# Linear Programming

Topics: Regression analysis, Linear regression, Simple linear regression Pages: 15 (3826 words) Published: January 18, 2013
QUANTITATIVE METHODS II
Mid-Term Examination
Monday, October22, 2012
Time : 150 minutes
Total No. of Pages :17Name ________________________
Total No. of Questions: 3Roll No. ________________________
Total marks:35Section: _______________________

Instructions
1. This is a Closed Book Exam. You are not allowed to carry anything other than stationary and calculator. 2. Answer all questions only in the space provided following the question. 3. Show all work and give adequate explanations to get full credit. 4. You may use the backside of the last page for rough work only if needed. Do NOT attach any rough work/sheets. 5. Encircle or underline your final answer for each part. 6. No clarifications will be made during the exam.

7. Assume 95% confidence level if necessary ( = 0.05).
8. Use approximate critical values for t, F, and 2 tests if the exact value is not available in the tables attached with the question paper.

Question 1 (15 points)
Software effort estimation, measured in number of hours required to develop software, is an important activity associated with any software development company. It is used for investment planning and pricing of the software development. One approach usually used for software effort estimation is through Function Point Analysis (FPA). First made public by Allan Albrecht of IBM in 1979, the FPA technique quantifies the functions contained within software in terms that are meaningful to the software users. The measure relates directly to the business requirements that the software is intended to address. It can therefore be readily applied across a wide range of development environments and throughout the life of a development project, from early requirements definition to full operational use. Other business measures, such as the productivity of the development process and the cost per unit to support the software, can also be readily derived.

Data is collected from all software projects completed by AT &T data center from 1986 through 1991. The data contains 104 observations and 5 variables; namely 1. Number of Worker Hours, 2. Values for function point count, 3. Operating systemused,4. Database management system and 5.Programming language.Variables, function point counts, operating system used, database and programming language are often used to help predict the number of work hours that will be required to complete a proposed software project.

Data description:
S.No| Variable Name| Variable Type| Code used in Regression| 1| Number of Worker Hours| Continuous| NWH| 2| Functional Point Counts| Continuous | FPC| 3| Operating System| Categorical0: Unix1: MVS| 0 = Unix1 = MVS| 4| Database Management System| Categorical1: IDMS2: IMS3: INFORMIX4: INGRESS5: Other| D1: IDMSD2: IMSD3: INFORMIXD4: INGRESS| 5| Language| Categorical1: COBOL2: PLI3: C4: Other| L1: COBOLL2: PL1L3: C|

A simple linear regression is carried between number of worker hours (Response) and functional point counts (predictor) using SPSS. The SPSS output for the model NWH = 0 + 1 x FPC is shown in tables 1.1 -1.3.

Table 1.1 Descriptive Statistics|
| N| Minimum| Maximum| Mean| Std....