This problem contains CD sales (in millions) for the years 1984-1994. The year 1990 is set as the base year. The goal is to develop least squares regression models to best fit the data. | |||||
Number of CD's Sold | |||||
Year | Year (1990 set to 0) | Original Data | Linear Model | Exponential Model | Quadratic Model |
1984 | -6 | 5.8 | -62.95 | 17.37 | 7.948 |
1985 | -5 | 22.6 | -0.81 | 26.19 | 27.545 |
1986 | -4 | 53.0 | 61.33 | 39.50 | 56.596 |
1987 | -3 | 102.1 | 123.47 | 59.56 | 95.101 |
1988 | -2 | 149.7 | 185.61 | 89.80 | 143.06 |
1989 | -1 | 207.2 | 247.75 | 135.41 | 200.473 |
1990 | 0 | 286.5 | 309.89 | 204.18 | 267.34 |
1991 | 1 | 333.3 | 372.03 | 307.88 | 343.661 |
1992 | 2 | 407.5 | 434.17 | 464.24 | 429.436 |
1993 | 3 | 495.4 | 496.31 | 700.02 | 524.665 |
1994 | 4 | 662.1 | 558.45 | 1055.53 | 629.348 |
Linear Regression | Exponential regression | ||||
y=62.14x+309.89 | y = | 204.18 e .4107x | |||
r 2 = | 0.9503 | r 2 = | 0.8804 | ||
r = | 0.9748 | r= | 0.9383 | ||
Quadratic Regression | |||||
y=4.727x2+71.594x+267.34 | |||||
r 2 = | 0.9931 | ||||
r= | 0.9965 | ||||
The quadratic regression model is the best formula for the actual data given. The r (and r 2) is closest to 1. This model best follows the actual data trend and appears to be the best predictor for future sales. The exponential model shows too much growth at the end of available data and should be considered unreliable as a predictor for future sales. The linear model is also a fairly accurate model (r=.9383) and should be considered as a conservative alternative to the quadratic model for future sales predictions. | |||||