.04 14 40.08 8 16.93 11.5 21.15 7.2 23.1 16.83 28.85 11.25 7.5 12 12 11 18 13 16 12 12 13 16 12 13 16 10 14 18 12 16 13 16 8 12 14 13 12 12 13 12 13 14 21 3 16 13 12 21 18 16 12 18 12 16 12 13 16 12 16 13 14 8 12 32 38 16 27 44 25 24 15 11 42 32 4 16 22 11 18 22 13 30 63 35 19 11 8 26 41 9 11 44 13 32 37 8 24 8 40 5 20 39 7 8 19 27 21 43 27 7 5 36 144 1024 1444 256 729 1936 625 576 225 121 1764 1024 16 256 484 121 324 484 169 900 3969 1225 361 121 64 676 1681 81 121 1936 169 1024 1369 64 576 64 1600 25 400 1521 49 64 361 729 441 1849 729 49 25 1296 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 8.5 13 22 484 0 1
