{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

IEOR 165 Lecture 7 June 9 2009

# IEOR 165 Lecture 7 June 9 2009 - Lec t ur e No t es IEOR...

This preview shows pages 1–3. Sign up to view the full content.

Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry Quiz 1 June 16 (2 – 3 pm) 2 Questions on Estimation HW 1 and 2 2 Sided Notes Quiz 2 June 23 (2 – 3:30 pm) 2 Questions on Hypothesis Testing HW 3 2 Sided Notes Regression Analysis Recap: Y = a + bx + ε , where x is the input and Y is the output = , = 0 Varε σ2 Data , , = , …, xk Yk k 1 n Objectives: : Find Estimates for a and b AND : Find Estimates that minimizes the sum of squared deviations SSD = = - - SSD k 1nYk A Bxk2 = = Ybar 1nk 1nYk = = xbar 1nk 1nxk = = - Sxx k 1 nxk xbar2 = = - ( - ) SxY k 1 nxk xbar yk ybar = = - SYY k 1 nyk ybar2 = - Ahat Ybar Bhatxbar | forecast for the mean response = = + * μx EYxis Yhat Ahat Bhat x = Bhat SxYSxx = + μx a bx = , = = We need to see if EYhat μx EAhat a?EBhat b?are they unbiased?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry (1) : = Let's calculate EAhat first to show it a = - * EAhat EYbar EBhat x We we first calculate E[Ybar] = = = = + = + * EYbar E1nk 1nYk 1nk 1na bxk a b xbar (2) Substitute: (3) = - * EAhat EYbar EBhat x = + * - * a b xbar EBhat xbar = + - * a b EBhat xbar , We conclude that if Bhat is an unbiased estimator of b then Ahat is unbiased estimator of a (4) = * EBhat 1Sxx ESxY (5) Now what is SxY? = = - - SxY k 1nxk xbarYk Ybar : Substitute = = - + - - * ESxY k 1nxk xbara bxk a b xbar = = - - = k 1nxk xbarxk xbarb bSxx : Therefore = * = EBhat 1Sxx bSxx b (6) So we are able to make the original conclusion. (7) (8) (9) So: Ahat is an unbiased estimator of a AND Bhat is an unbiased estimator of b (10) (11) Next Objective: So now we need to construct CI for a and b. To do so, we need
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern