Multiple Regression
Chi-Hyuck Jun
IME, POSTECH
[email protected]
Multiple Regression Model (1/2)
Multiple linear regression model is to analyze the relationship
between several independent or predictor variables and a
dependent variable.
Yi 0 1 X 1i 2
Stationary Processes
C.-H. Jun
IME, POSTCH
Basic Properties - Stationarity
Stationary time series
cfw_Zt is a strictly stationary time series if (Z1,Zn) and
(Z1+h,Zn+h) have the same joint distribution.
Zts are identically distributed.
cfw_Zt is weakly st
Simple Regression
IME, POSTECH
Jun, Chi-Hyuck
[email protected]
Introduction (1/3)
Relations between variables
a causal relationship between two variables
family income and family expenditures for housing
sales and amount of advertising expenditures
Time Series - Introduction
C.-H. Jun
IME, POSTCH
IMEN 677 Syllabus
Objectives: This course deals with the basic theory and
the recent developments in time-series analysis, which will
cover
Stationary time series models: AR, MA, ARMA
Nonstationary time ser
Nonstationary Time Series
C.-H. Jun
IME, POSTCH
Nonstationary Series
Series
3000.
Deviations from stationarity may be
suggested by the graph of the series itself
or by the sample autocorrelation function
or both.
2500.
2000.
1500.
when there is a strong
Syllabus
Introduction to Experimental Design
Fall 2017
Chi-Hyuck Jun
IME, POSTECH
Goal
Students should learn theories and
applications of linear regression models and
designs of experiments including
- simple regression
- multiple regression
- single fac
IMEN763 Nonlinear Programming ()
Fall 2017
Instructor
Young Myoung Ko, Ph.D.
[email protected], 054-279-2373, Bldg 4-323
Class Meetings
MW 2:00 PM ~ 3:15 PM, Bldg 4-405
TAs
Seung Min Baik ([email protected])
Office Hours
By appointment
Textbook
Boy
Automobile Painting Scheduling for
Batch Run
Discrete Optimization Term-Project
20152595 Onyu Yu
20152541 Hyeji Jang
2016.06.0
7.
Problem Description
Single-line production plan
Constant speed
C1
C2
C3
Problem Description
Single-line production plan
Const
618 Chapter Eleven . Discrete Optimization Models
1 7 S 6 14 15
2 18 20 5 S
3 7 19 9 10
4 7 6 11
5 A 16
Awesome wants to nd a product pairing that max-
imizes the appeal, with each product in exactly one
pair.
(a) through (c) as in Exercise 11-19.
11-
622 Chapter Eleven 0 Discrete Optimization Models
11-36 Space structuresu designed for zero gravity using the decision variables (j = 1, . , . , 22)
have no structural weight to support and nothing . .
. . 1 f osal 3 selected
to which a foundation can b
624 Chapter Eleven - Discrete Optimization Models
of this volume discount problem using the decision
variablesU: l,.,25;j=1.,200;k=1,.,5)
x,_, quantity of product] purchased from
supplier i
w. ; dollar volume of goods from supplier i
when discount range k
620 Chapter Eleven 0 Discrete Optimization Models
more than 50 can be assembled in any quarter. There
is a xed cost of $2000 each time the line is setup for
production, plus $200 per unit assembled. Engines
may be held over in inventory at the plant for $
616
(a) E Formulate this problem asaset partitioning
11-12 A special court commission appointed to re-
solve a bitter ght over legislative redistricting has
proposed 6 combinations of the 5 disputed counties
that could form new districts. The followin
i 614 Chapter Eleven - Discrete Optimization Models
l
Building
1 2 3 4
Return 4.5 4.1 8.0 7.0
Price 4.0 3.8 6.0 7.2
l
The executive wishes to choose investments that
maximize his total return. Assume that every op-
tion is available only on an allor
Chinese Postman Problem
Postmen deliver letters down roads.(Kwan,M-K, 1962)
Find the shortest route in a network that uses every arc (directed edge) and
Why Not Change the World?
gets back to where they started (closed problem) or doesn't go back (open
Modeling Tricks
All or nothing
Fixed Charge
Either-or constraints
K out of N constraints
Function with N possible values
Maximize Min (g1(x), g2(x)
Knapsack Problem
Knapsack Problem
Hiker wishes to take n items on a trip.
The weight of item i is wi.
Th
Assignment Model
Optimal matching or pairing of objects of two types jobs
to machines
N to N. If not, add
i is assigned to j
1 ifdummy
Let xij
0 if not,
n
n
Z cij xij
Minimize
i 1 j 1
subject to
n
x
ij
1,
for i 1,2,., n
1,
for j 1,2,., n
j 1
n
x
ij
i 1
Class 2013s Student Term Project
List
Name
Title
Symmetric traveling salesman problem: heuristic approach
Problem of allocating CPU frequency on servers in datacenter
Optimizing multiple kernel based on genetic algorithm
Heat exchanger network synthesis f
P20 cfw_PP. P; o O D 7,-9.
' 04>? aw. P o -~,.
1 o 0 Cl\; 0- P; -.
ibis 3 R2: 5,0115%) :2 P L X(&) : ix I st): 5! [ X(t.+$):4x Ycfw_tcfw_$)=i\1
:Ft5335x,\():<3r , mm=3r14s>ixj U
P that) :3; , Yfkt)
IMEN666 Applied Stochastic Processes
Spring 2014
Final Exam
Date : Friday 06/20/2014
Time : 10:00am 12:00pm
Closed book, open notes, absolutely NO discussing
Write down your answer in the most simplified form as possible (but do not skip
important procedu
IMEN666 Applied Stochastic Processes
Spring 2016
Homework4 Solution
1. (Problem 4.1)
Future state Xn+1 depends on only present state Xn , so cfw_Xn , n 1 is a Markov chain. The
transition probabilities cfw_Pij are:
S Dn+1 0 for i < s, j = 0
= Pij =
X
k
k
IMEN666 Applied Stochastic Processes
Spring 2016
Homework5 Solution
1. (Problem 5.4)
Let Ti be the time between (i 1)st birth and ith birth. Then SN =
PN
i=1
Ti means the time to go
from size 0 to size N . But cfw_Ti , i 1 are independent and Ti exp(i1 )