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%.

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