Stamps
Consider the following data set of first class
postage stamp prices over the past several decades.
|
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 |
|
1997 |
33 |
|
1999 |
34 |
|
2002 |
37 |
It would be useful to use this data to form
some predictions of what stamp prices will be in the future. A spreadsheet is an
ideal tool for accomplishing this task. After entering this data into a
Microsoft Excel spreadsheet, we can use Excel's chart capabilities to create a
scatter-plot of stamp prices as a function of year to get a feel for what the
data looks like.
The spread of the data strongly suggests an
exponential relationship between the price of stamps and the year. Excel has a
built in function that allows the user to fit a trendline or curve to the data.
The user can specify an equation or the user can let Excel select the
"best fit" for a certain kind of equation. We've hypothesized that an
exponential equation would be a good fit for the data.
So we have used Excel to fit a curve with the
equation y=1E-33e0.00397x. Looking at the chart, this seems like a
reasonable fit.
Now we have a few ways we can use this chart to predict the future. We can use Excel to use the trendline equation to forecast the next x units. Then we can visually look and estimate our predictions.
So if we wanted to predict when the price
would be 64 cents we could look at our curve and say that that would be the
price sometime around 2018. If we wanted to predict when the price would be one
dollar, we could look and estimate that it would be around 2027.
If we wanted to be more precise in our predictions, we could use the trendline equation to calculate our predictions directly or by typing it into Excel as a formula.
|
year |
Predicted price (in
cents) |
|
2015 |
55.157 |
|
2016 |
57.391 |
|
2017 |
59.716 |
|
2018 |
62.134 |
|
2019 |
64.650 |
|
2020 |
67.268 |
|
2021 |
69.993 |
|
2022 |
72.827 |
|
2023 |
75.777 |
|
2024 |
78.846 |
|
2025 |
82.039 |
|
2026 |
85.361 |
|
2027 |
88.818 |
|
2028 |
92.415 |
|
2029 |
96.158 |
|
2030 |
100.052 |
|
2031 |
104.104 |
|
2032 |
108.320 |
|
2033 |
112.707 |
|
2034 |
117.272 |
|
2035 |
122.021 |
I created this table by typing in our prediction equation in the cells in the Predicted price column. The price is calculated according to the year in the corresponding cell in the year column. So we predict from this table that a stamp will cost 64 cents sometime between 2018 and 2019. We can then go on and predict that a stamp will cost 1 dollar sometime around 2030.