Take Home Midterm (2015)

Take Home Midterm (2015) - MS&E 226 Small Data Take-Home...

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MS&E 226 Take-Home Midterm Examination “Small” Data October 20, 2015 Instructions (a) The exam is due by 1:00 PM on October 22, 2015 . No exceptions to this deadline will be made, except for medical necessity. (b) If you hand in your exam on paper, turn it into the homework box in the basement of Huang Engineering Center. (c) You may use any textbooks and the lecture notes from the class as resources, as well as R (or equivalent software), online tutorials and references for programming, etc.; however, you may not seek help from any other individuals (students or otherwise) on the exam. All work you submit should be your own. (d) Include a signed acknowledgment of the honor code (below). (e) If you e-mail your exam, please send it to the following e-mail address: [email protected] Please only submit once! Make sure to include “226 Midterm” in your subject line. Include an acknowledgment of the honor code (below) in your e-mail. (f) The exam will be scored out of 30 points. (g) You will receive partial credit, so please show your work. However, note that any incorrect answer will be marked down accordingly. Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
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PROBLEM 1. In this problem we will investigate some of the properties of weighted least squares . If you haven’t already done so, you should review the notes for Discussion Section 3. Suppose we are given n observations ( Y i , X i ) , together with positive weights w i , i = 1 , . . . , n . In weighted least squares, we find the coefficients ˆ γ that minimize the following objective function: n X i =1 w i ( Y i - ˆ γ 0 - ˆ γ 1 X i 1 - · · · - ˆ γ p X ip ) 2 . (1) We refer to the resulting coefficients ˆ γ as the weighted least squares (WLS) solution; we refer to w = ( w 1 , . . . , w n ) as the vector of weights .
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