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) Shares of option Grants Outstanding ( millions) X Common shares outstanding (millions) Y Adobe Systems 20.3 61.8 Apple computers 52.7 160.9 Applied materials 109.1 375.4 Autodesk 15.7 58.9 Best Buy 44.2 203.8 Fruit of the Loom 14.2 66.9 ITT Industries 18.0 87.9 Merril Lynch 89.9 365.5 Novell 120.2 335.0 Parametric Technology 78.3 269.3 Reebok International 12.8 56.1 Silicon Graphics 52.6 188.8 Toys "R" Us 54.8 247.6
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?