By

Jeffrey R. Frye

This write up covers the initial stamp problem with the data and questions asked in assignment 12 problem 12.  I used an Excel spreadsheet to conduct my exploration, in conjunction with a TI-83 plus graphing calculator.  The initial data given was input into the Excel spreadsheet as shown below.  Several different possibilities were considered to find the line of best fit of the scatter plot that resulted from the year and cost data for stamps.  The curves that I considered were linear, exponential, and cubic.  Based upon this investigation, I determined that the power of 3, or cubic graph, gave the best fit to the data.  It also had the highest   value.  The higher the value, the better the fit is for the data.  The different graphs are shown below.  The data is also shown.

 Year Price 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

To answer the questions posed in this assignment, I looked at two different data sets.  One set was the data given above, and the other was using what seemed to be asked for in the question.  The question asked for predictions based upon using the data for price of stamps from 1933 to 1996.  Using this data, the cubic equation was still the better predictor, having a  value of .9877.  The prediction for the cost of the stamp to be \$.64 is the year 2013.  The prediction for the cost to be \$1.00 is the year 2030.  Finally, the next increase of \$.03 was predicted to occur in 1996, making the cost of a stamp \$.35.  This result is ahead of what has occurred.  The cubic regression equation that is obtained is.

When the data shown in the above pictures is included in the analysis, a slightly different result occurs. The \$.64 price stamp is predicted to happen in year 2020.  The \$1.00 stamp is predicted to occur in the year 2042.  The next \$.03 increase was predicted to occur in the year 2003.  Once again, it appears that the immediate predictions are ahead of the actual result.  The equation and value are shown on the graph.