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Question 3: The dataset _data2 contains information about score, study hours, age of student, family income, and whether the student participated in an after-school education
Question 3:
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%.
- The regression equation is _ _ ___
- 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.
- 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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