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# Regression Optimization to Determine Price

1. You decide to buy'a diamond ring. To make sure you get a quality ring for your money, you educate yourself on things to look for in buying a diamond. After some research on the web, you learn about the 4C's of diamonds: cut, clarity, color and carat. You decide the ring you want to purchase will have a a round-cut diamond and you narrow your search for various ring with that cut.

After searching the Internet, you come up with a set of possible rings for purchase. But you have also learned, pricing can vary considerably with diamond purchases. Not wanting to be ripped off, you remember 0S4680 and decide to do a regression analysis to develop a model to predict what a good retail price of a round cut diamond ring should be.

a. Utilizing the data you collect (Tab Diamond Ring Data Set), prepare scatter plots for each of the independent variables to determine what type of relationship exists in predicting the price of the ring.
b. Continue with your analysis and determine which combination of . independent variables you would use to predict the cost of the ring. Which would you use and why?
c. If you decided to use just Clarity and Carat, what would be the regression model equation?
d. Using the Regression equation from part c, create an estimated price for each ring within your data set. Are there any rings which are overpriced? Are there any which appear to be bargains? Based on your analysis, which ring would you buy?

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Solution:
a.

The coefficient of determination (0.0554) is far away from its ideal value of +1, thus indicating a very weak association between colour and price. The slope of the regression line is negative, which indicates an inverse relationship between colour and price.

The coefficient of determination (0.1419) is indicates a weak association between clarity and price. The slope of the regression line is negative, which indicates an inverse relationship between clarity and price.

The coefficient of ...

#### Solution Summary

This solution is comprised of a detailed explanation of various aspects of Regression Analysis and Optimization as it pertains to the given problem. Supplemented with EXCEL output, this step-by-step explanation of this complicated topic provides students with a clear perspective of Regression Analysis.

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