Megan Langford

We will attempt to predict future values for stamp prices in the United States by analyzing the historical behavior of the prices over time.

Here is a graphical display for the actual stamp prices in the United States over its history.

Now we will apply several different types of functions to see which one best represents the behavior of the data.

First, by using an exponential function to best explain the shape of the data, we get the following graph:

Next, by using a linear function to best explain the shape of the data, we get the following graph:

Finally, by using a power function to best explain the shape of the data, we get the following graph:

Notice that for each of our graphs, the equation for the trend line is shown above the data in y= format.

The value rates the predictability strength of the function for the data set. For regression analysis purposes, the value closest to 1 indicates which function most closely relays the data behavior.

Although all three function types appear closely related to the data, the value closest to 1 is the one for the exponential function. We can also see it is very close to the data set because the data points all fall very close to the graph of the function.

We now know which method will best predict the values of stamp prices for years to come. Now let’s expand our data table using the exponential function created to best fit the data in order to predict future stamp prices.

Year Stamp Price (cents)

2006	41
2008	42
2009	44
2010	48.8503725
2017	64.21871262
2018	66.77780289
2019	69.43887189
2028	98.70460924
2029	102.6379488
2039	151.7096729
2049	224.2428372

We can now see that we can expect the price to rise more than 3 cents (actually, close to 5 cents) in the next year. The price should reach 64 cents by 2017, and $1 by 2029.

So will this function be accurate for predicting stamp prices for any year we ask it to?

First, let’s attempt to obtain an expected stamp price for a year prior to the start of the data set. When we input the year 1800, the function gives us an expected stamp price of about a hundredth of a cent. In reality, U.S. stamps were not created until 1847.

Taking a look 100 years from now, our function predicts the stamp price will reach $23.38 by 2109. Even with a high rate of inflation from now until then, this seems rather unlikely. In perspective, this means that stamp prices have increased from 2 cents to 44 cents over the last 100 years, and they will rise from 44 cents all the way to $23.38 over the next 100 years.

The lesson to learn from this exercise is that although our function is extremely useful for the years relatively near our data set, the variables may have very different behavior as we get further away from our known data set. In reality, this is true for most methods of creating best fit lines.