neighbor983/machine_learning_assignment_four

machine_learning_assignment_four

Assignment 4

A group of 20 students studied 0 to 6 hours for the exam. Some passed and others failed. Results are given below (Data is taken from Wikipedia).

Student	Hours Studied - x	Result (0 – fail, 1 – pass) - y
1	0.5	0
2	0.75	0
3	1.00	0
4	1.25	0
5	1.50	0
6	1.75	0
7	1.75	1
8	2.00	0
9	2.25	1
10	2.50	0
11	2.75	1
12	3.00	0
13	3.25	1
14	3.50	0
15	4.00	1
16	4.25	1
17	4.50	1
18	4.75	1
19	5.00	1
20	5.50	1

1. Determine the optimal linear hypothesis using linear regression to predict if a student passes or not based on the number hours studied.
2. Determine the optimal logistic hypothesis using logistic regression to predict if a student passes or not based on the number hours studied.
3. Plot both hypothesis function 0 < x < 6. Compare and explain the two results obtained.
4. Develop a logistic regression-like algorithm for the following cost function.

Y = 1 - Cost function goes from 100 to 0 linearly as hypothesis function goes from 0 to 1

Y = 0 - Cost function goes from 0 to 100 linearly as hypothesis function goes from 0 to 1

Compare results with those of the standard logistic algorithm.