W3_SRN_The Optimal Grade for Polynomial Trend line


Opportunity Statement:

The purpose is to have equation model with optimal grade Polynomial Trend line, providing desired high Coefficient of Determination R2. The model will describe Gold Price Purchasing Power in Oz per US$1000 CPI Basket in 2011. Data period is between January 2006 and December 2011, total 72 points.

Feasible Alternatives of Polynomial Trend line can be used for the case:

  • 2nd Grade
  • 3rd Grade
  • 4th Grade
  • 5th Grade
  • 6th Grade

Tools and Techniques:

Regression Polynomial Trend-line in Microsoft Excel

Selection Criteria:

The simplest equation with desired high Coefficient of Determination R2

Calculation Result:

  • 2nd Grade

  • 3rd Grade

  • 4th Grade

  • 5th Grade

  • 6th Grade

Comparison:

The result shows that they are slighly difference, the 5th and the 6th provide same R2 (95.77%). The difference between the 2nd (simplest equation) and the 6th (most complex equation) is only 0.44%.

Controlling and Monitoring:

We can use update data to confirm whether the equation model is still relevant or not. If the difference is not significant (<1%), we may conclude the model can be used for next step.

Pre-Conclusion and Next Step:

  • The optimal equation model for Gold PPP is using 2nd Grade Polynomial Trend line:

Y = 0.0000000522 X2 – 0.0047067776 X + 105.6680014065

The equation provides Coefficient of Determination R2 = 0.9534875826

  • Gold PPP indicates decreasing buying power, in other words that purchasing power of US$ against Gold is dropping and inverse that curve is the inflation rate.
  • Next step is how to convert the Gold PPP into practical oil price unit, thus we can use it as basis of further economical evaluation.

References:

  1. Sullivan, William G., Wicks, Elin M. & Koelling, C. Patrick. (2012). Engineering Economy 15th Edition Chapter 8 – Price Changes and Exchange Rates. Singapore: Prentice Hall, Inc.
  2. Wasitova, Lilly. (2011). Using the Purchasing Power of Gold (Gold Equivalency) as the Basis for Creating Class 5, Class 4 or Class 3 Cost Estimates. AACE Draft Paper Submission.
  3. KITCO Gold Index. (2012, January 30). Gold Historical Charts. Retrieved from http://www.kitco.com/scripts/hist_charts/yearly_graphs.plx.

1 thought on “W3_SRN_The Optimal Grade for Polynomial Trend line

  1. Awesome again this week, Sudirman!!!

    I really like where you are going with this and about the only request will be sooner or later, you need to project these numbers out say 5 years. The question is whether you want to do this NOW or would you be better off to do it later. Think about this and whichever decision you make is fine with me. But in the end, you will need to project it forward……

    Also, nice job you did on the citations!!

    Keep up the good work and really looking forward to seeing more on this exciting and very interesting topic.

    BR,
    Dr. PDG, Jakarta

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