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louv

Staff

Joined:

Jun 23, 2011

Diamonds Are Forever ... or Not

On a recent vacation cruise, while snorkeling with my wife in Cozumel, the diamond in her wedding band unfortunately was dislodged and became one with the ocean floor. After futile efforts to find the lost diamond, it was evident to me that I needed to get her a replacement ring to lessen the pain of the loss. The lost diamond had a 32-year run, and its days were numbered when it met its match, the ocean.

I don’t recall how I chose that diamond 32 years ago. However, I am now older and perhaps wiser this second time around. I decided to do my homework and leverage my JMP savvy for my decision making process. To begin, I collected some data on diamond rings. Gemologists characterize a diamond using a rating system called the Four Cs. These stand for carat size, color, cut and clarity. The one “C” that is not included is cost, but that is the response that I wanted to understand by modeling it using JMP.

The carat size is a unit of weight where one carat is equal to 0.2 grams. The clarity scale is broken down into categories IF, VVS1, VVS2, VS1, VS2, SI1 and SI2, representing the ranges from internally flawless to slightly included. These inclusions affect the diamonds clarity because they interfere with the light as it passes through the stone. The color scale runs D, E, F for colorless and G, H, I, J, K for nearly colorless. Finally, the cut, which measures the precision of the cut with respect to the table and depth of the stone, is expressed on a grading scale of ideal, excellent, very good and good. The cut determines the brilliance of the diamond and how well it reflects light.

So after assembling my JMP table with data from 2,690 diamonds, I modeled the cost as a function of the Four Cs. You can download my JMP file from the JMP File Exchange. With a target cost in mind, I interacted with the JMP Prediction Profiler to see what options were available to me. As you can see from the Profiler, the carat size is the biggest driver of cost, so I locked into a 0.75 carat size diamond and then used the Profiler interactively to see how the other factors affected the price of the diamond. I've embedded the Flash version of my Profiler below, so you can try it out yourself. If you're not seeing the Profiler without having to scroll, you can either make your browser window larger or resize one of the Profiler graphs by grabbing a corner of the graph.

I discovered that I could probably obtain the same size diamond with an H color rating and VS2 clarity for $1,000 less than one with a G color rating and a VS1 clarity. After this exercise, I felt armed and ready to negotiate my new diamond purchase. I’ve also learned that it’s a good idea to remove the diamond ring before snorkeling.

[iframe width="100%" height="300" src="http://blogs.sas.com/jmp/uploads/swf/DiamondsData.htm" frameborder="0"]

4 Comments
Community Member

Lou Valente wrote:

I have made the changes to the Profiler to reflect the great suggestions made above. By using the log transform model within the Fit Model dialog the Profiler maintains it's original units. Thanks Mark and Jason!

Community Member

Mark Bailey wrote:

You can apply the logarithm transform within the fitting process. At the bottom and center of the Fit Model launch dialog is a menu of transformations. Simply select the response and then apply the transform.

This way, JMP will model the response as its log, but it will display the response values (e.g., in the Prediction Profiler) in the original units.

Community Member

Lou Valente wrote:

Thanks Jason, excellent point! I considered this when I posted this blog and decided to keep the response in dollars. However to cover both cases I am in the process of updating my data file in the file exchange to include the transformation for users to compare.

Community Member

Jason Brinkley wrote:

Great Article!

One thing: If you log transform Price you will get a much better fit, in addition you won't have any negative estimates of price in the prediction formula. I plan on using this datafile in a classroom example today, thanks again!

Jason Brinkley

Assistant Professor of Biostatistics

East Carolina University