WU Number 12, Problem 12

David W. Stinson

This data set is based on the first class letter postage for the Us mail form 1933 to 1996. Plot the data and develop a predicating function. When will the cost of a first class postage stamp reach \$1.00? When will the cost be 64 cents? How soon should we expect the next 3 cent increase?

 YEAR RATE (IN CENTS) 1919 2 1932 3 1958 4 1963 5 1968 6 1971 8 1974 10 1975 13 1978 15 1981 20 1985 22 1988 25 1991 29 1994 32

Graph of the above data:

The regression model is an exponential model-
y= a*b^x. With a=4.484x10^-33, b = 1.04. The r and r-square factors are .94 and .89 respectively, indicating that the model is a strong indicator.

These values have been calculated by performing a logarithmic transformation on the data since these calculations are only valid for linear models. From extrapolation one can predicate that the cost of a postage stamp will reach approximately \$1.00 in 2028-98 cents and 2029-\$1.02, the cost of the stamp will be approximately 64 cents in the year 2017. However, this is an excellent time to enter into class discourse of what extrapolation is and the dangers in extrapolating too far away from actual data available.

The next three cent increase, based on the model, should be next year in 2002.