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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