The dataset “_data2” contains

The dataset “_data2” contains information about score, study hours, age of student, family income, and whether the student participated in an after-school education program for a sample of students, which are randomly chosen from a large population.

Run a nonlinear regression with study hours and age on score, and test if the marginal effect of an additional hour of study on score depends on the level of study hour itself and the level of age. Assume the significance level is 5%.

1. The regression equation is _ _ ___
1. Analyze the summary of regression results (i.e. state the estimated value of regression coefficients, determine if each regression coefficient is different from zero for population by using t-value or P-value, interpret the use of adjusted R-squared). Conclude if the marginal effect of an additional study hour on score depends on the level of study hour itself and the level of age.

1. Screenshot the code and results.

 ID score study_hours age family_income joined_program 1 66 5 18 1500 Yes 2 77 5 19 13000 Yes 3 79 5 21 8000 No 4 87 6 19 9000 Yes 5 40 3 21 7500 Yes 6 31 1 18 8000 No 7 97 7 21 13000 No 8 42 3 19 3500 No 9 96 8 22 14000 Yes 10 77 5 20 10000 Yes 11 60 3 18 7200 Yes 12 87 6 20 14600 Yes 13 99 8 19 13080 No 14 25 1 20 7200 No 15 100 9 23 13400 Yes 16 42 3 18 1700 No 17 60 4 23 1600 Yes 18 57 4 19 1800 No 19 50 3 23 8000 Yes 20 72 5 20 1400 Yes 21 46 3 18 1400 Yes 22 39 1 24 1400 No 23 42 3 25 8500 No 24 87 6 19 11000 Yes 25 30 1 18 6600 No 26 42 3 18 700 Yes 27 76 5 19 15300 No 28 47 3 21 1500 Yes 29 72 5 19 5500 Yes 30 42 3 21 11000 Yes 31 57 4 18 5800 No 32 55 1 21 6600 No 33 80 5 19 6900 Yes 34 98 9 22 8500 No 35 27 2 20 6200 Yes 36 72 5 18 8600 No 37 87 6 20 16000 Yes 38 100 9 19 10500 Yes 39 57 4 20 13000 Yes 40 72 5 23 8000 No 41 27 2 18 6300 No 42 100 10 26 14000 Yes 43 88 9 18 21000 No 44 57 4 22 1800 Yes 45 38 2 22 5500 No 46 57 4 18 11000 Yes 47 80 12 21 12000 Yes 48 100 10 22 14000 Yes 49 89 7 18 16000 No 50 87 7 18 16000 Yes

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