We are given a 186 x 7 matrix that contains the points each student received on a seven question final exam. There are seven questions per student, where each question can give the grade 0 to 12. All seven questions give the final grade for each student. Each row is equal to one student.

a) Find the mean and standard deviation of the grades (two numbers). Find the mean and standard deviation of the grades for unique questions on the exam (10+10 = 20 numbers).

b) A simple way to predict the final grade on unique exams is to add together the points in the first five questions, and then double it. What is the RMS estimation error if we use the method?

c) Using regression analysis, create a model that predicts the final grade for unique exams, that only uses points received on question 1-5 as inputs. Specify the coefficients, and interpret them. What is the RMS estimation error for the model?

If the following information is put into Excel, it is possible to retrieve the data, while coding, by using scores = np.loadtxt('FILENAME.csv', delimiter=','):

12	12	11	0	12	12	8
6	4	0	0	0	3	12
12	12	9	0	12	12	12
12	12	9	12	10	12	12
12	12	12	12	12	12	12
12	12	11	12	12	12	8
12	12	12	12	2	12	8
12	12	6	12	0	8	12
12	12	6	0	0	0	8
12	4	0	12	0	12	12
12	8	12	12	12	12	8
12	12	9	12	12	12	12
6	12	12	0	10	12	6
12	12	9	12	0	12	8
12	12	7	0	9	12	10
6	12	0	0	0	3	10
12	4	2	12	12	12	12
12	12	0	12	12	10	10
12	12	0	0	0	3	0
12	12	12	12	3	3	12
12	12	9	0	12	0	12
8	12	9	12	0	3	12
12	10	12	12	0	10	4
12	12	12	0	0	12	12
12	12	9	12	12	3	8
0	6	0	12	0	3	6
6	12	0	12	12	8	12
12	12	0	12	0	2	7
6	12	4	0	0	12	6
12	12	12	12	0	10	12
12	12	9	12	2	2	12
6	4	0	0	0	2	6
12	12	9	12	12	3	12
6	12	11	0	0	12	12
12	12	0	12	0	10	4
12	12	6	0	3	3	8
12	8	12	12	4	12	10
12	12	6	12	12	3	8
12	12	6	12	3	12	8
6	8	3	12	12	0	12
6	2	8	0	0	0	0
12	12	0	12	9	0	12
0	12	4	0	0	12	8
12	12	6	12	3	12	12
12	12	6	0	3	12	6
12	12	0	12	0	3	10
12	12	9	0	12	12	12
12	4	0	12	12	6	10
12	2	11	12	3	2	12
12	12	11	12	0	0	12
12	12	12	12	0	0	12
6	12	3	12	3	10	12
12	12	8	12	12	12	12
6	12	12	12	12	12	12
12	12	6	0	12	12	4
12	12	9	0	12	12	8
12	12	12	0	12	12	12
12	12	6	12	3	10	8
12	8	12	12	0	7	12
12	12	0	12	12	7	12
12	12	12	12	10	3	10
12	12	12	12	12	12	12
6	12	6	12	0	3	10
7	12	6	4	3	12	10
12	12	6	12	12	12	10
12	12	12	0	12	12	8
6	8	12	12	3	12	8
6	12	0	0	0	12	6
12	12	12	12	0	10	8
12	12	12	12	12	12	12
12	12	12	12	12	12	12
12	12	3	12	0	3	12
12	12	0	12	0	12	12
6	12	12	12	12	3	4
6	12	3	12	0	12	6
12	12	6	0	12	10	8
6	12	12	12	12	0	8
12	12	9	12	0	3	8
12	12	0	12	0	3	10
12	12	9	12	0	11	10
12	12	12	12	12	12	8
12	6	0	0	0	0	6
12	12	3	12	0	12	8
12	12	0	12	0	12	6
0	12	9	0	10	3	8
12	4	9	12	0	10	12
2	12	6	12	12	2	12
0	12	2	12	12	3	12
6	12	6	12	0	12	8
12	12	0	12	0	12	6
12	12	9	12	12	12	8
12	12	0	12	3	12	12
0	4	0	0	0	3	8
12	12	0	0	12	10	8
12	12	12	12	0	12	12
12	12	12	0	0	12	8
0	6	6	0	6	3	4
12	12	3	12	10	12	12
12	12	12	12	12	12	6
6	4	6	0	12	3	0
12	12	9	0	0	12	12
6	12	12	12	12	12	12
6	12	8	12	12	0	12
12	12	6	0	0	6	12
12	12	12	12	12	11	12
12	12	12	12	10	12	12
12	12	9	12	3	10	12
12	12	12	12	12	10	8
12	12	0	12	6	3	12
12	12	0	12	0	3	12
12	12	12	12	12	12	12
12	12	12	12	0	12	12
12	12	12	12	12	12	8
12	12	12	12	10	12	12
12	12	12	12	0	12	12
12	12	0	12	0	12	8
12	12	5	12	0	12	8
12	12	9	0	0	10	8
12	12	0	12	0	3	12
12	12	12	12	6	12	8
12	12	0	0	12	3	10
12	0	0	0	12	0	12
12	4	12	12	3	0	12
12	12	12	12	10	12	12
12	12	12	0	12	3	12
12	4	12	12	0	3	10
6	12	12	12	0	2	8
6	12	0	12	0	11	5
12	8	0	12	5	3	8
12	12	12	12	12	12	8
12	12	1	12	2	12	12
12	12	6	12	12	3	10
6	12	9	12	5	12	12
12	12	12	12	12	10	8
12	2	12	12	3	10	12
12	12	1	12	12	3	12
12	4	10	12	12	12	12
6	12	0	0	0	12	12
6	12	11	0	0	3	8
0	0	6	12	0	3	12
12	12	10	12	12	3	12
12	4	10	0	0	0	6
12	12	12	12	0	3	12
12	12	12	12	0	10	8
6	4	6	0	0	2	12
6	12	6	12	12	12	12
12	12	11	12	5	12	10
12	12	6	12	0	12	8
12	8	11	12	3	3	6
12	12	9	12	0	3	12
6	12	0	0	0	12	12
12	12	11	12	0	10	12
12	12	12	0	0	12	12
12	12	12	12	0	0	12
12	12	7	12	0	3	8
12	12	0	12	12	10	12
12	12	6	12	12	11	12
12	12	10	0	0	3	8
12	12	12	12	0	10	12
12	4	7	12	12	0	10
6	12	1	12	0	11	8
6	12	9	12	2	12	12
12	12	12	12	12	12	8
12	0	6	12	3	2	4
12	12	12	12	12	12	12
12	12	6	12	0	2	6
12	12	12	12	12	0	12
12	12	12	12	12	12	12
12	12	0	0	0	2	8
12	12	6	12	0	12	8
12	12	9	12	12	12	12
12	12	12	12	0	12	12
12	12	0	12	0	3	4
12	12	0	12	0	12	6
12	12	9	12	12	12	8
6	12	0	12	0	2	12
6	12	10	12	10	12	12
6	4	0	12	0	10	12
12	12	7	12	12	12	12
6	12	12	12	5	0	8
12	12	12	12	12	12	12
12	12	12	0	0	6	12
12	8	9	12	12	12	12
12	12	12	12	12	12	12
12	12	12	12	12	12	12
12	12	12	12	12	10	12