UANTITATIVE METHODS FOR MANAGEMENT ASSIGNEMENT 2 MAXIMUM MARKS : 15 Answer any THREE questions. 1. Corporate share repurchase programs are often touted as a benefit for shareholders. But Robert Gabele, director of insider research for First Call/ Thomson Financial, noted that many of these programs are undertaken solely to acquire stock for a company's incentive options for top managers. Across all companies, existing stock options in 1998 represented 6.2 per cent of all common shares outstanding. The following data show the number of shares covered by option grants and the number of shares outstanding for 13 companies ( Bloomberg personal Finance, January/February 2000) Adobe Systems Apple computers Applied materials Autodesk Best Buy Fruit of the Loom ITT Industries Merril Lynch Novell Parametric Technology Reebok International Silicon Graphics Toys \"R\" Us Shares of option Grants Outstanding ( millions) X 20.3 52.7 109.1 15.7 44.2 14.2 18.0 89.9 120.2 78.3 12.8 52.6 54.8 Common shares outstanding (millions) Y 61.8 160.9 375.4 58.9 203.8 66.9 87.9 365.5 335.0 269.3 56.1 188.8 247.6 a. Develop the estimated regression equation that could be used to estimate the number of shares of option grants outstanding given the number of common shares outstanding. b. Use the estimated regression equation to estimate the number of shares of option grants outstanding for a company that has 150 million shares of common stock outstanding. c. Do you believe the estimated regression equation would provide a good prediction of the number of shares of option grants outstanding? Use r2 to support your answer. d. What is the value of sample correlation coefficient? 2. PURCHASE BEHAVIOUR REGARDING PLASMA-SCREEN TELEVISION AND DVR ARE GIVEN BELOW: PURCHASED PLASMA SCREEN PLASMA SCREEN PURCHASED DVR YES NO 38 42 TOTAL 80 NOT PLASMA SCREEN TOTAL 70 108 150 192 220 300 a. Find the probability that if a household that purchased a big screen television is randomly selected, the television purchased is a plasma screen b. Find the probability that a randomly selected household that purchased a big-screen television also purchased a plasma screen television and a DVR c. Find the probability that among households that purchased a big screen television, they purchased a plasma- screen television or a DVR d. If a household purchased a plasma- screen television, what is the probability that it also purchased a DVR? e. Use decision tree to find the probability that a household purchased a DVR, given that the household purchased a plasma screen television. 3. Data indicates that the time to download check$mart's home page is normally distributed with mean 7 seconds and standard deviation of 2 seconds. a. what is the probability that the download time will be more than 9 seconds b. what is the probability that the download time will be between 7 and 9 seconds c. what is the probability that the download time is under 7second or over 9 seconds d. what is the probability that the download time will be between 5 and 9 seconds e. what is the probability that the download time is less than 3.5 seconds f. How much time ( in seconds) will elapse before 10% of the download are complete. g. What are the Upper Limit and Lower limit of X , located symmetrically around the mean, which include 95% of the download times 4. A large corporation is interested in determining whether an association exists between the commuting time of its employees and the level of stress related problems observed on the job. A study of 116 assembly line workers reveals the following: STRESS Commuting High Moderate time Under 15 min 9 5 15-45 mins 17 8 Over 45 mins 18 6 Total 44 19 At the 0.01 level of significance, is there evidence of a significant and stress? All the best Low Total 18 32 28 53 7 31 53 116 relationship between commuting time SUMMARY OUTPUT Regression Statistics Multiple R 0.9586180116 R Square 0.9189484922 Adjusted R 0.9115801734 Standard E 35.8029801725 Observatio 13 ANOVA df Regression Residual Total Intercept X Variable SS MS F Significance F 1 159867.8419492 159867.8419492 124.7162 2.426731637E-007 11 14100.38728159 1281.8533892353 12 173968.2292308 Coefficients Standard Error 27.3646937785 17.671318416 3.1080242837 0.2783062921 t Stat P-value 1.5485371908 0.149766 11.1676392966 2.43E-007 Lower 95% -11.5296158144 2.4954762649 Upper 95%Lower 95.0% Upper 95.0% 66.259 -11.52962 66.259 3.720572 2.495476 3.720572 Shares of option Grants Outstanding ( millions) X Adobe Systems Apple computers Applied materials Autodesk Best Buy Fruit of the Loom ITT Industries Merril Lynch Novell Parametric Technology Reebok International Silicon Graphics Toys \"R\" Us 20.3 52.7 109.1 15.7 44.2 14.2 18 89.9 120.2 78.3 12.8 52.6 54.8 Common shares outstanding (millions) Y 61.8 160.9 375.4 58.9 203.8 66.9 87.9 365.5 335 269.3 56.1 188.8 247.6 SUMMARY OUTPUT Regression Statistics Multiple R 0.9586180116 R Square 0.9189484922 Adjusted R 0.9115801734 Standard E 35.8029801725 Observatio 13 ANOVA df Regression Residual Total Intercept X Variable SS MS F Significance F 1 159867.8419492 159867.8419492 124.7162 2.426731637E-007 11 14100.38728159 1281.8533892353 12 173968.2292308 Coefficients Standard Error 27.3646937785 17.671318416 3.1080242837 0.2783062921 t Stat P-value 1.5485371908 0.149766 11.1676392966 2.43E-007 Lower 95% -11.5296158144 2.4954762649 Upper 95%Lower 95.0% Upper 95.0% 66.259 -11.52962 66.259 3.720572 2.495476 3.720572 Shares of option Grants Outstanding ( millions) X Adobe Systems Apple computers Applied materials Autodesk Best Buy Fruit of the Loom ITT Industries Merril Lynch Novell Parametric Technology Reebok International Silicon Graphics Toys \"R\" Us 20.3 52.7 109.1 15.7 44.2 14.2 18 89.9 120.2 78.3 12.8 52.6 54.8 Common shares outstanding (millions) Y 61.8 160.9 375.4 58.9 203.8 66.9 87.9 365.5 335 269.3 56.1 188.8 247.6