Spreadsheet Modeling & Decision Analysis:

Spreadsheet Modeling Decision Analysis -ppt Download

  • Date:17 Oct 2020
  • Views:29
  • Downloads:0
  • Size:733.50 KB

Share Presentation : Spreadsheet Modeling Decision Analysis

Download and Preview : Spreadsheet Modeling Decision Analysis

Report CopyRight/DMCA Form For : Spreadsheet Modeling Decision Analysis


Transcription:

Introduction to MathematicalProgrammingMachine Learning Discriminant AnalysisNeural Networks.
Chapter 7Part 1 Discriminant Analysisand Mahalanobis Distance Introduction toDiscriminant Analysis DA .
DA is a statistical technique that uses information from aset of independent variables to predict the value of adiscrete or categorical dependent variable The goal is to develop a rule for predicting to which of twoor more predefined groups a new observation belongs.
based on the values of the independent variables Examples Credit Scoring Will a new loan applicant 1 default or 2 repay Insurance Rating.
Will a new client be a 1 high 2 medium or 3 low Types of DA Problems 2 Group Problems regression can be used k Group Problem where k 2 .
regression cannot be used if k 2 Example of a 2 Group DA Problem ACME Manufacturing All employees of ACME manufacturing are given a pre employment test measuring mechanical and verbal.
Each current employee has also been classified into oneof two groups satisfactory or unsatisfactory We want to determine if the two groups of employeesdiffer with respect to their test scores If so we want to develop a rule for predicting whether.
new applicants will be satisfactory or unsatisfactory The DataSee file Fig7 1 xls Graph of Data for CurrentGroup 1 centroid.
Verbal Aptitude40 Group 2 centroidSatisfactory EmployeesUnsatisfactory Employees25 30 35 40 45 50.
Mechanical Aptitude Calculating Discriminant ScoresY i b o b1 X 1 b 2 X 2X1 mechanical aptitude testX2 verbal aptitude test score.
For our example using regression weY i 5 373 0 0791X 1i 0 0272 X 2 iFigure 7 2 A Classification Rule If an observation s discriminant score is.
less than or equal to some cutoff value then assign it to group 1 otherwiseassign it to group 2 What should the cutoff value be Possible Distributions of.
Discriminant ScoresGroup 1 Group 2 Cut off Value Cutoff Value For data that is multivariate normal with.
equal covariances the optimal cutoffvalue is Cutoff Value For our example the cutoff value is 1 764.
Cutoff Value 1 479 Even when the data is not multivariate normal this cutoff value tends to givegood results Calculating Predicted Group.
See file Fig7 3 xls A Refined Cutoff Value Costs of misclassification may differ Probability of group memberships may differ The following refined cutoff value.
accounts for these considerations S p2Y1 Y2 p C 12 Cutoff Value LN 2 2 p C 2 .
Y1 Y2 1 Classification AccuracyActual 1 9 2 11Group 2 2 7 9Total 11 9 20.
Accuracy rate 16 20 80 Classifying New EmployeesSee file Fig7 4 xls The k Group DA Problem Suppose we have 3 groups A 1 B 2 C 3 .
and one independent variable We could then fit the following regressionfunction Y i b 0 b1 X 1 i The classification rule is then If the discriminant score is Assign observation to group .
Y i 1 5 A1 5 Y 2 5Y i 2 5 C Graph Showing LinearRelationship.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 The k Group DA Problem Now suppose we re assign the groups numbersas follows A 2 B 1 C 3 The relation between X Y is no longer linear .
There is no general way to ensure group numbers are assigned in a way that willalways produce a linear relationship Graph Showing NonlinearRelationship0 1 2 3 4 5 6 7 8 9 10 11 12 13.
Example of a 3 Group DA Problem ACME Manufacturing All employees of ACME manufacturing are given apre employment test measuring mechanical andverbal aptitude .
Each current employee has also been classified intoone of three groups superior average or inferior We want to determine if the three groups ofemployees differ with respect to their test scores If so we want to develop a rule for predicting.
whether new applicants will be superior average or The DataSee file Fig7 5 xls Graph of Data for Current EmployeesGroup 1 centroid.
40 0 Group 3 centroidVerbal Aptitude30 0 Superior EmployeesAverage EmployeesGroup 2 centroid.
Inferior Employees25 0 30 0 35 0 40 0 45 0 50 0Mechanical Aptitude The Classification Rule Compute the distance from the point in.
question to the centroid of each group Assign it to the closest group Distance Measures Euclidean DistanceD istance A 1 A 2 2 B 1 B 2 2.
This does not account forpossible differences invariances 99 Contours of Two Groups Distance Measures.
Variance Adjusted Distance xik x jk D ij 2where xik is value of obs i on k indep variablex jk is the mean value of group j on k indep variable.
s jk is the sample variance of group j on k indep variable This can be adjusted further to account fordifferences in covariances The DA xla add in uses the Mahalanobisdistance measure .
Mahalanobis DistanceD 2 x m T C 1 x m D 2 Mahalanobis distancex vector of datam vector of mean values of independent variables.
C 1 inverse of covariance matrix of independent variables Using the DA XLA Add InSee file Fig7 6 xlsFor detail seeSee file Fig 7 7.
Multivariate Normal DistributionCovariance Matrixx N d 1 1 T 1 p x d 2 1 2.
2 x x 2 Bivariate NormalIf X and Y are independent then Cov X Y 0 However if 30Cov X Y 0 then X and Y may not be independent .
Suppose X Y bivariate normal 500 6292 3754 1 00025 00015 C C 500 3754 6280 00015 00025 For X Y 410 400 D 2 1 825.
MBA Admissions Salterdine Univ wants to use DA to determinewhich applicants to admit to the MBA program Director believes undergraduate GPA and GMATscore provide useful information for predicting.
which applicants will be good students Faculty classify 30 current students in the MBAprogram into 2 groups 1 good students 2 weak Information for 5 new applicants has beenreceived by the director .
See Fig 7 8 Bank Loans Commercial loan dept mgr evaluates loanapplications Important company characteristics for evaluating.
loan application 1 Liquidity ratio of current assets to current liabilities 2 Profitability ratio of net profit to sales 3 Activity ratio of sales to fixed assets 18 past loans bank has made are categorized.
1 Acceptable2 One or two late payments3 Unacceptable 3 or more late payments Must evaluate 5 new loan applications End of Chapter 7.
Introduction to Mathematical Programming MA/OR 504 Chapter 7 Machine Learning: Discriminant Analysis Neural Networks 6-*

Related Presentations

MULTI CRITERIA DECISION ANALYSIS AND DECISION SUPPORT SYSTEMS

Quantify uncertainty. Quantify preferences. Combine uncertainty and preferences . Choice of A Decision Rule Depends On. Importance of decision consequences. Complexity of decision task. Time pressure. Similarity of alternatives. Rating on twodimensions: Value ofconsequences. Probabilityoftheiroccurence.

20 Views0 Downloads

NMI Implementation Spreadsheet Updates STD and CS MMG

Provides Datatype definitions as specified in the PHIN Messaging Guide for Case Notification_v3.0. Compiles segment definition tables and MMG-specified data elements. Revision Log. Tab Descriptions. Column Descriptions. Provides a history of changes made to the implementation template. Condition/MMG

20 Views0 Downloads

Creating a What If Spreadsheet Application

Creating a “What-If” Spreadsheet Application GPA Prediction Calculator Becoming Operationally Attuned to GPA Calculations (Part 1) Calculate current semester’s weighted GPA: For each course, calculate the product of credits and grade points Add products from a) together for all courses this semester Add credits together for all courses Divide sum of the products in b) by total credits in ...

5 Views0 Downloads

Basic Spreadsheet Commands

Basic spreadsheet commands (note on powerpoint) These powerpoint slides were made using the following menu options: View -- normal Insert -- new slide Format -- slide format, and choosing the one that allows a title and notes Before you sit at the computer 1.

17 Views0 Downloads

Angular Motion in Cars SPREADSHEET LAB MANUAL LLC

The gear will determine the torque from the table given and the time to reach a given speed can be calculated using equations of motion. Open Excel and get started! Title: Angular Motion in Cars Last modified by: Mike Created Date: 2/9/2011 2:06:57 PM Document presentation format:

7 Views0 Downloads

Inventory Count Order Call In Spreadsheet

Inventory Count / Order Call-In Spreadsheet Day on Hand Worksheet Inventory Count / Order Call-In Spreadsheet Day on Hand Worksheet * * Sheet3

4 Views0 Downloads

Excel2007 Excel 2007 is the spreadsheet software in the

To Create a New, Blank Workbook: Left-click the . Microsoft Office Button. Select . New. The New Workbook dialog box opens and Blank Workbook is highlighted by default. Click . Create. A new, blank workbook appears in the window. When you first open Excel, the software opens to a new, blank workbook. Excel2007. Starting a Workbook

2 Views0 Downloads

Electronic Spreadsheet Eastern Kentucky University

ELECTRONIC SPREADSHEET Chang-Yang Lin Eastern Kentucky University EXCEL BASICS Electronic Spreadsheet Cells: The Basic Building Blocks Navigate Excel Explore the Menus Select Multiple Cells Create a Spreadsheet Edit the Spreadsheet Formulas Electronic Spreadsheet Excel is a spreadsheet application for analyzing, organizing, and charting numerical data.

6 Views0 Downloads

Advanced Spreadsheet Skills for Game Designers

To enable Solver, click on the Microsoft Office Button -> Excel Options -> Add-Ins. Then in the Manage box, select Excel Add-Ins. Click GO. Select the Solver Add-in Check box.

7 Views0 Downloads

Energy Assessment Spreadsheet utoledo edu

Energy consumed by motors can be reduced by 18% by the application of proven technologies & sound management practices. Thus improvements to motor systems in the industries can yield enormous energy and cost savings. Motors(contd.) This section has two worksheets – Motors, and Motor Operating Cost.

1 Views0 Downloads

Spreadsheet concepts

(comma, colon) =SUM(B4:F4) =SUM(B4,M6) Comparison – tests relationship between two items… = < > IF (C3<D6, “Yes”, “No”) Concatenation – joins text entries into one… & (ampersand) =C4&C3 Formula Concepts (con’t) -- 3 ways to enter formulas – Type an equation into a cell when equations are simple Type-and-point in cell when ...

1 Views0 Downloads

Reading Data From an Excel Spreadsheet

More recently SAS has made available online and in the help within PC SAS essentially every manual. The online help is entirely free. The web site for the current version of SAS is listed here. This is where I go for SAS help the most. Lastly, UCLA has a web site that has several free tutorials you can try.

0 Views0 Downloads