2 Question 2 Suppose we have some binary observations on whether a student pass the course optimization method, and the

[answerhappygod]

2 Question 2 Suppose We Have Some Binary Observations On Whether A Student Pass The Course Optimization Method And The 1 (57.15 KiB) Viewed 55 times

2 Question 2 Suppose We Have Some Binary Observations On Whether A Student Pass The Course Optimization Method And The 2 (137.69 KiB) Viewed 55 times

2 Question 2 Suppose we have some binary observations on whether a student pass the course optimization method, and the the number of hours each student spending studying Hours (tk) 0.50 0.75 1.00 1.25 1.50 1.75 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 4.00 4.25 4.50 4.75 5.00 5.50 Pass ( 4 ) 0 1 0 0 11 1 1 Suppose that we want to fit some binary observations with the following function 1 Yk = = f(xk) = 1+e-(Bo+B12k) 0 0 0 0 0 0 1 1 0 1 1 1 1 =
which is often referred to logistic regression. Pk are the probabilities that corresponding yk will be (pass) and 1 – Pk are the probabilities that will be zero(failed). We wish to find the parameters Bo and B1 which give the best fit to the data. The measure of goodness fit is given by the likelihood functions L= II px II (1 – Px) k:Vk=1 k:gi=0 and the best fit is obtained when L is maximized. The maximum of L will also be the maximum of the log-likelihood l,defined as K l= In (Px) + In (1 – Px) = (4x In (Px) + (1 – Yx) In (1 – Px)) (1) k:9k=1 kyk=0 k=1 1. verify (1). 2. calculate ve 3. calculate vel 4. use the given data, write a Newton methods to fit the data, make a contour plot to denote how the solutions converge in the Bo - Bi plan. 5. specify that how you choose the initial values. 6. compare your results with other fitting tool box, and write your own logistic regression program which can work versatily with as little as human interactions.