Rates of Change for CD's Sold |
Year |
Year (1990 set to 0) |
Original Data |
Linear Model |
Exponential Model |
Quadratic Model |
1984 |
-6 |
5.8 |
62.14 |
7.13 |
14.87 |
1985 |
-5 |
22.6 |
62.14 |
10.76 |
24.324 |
1986 |
-4 |
53.0 |
62.14 |
16.22 |
33.778 |
1987 |
-3 |
102.1 |
62.14 |
24.46 |
43.232 |
1988 |
-2 |
149.7 |
62.14 |
36.88 |
52.686 |
1989 |
-1 |
207.2 |
62.14 |
55.61 |
62.14 |
1990 |
0 |
286.5 |
62.14 |
83.86 |
71.594 |
1991 |
1 |
333.3 |
62.14 |
126.45 |
81.048 |
1992 |
2 |
407.5 |
62.14 |
190.66 |
90.502 |
1993 |
3 |
495.4 |
62.14 |
287.50 |
99.956 |
1994 |
4 |
662.1 |
62.14 |
433.51 |
109.41 |
|
|
|
|
|
|
|
Linear Regression |
Exponential regression |
|
y'=62.14, r=.9748 |
y'=204.18*.4107e.4107x, r=.9383 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Quadratic Regression |
|
|
|
y'=4.727*2x+71.594, r=.9965 |
|
|
|
|
|
|
|
|
|
|
|
|
The
rate of change data further indicates the conservative nature of the linear
model with a moderate rate of chane in CD sales equal to 62.14 (million) per
year. The quadratic model, although it
best fits the original data, is perhaps a bit too aggressive with an
instantaneous rate of change equal to 109.41 million in 1994 (with x=4). |
|
|
|
|
|
|
|
|
|
|
|
|