Please follow these guidelines when preparing your answers:

Transcription

1 PR- ASSIGNMNT Quantitative mpirical Research The objective of the pre- assignment is to review the course prerequisites and get familiar with SPSS software. The assignment consists of three parts: (i) basics of data- manipulation in SPSS; (ii) statistics review; and (iii) linear algebra review. Please follow these guidelines when preparing your answers: a) Use A4 paper, portrait orientation; b) Use the provided cover page, include your name and student number; c) Prepare your answers in numerical order; d) Start each problem on a new page; e) Include necessary formulas and calculations in your answer, a mere answer or a printout of an xcel sheet is not enough; f) Highlight your final answers clearly. Submit your solutions by January 5th, 2016, by 16:00. The pre- assignment will be evaluated as part of the overall course grade as one completed exercise. The grading will be done based on the correctness and overall clarity of the answers. While writing your answers, remember to show your reasoning and intermediate steps needed to obtain the solution. 1

2 Data files come in a wide variety of formats, and this software is designed to handle many of them, including: Spreadsheets created with xcel and Lotus Database tables from many database sources, including Oracle, SQLServer, Access, dbas, and others Tab-delimited and other types of simple text files SAS data files ACCSSING TH Stata SOFTWAR data files AND MANUAL SPSS is available for students from GTTING STARTD WITH SPSS Data files in IBM SPSS Statistics format created on other operating systems SYSTAT data files Opening Data Files Download also the software manual (SPSS Manual.pdf) from the Additional reading page of the course website. If you have not used SPSS before, it is a good idea to start by In addition to files saved in IBM SPSS Statistics format, you can open xcel, SAS, Stata, first reading tab-delimited, Chapters 1-2 and to get other an files idea without on the converting basic functionalities the files to an offered intermediate by the format or entering software. The data manual definition provides information. a lot of links to additional resources and explains where you can find help on SPSS related issues. Opening a data file makes it the active dataset. If you already have one or more open data For further guidance, files, see they also remain the Help- dialogue open and available in the for software. subsequent There use you in the will session. be able Clicking anywhere to search a list of in Topics the Data and ditor take guided window Tutorials for an open on data selected file will themes. make it the active dataset. For more information, see the topic Working with Multiple Data Sources in Chapter 6 on p. 91. In distributed analysis mode using a remote server to process commands and run procedures, RADING DATA the available data files, folders, and drives are dependent on what is available on or from the SPSS supports several remote data- formats. server. The current A comprehensive server name description is indicated on at the alternatives top of the dialog is box. You will given in Chapter not 3 of have the access manual. to The data data files formats on your local used computer during the unless course you are specify mainly the drive as a shared sav- files (the native device SPSS and format), the folders excel- files containing and your text- datafiles as (tab- delimited, shared folders. space- For more information, see the topic Distributed Analysis Mode in Chapter 4 on p. 61. delimited, comma- delimited). To Open Data Files 28 Chapter 3 From the menus choose: File > Open > Data... In the Open Data dialog box, select the file that you want to open. Click Open. To Read Text Data Files CopyrightIBMCorporation1989, From the menus choose: File > Read Text Data... Select the text file in the Open Data dialog box. Follow the steps in the Text Wizard to define how to read the data file. Text Wizard: Step 1 Figure 3-13 Text Wizard: Step 1 2

3 DITING DATA Once you have successfully uploaded your dataset, SPSS opens a data- editor window, which provides you a spreadsheet- like access to the data. See Chapters 4 and 7 in the manual for a description on how to use (i) data view; and (ii) variable view to add, change, and delete information in your dataset. TASK 1. To verify that you know how to read, edit and sort data in SPSS, consider dataset math- grades.xls. a) Use the instructions provided in Chapter 3 of the manual to open the xcel- dataset in SPSS. b) Check variable view to ensure that all variables are correctly defined. c) Filter the dataset to identify cases with missing values. Which cases did you find? d) Replace the missing values with your guess for suitable values. (Note: we will later discuss the missing value problem in more detail and provide guidance on techniques for handling them properly.) e) Transform the variable Smoking into a binary 0-1 variable. f) Sort cases by weight in ascending order. Are all observed values realistic? g) Feel free to experiment with the other data manipulation features described in Chapters 4, 7 and 8. Compute descriptive statistics for the variables in the dataset. DSCRIPTIV STATISTICS AND GRAPHS IN SPSS TASK 2. Open the datafile bulbs.xls. The data table deals with lengths of life (in hours) of a sample of forty 100- watt light bulbs produced by manufacturer A and a sample of forty 100- watt light bulbs produced by manufacturer B. a) Form the frequency distribution for each brand. Choose class interval size 100. b) Form the frequency distribution for each brand using class interval size 50. Comment on the results of the change. c) Form the percentage distributions from the frequency distributions developed in part (b). d) Which manufacturer has bulbs with a longer life: manufacturer A or manufacturer B? xplain. 3

4 How to create a histogram In the Chart Builder, click the Gallery tab and select Histogram in the Choose From list. Drag the Simple Histogram icon onto the canvas. Drag a scale variable to the x-axis drop zone. Note: The statistic for a histogram is Histogram or Histogram Percent. These statistics bin the data and calculate a count for each bin. If you change the statistic, the chart will no longer be a histogram. TASK 3. Suppose that you wish to study characteristics of the model year 2000 automobiles using the variables in dataset auto2000.xls. (Source: The 2000 Cars. Copyright by Consumers Union of U.S., Inc. Adapted from Consumer Reports, April 2000, 66-71, by permission of Consumers Union, U.S., Inc. Yonkers, NY ) a) Form a contingency table cross- classifying type of drive (front versus rear) with type of gasoline. (Tip: Analyze - > Descriptive Statistics) b) Plot a side- by- side bar chart of type of drive (front versus rear) with type of gasoline. c) Based on the results, does there appear to be a relationship between type of drive (front versus rear) with type of gasoline? 4

5 RVIW QUSTIONS FOR STATISTICS BACKGROUND MATRIAL If you have difficulties with the problems, please use background material. You may use e.g. the book that has been previously used in the basic statistics course: Levine, Krehbiel, and Berenson (2003), Business Statistics: A First Course, 3rd dition, Prentice Hall, Chapters 1-7, and The data (in xcel, Minitab, SPSS and text format), Power Point slides, and extra exercises are available electronically on the publisher's web page: Note: The numbers in brackets at the beginning of each problem, and the data file names refer to the book by Levine, Krehbiel and Berenson (2003): Business Statistics: A First Course, 3rd d, Prentice Hall. When completing the following exercises, feel free to utilize SPSS / xcel whenever you consider them helpful. PROBLM 1. [Modified from 3.11] A software development and consulting firm located in the Phoenix metropolitan area develops software for supply chain management systems using systematic software reuse. That is, instead of starting from scratch when writing and developing new custom software systems, the firm uses a database of reusable components totaling more than 2,000,000 lines of code collected from 10 years of continuous reuse effort. ight analysts at the firm were asked to estimate the reuse rate when developing a new software system. The following data are given as a percentage of the total code written for a software system that is part of the reuse database (datafile: reuse.xls ). a) Compute the mean, median, mode, first quartile and third quartile. b) Compute the range, variance and standard deviation. c) Interpret the summary measures calculated in (a) and (b). 5

6 PROBLM 2. [Modified from 6.77] In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLL). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage where the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was recorded, with the results shown in dataset insurance.xls. a) Set up a 95% confidence interval estimate of the population mean processing time. b) What would you tell a customer who enters the bank to purchase this type of insurance policy and asks how long the approval process takes? PROBLM 3. [Modified from 7.79] La Quinta Motor Inns developed a computer model to help predict the profitability of sites that are being considered as locations for new hotels. If the computer model predicts large profits, La Quinta buys the proposed site and builds a new hotel. If the computer model predicts small or moderate profits, La Quinta chooses not to proceed with that site. This decision- making procedure can be expressed in the hypothesis- testing framework. The null hypothesis is that the site is not a profitable location. The alternative hypothesis is that the site is a profitable location. a) xplain the risks associated with committing a Type I error. b) xplain the risks associated with committing a Type II error. c) Which type of error do you think the executives at La Quinta Motor Inns are trying hard to avoid? xplain. d) How do the changes in the rejection criterion affect the probabilities of committing Type I and Type II errors? 6

7 PROBLM 4. [Modified from 10.3 and 10.14] The marketing manager of a large supermarket chain would like to determine the effect of shelf space on the sales of pet food. A random sample of 12 equal- sized stores is selected, and the results reported in the datafile petfood.xls. a) Set up a scatter diagram. b) Compute the coefficient of correlation. c) Assuming a linear relationship, use the least- squares method to find the regression coefficients b 0 (intercept) and b 1 (slope). d) Interpret the meaning of the slope b 1 in this problem. e) Predict the average weekly sales (in hundreds of dollars) of pet food for stores with 8 feet of shelf space for pet food. f) Determine the coefficient of determination r 2 and interpret its meaning. g) Determine the standard error of the estimate. h) How much shelf space would you recommend that the marketing manager allocate to pet food? xplain. i) How useful do you think this regression model is for predicting sales? 7

8 12 MATRIX ALGBRA Then AB = ( LINAR ALGBRA RVIW ), BA = ( ). BACKGROUND Thus we must be careful MATRIAL to specify the order of multiplication. If we wish to multiply both sides of a matrix equation by a matrix, we must multiply on the left or on the Understanding right and be consistent the basics on of both linear sides algebra of the is one equation. of the prerequisites for the course. Multiplication is distributive over addition or subtraction: Matrix operations are often used in statistics to simplify representation of models. Here are a few additional links to resources that may help you to review some of the basic concepts in linear algebra: A(B + C) = AB + AC, (2.21) A(B C) = AB AC, (2.22) (A + B)C = AC + BC, (2.23) (A B)C = AC BC. (2.24) Note that, in general, because of (2.20), PROBLM 1. Consider the following data matrix A(B + X, C) which = BA consists + CA. of five observations and (2.25) three variables (Tip: you may want to use xcel). Using the distributive law, we can expand products such as (A B)(C D) to obtain (A B)(C D) = (A X = B)C 0 8(A 5 B)D = AC BC 5 5 AD + 5 BD [by (2.22)] [by (2.24)]. (2.26) a) Compute the matrices Y = X + X and Z = 5X. The transpose of a product is the product of the transposes in reverse order: b) Compute the matrix V = X! X (where X! denotes transpose of the matrix). c) Compute the inverse matrix V!! and show that V!! V = I (identity matrix). (AB) = B A. (2.27) Note that (2.27) holds as long as A and B are conformable. They need not be square. PROBLM Multiplication 2. involving vectors follows the same rules as for matrices. Suppose A is n p, a is p 1, b is p 1, and c is n 1. Then some possible products are Consider Ab, c A, the a b, following b a,andab vectors.forexample,let and matrices: A = ( ), a = Then Compute the following products: ( ) a) Between matrix 3 2 and 4 vectors: Ab, c T A, c T Ab; Ab = 2 ( ) b) Between two 1 vectors: 3 5 a! 3 16 b, ab! =,. 31 4, b = 2 3 4, c = ( 2 5 ). 8