Report

Yuhana Kennedy July 2011 Hypothesis The growth of cell phone usage in the U.S. has leveled off due to the fact that even though the U.S. population will continue to increase it does not do so without bound. This is important to U.S. manufacturers and distributors as they continue to market cell phones. It is the reason for the widespread manufacture and distribution of cell phones in other countries. Number of U.S. Cell Phone Users (Subscribers) vs. Years Year, t Number of Subscribers (in millions), S 1985 (t = 1) 0.34 1986 (t = 2) 0.682 1987 (t = 3) 1.231 1988 (t = 4) 2.069 1989 (t = 5) 3.509 1990 (t = 6) 5.283 1991 (t= 7) 7.557 1992 (t = 8) 11.033 1993 (t = 9) 16.009 1994 (t = 10) 24.134 1995 (t = 11) 33.786 Source: 2010 CTIA – The Wireless Association Number of U.S. Cell Phone Users (Subscribers) vs. Years (cont’d) Year, t Number of Subscribers (in millions), S 1996 (t = 12) 44.043 1997 (t = 13) 55.312 1998 (t = 14) 69.209 1999 (t = 15) 86.047 2000(t = 16) 109.478 2001 (t = 17) 128.375 2002 (t = 18) 140.767 2003 (t = 19) 158.722 2004 (t = 20) 182.14 2005 (t = 21) 207.896 2006 (t = 22) 233.041 Source: 2010 CTIA – The Wireless Association Number of U.S. Cell Phone Users (Subscribers) vs. Years (cont’d) Year, t Number of Subscribers (in millions), S 2007, (t = 23) 255.396 2008, (t = 24) 270.334 2009, (t = 25) 285.646 2010, (t = 26) 302.86 Source: 2010 CTIA – The Wireless Association Exponential Regression Results 900 y = 1.0339e0.2564x R² = 0.917 800 700 600 Subscribers, S 500 (in millions) 400 Series1 300 Expon. (Series1) 200 100 3500 0 0 10 20 Year, t 30 y = 1.034e0.2564x R² = 0.93 3000 2500 2000 Subscriber, S (in millions) 1500 Series1 Expon. (Series1) 1000 S(t) = 1.0339 S(t) =1.0339(1.2923)x r=0.9576 500 0 0 10 20 Year, t 30 40 Exponential Regression Results (cont’d) The Excel graphs of the data points do not show a strong exponential correlation even though the value of the correlation coefficient is approximately equal to 1, r=0.9576. This illustrates why it is important to closely observe the graph of a given set of data points before drawing a conclusion about the type of correlation one has. This also shows the limitations of technology in assessing the type of correlation one has. Logistics Regression Results Conclusion By graphing the function using Maple and using my calculator to find the logistic function, my hypothesis is supported in the logistic functions in the previous slide. They both show how the data points start off increasing slightly, then rapidly before leveling off to a maximum value C = 343.0837 millions. I conclude that the correlation is strong logistically more so than exponentially.