Assignment 12:

Price of Stamps

by: Katie Gilbert

This data set is based on the first class letter postage for the US Mail from 1933 to 1996. Plot the data and develop a prediction 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..............PRICE IN CENTS

 

The first thing we will do is plot our data using excel into a scatter plot graph and take a look at our trends.......

Now let's try and develop a prediction function that will allow us to figure out the price of stamps in the future. There are a few that might come to mind when looking at the trend of our scatter points, I think you might agree that our points take on a linear look (especially from 1960-present), we can also see that a power function could fit our data, or maybe even an exponential function. We will take a look at all three of these possibilities and see which best fits our data and will allow us to predict future postage rates.

WHAT ALL THAT SAYS IS THAT WE WANT OUR COEEFICIENT OF DETERMINATION TO BE AS CLOSE TO 1 AS POSSIBLE!

 

Let's begin by looking at a linear function for our graph.

We see that from our regression analysis that the linear fucntion does not fit our data. Let's try and see if we can get a better function for our data.

We will try the power function next.....

We see from our regression analysis that our power function fits our data much better, but let's try one more function to see if we can get an even better result.

Let's take a look at our exponential function.....

We see from our regression analysis that this graph fits our data a little bit better than our power function. This looks like the winner!

 

Now let's use our function to see when the price of a first class stamp will be $1.00.....

When we plug $1.00 into our equation we got above we get.....

So it looks like our first class postage stamp will reach $1.00 around October of 2027.

Now to answer the question of when it will reach 64 cents, we will use our same exponential equation and plug in 64 cents...

So according to our current trend in postage increases the cost of a first class stamp will reach 64 cents around June of 2016.

We will now see if we can figure out when our next 3 cent increase will be for our first class stamp. If we plug in 44 cents into our equation we get..........

So from this result we see that our equation is not a perfect predictor, but that we should expect another 3 cent increase in the near future!

RETURN