# Professor Proposes

Topics: Regression analysis, Mean squared error, Linear regression Pages: 11 (3132 words) Published: November 6, 2012
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Contents:

Case Overview
Characteristics of a Diamond
* The Four C’s (Color, Carat, Cut and Clarity)
* Symmetry and Polish
* Certification
Pricing
Data Set
Regression Analysis
* Full Level – Level type Model * Partial Level – Level Model (Carat) * Partial Level – Level Model (Carat*Color) * Ln – Ln Model * Ln – Level Model * Level – Ln Model Comparison

Appendix

Case Overview

This paper tries to assist a professor in making an educated decision regarding the diamond he should buy. He feels that his girlfriend has already hinted about marriage three times, and the time has come to finally do something about it. So, he decides to propose to her and sets aside \$2000 to \$4000 for a diamond ring. At the store, the professor finds out that picking the right diamond is not a straightforward task. Characteristics of a Diamond

The value of a diamond is determined by a lot of characteristics, out of which some of the most important ones are listed below: Color
Diamonds vary on a scale from colorless to yellow, with the yellower shades being the cheapest and the colorless ones being the most valuable. Other colors are extremely rare and very exorbitant. Carat

This is the unit of measurement for diamonds, where 1 Carat equals 0.2 grams. Higher Carat diamonds are more rare and as a result more valuable. For instance, a two carat diamond will be more expensive than two one carat diamonds combined. Cut

Cut is the main determinant of reflective properties and it refers to the shape and proportion of the diamond. One with the right cut results in the ideal proportions in its facets as well as its depth and width, reflecting light brilliantly. Clarity

Clarity of a diamond signifies the flaws that can be detected within it. (Appendix). Symmetry and Polish
Symmetry measures how well the top of the diamond (facets) and the bottom of the diamond (pavilion) match. A bad facet alignment may lead to light leaking out before being reflected. Polish means how smooth and reflective the surface of the stone is. Polish and Symmetry are measured on a scale of poor, fair, good, very good, excellent and ideal. Certification

Diamonds are evaluated on the characteristics listed above. There are numerous labs that carry out this task, but there are only a few well-known sources of diamond certification. Gemological Institute of America (GIA) and American Gemological Society (AGS) are two of the most respected labs. Some other labs include European Gemological Laboratories (EGL) and International Gemological Institute (IGI) and many other small labs.

Pricing
This paper attempts to predict a range of values of diamond prices by regressing price (dependent variable) against the four C’s, Polish, Symmetry and Certification (independent variables). The analysis comprises of running various regression models and comparing them to see which one fits the data the best. This will be done by making inferences on the outputs of these models and with the help of graphical analysis. The Data Set

The data set being used to carry out the analysis consists of 440 diamonds, which are grouped under three different wholesalers. Characteristics of each diamond are provided in the Appendix. Prices in the data set vary from \$160 to \$3145. Various models will be fit to this data, with each model being refined as inferences are made. Regression

1. Level – Level Full Model:
The first model we are going to consider is the one which regresses price on all the seven variables and shows how...