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.