1. 1. DIAMONDS
2. 2. Bruce Pollard ..
3. 3. THE POWER OF Diamonds We thirst for diamonds because we believe them to be rare and because they are perceived by others to have a certain power power from wealth, power from love, power from crackling sexuality, power from kinship with all of the above. The belief in a diamonds power is its power. (Tom Zoellner )
4. 4. THE IMPORTANCE OF Diamonds Social: Marriage, Feminism, Class, Values Economic: Globalization, Investment, Market, Advertisement... Political: Colonialism, Environmental, Conflict & War (Blood Diamond)
5. 5. The 4 Cs Carat Color Clarity Cut factors for pricing a Diamond
6. 6. The Classic 4 Cs Carat: Weight of the diamond. One carat equal to 200 milligrams. Color: Based on absence of color. D-E-F represent colorless. Clarity: Measures internal characteristics of stone, referred to as inclusions and blemishes. Cut: Not the design (round, emerald, etc.) but how the facets of the stone interact with light, which is the sparkle factor. factors for pricing a Diamond
7. 7. Our 4 Cs (substituting certification for cut) Carat: Weight of the diamond. One carat equal to 200 milligrams. Color: Based on absence of color. D-E-F represent colorless. Clarity: Measures internal characteristics of stone, referred to as inclusions and blemishes. Certification: Evaluation by a gemologist grading the diamond according to the 4 Cs. factors for pricing a Diamond
8. 8. Which Diamond Costs More?
9. 9. Data File: DIAMONDS (1st ten observations)
10. 10. Scatter Plot Matrix VISUAL (relation among all variables) Non-linearity between price and carat No interaction among other predictors
11. 11. Correlation Matrix STATISTICAL (relation among all variables) Strong correlation: price * carat No interaction among other predictors
12. 12. Partial Plots VISUAL (inspection of residuals) Price * Predictors (intercept, carat, colors D, E, F, G) All plots indicate linear relation
13. 13. Partial Plots (continued) Price * Predictors (color: H, clarity: IF, VVS1, VVS2, VS1, VS2, certification: GIA) All plots, except GIA, indicate linear relation
14. 14. Partial Plots (continued) Predictors * Price (certification: IGI) Plot does not indicate linear relation exists
15. 15. Scatter Plot VISUAL relation between (price * carat) Non-linearity issue - see stacked data on Carat axis between 1.0 and 1.1 Large concentration of pricing on lower and higher ends
16. 16. Normal Plot VISUAL relation between (price * carat) Consistent with scatter plot Issue with the normality assumption
17. 17. Residual Plot Initial Model All Variables VISUAL (inspection) Non-linearity issue (curvilinear clearly reflected in plot) Issue with the constant variance assumption
18. 18. Normal Plot Initial Model All Variables VISUAL (inspection) Inconsistent data with the expected line - low to high Issue with the normality assumption
19. 19. Residual Plot Transformation All Variables (log Price) VISUAL (inspection) Non-linearity issue (curvilinear clearly reflected in plot) Issue with the constant variance assumption
20. 20. Normal Plot Transformation All Variables (log Price) VISUAL (inspection) Improvement but more correction needed Issue with the normality assumptionstill
21. 21. Residual Plot Difference (Carat Diff + Square) VISUAL (inspection) Regression is linear Constant Variance assumption satisfied
22. 22. Further improvement but close enough? Assumption of normality satisfied Normal Plot Difference (Carat Diff + Square) VISUAL (inspection)
23. 23. BEST *5* MODELS (GIA removed from highlighted number one choice)
24. 24. STEPWISE Summary Selection (GIA removed)
25. 25. PARAMETERS Tolerance, VIF, CLimits
26. 26. REGRESSION SIGNIFICANT (P-value < .0001 and Adj R-Sq = .9947)
27. 27. INFLUENTIAL POINTS (no remedial action required)
28. 28. Diagnostic Analysis ASSUMPTIONS Normality: YES! Linearity: YES! Homoscedasticity: YES! Independence: YES!
29. 29. FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427Carat Difference - 2.10368Carat Difference Squared + 0.44273D + 0.36280E + 0.28604F + 0.19683G + 0.10260H + 0.31905IF + 0.22444VVS1 + 0.14267VVS2 + 0.07602VS1 - 0.02377IGI
30. 30. ORIGINAL QUESTION: Which Diamond Costs More?
31. 31. SMALL DIAMOND Certified by GIA (Carat=.58, Color=G, Clarity=VVS2) FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(-.0509091) - 2.10368(.002591736) + 0.19683(1) + 0.14267(1) => PREDICTION=> exp(PREDICTION): $3,010.30
32. 32. LARGE DIAMOND Certified by GIA (Carat=1.03, Color=H, Clarity=VS2) FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(.3990909) - 2.10368(.159273546) => PREDICTION=> exp(PREDICTION): $5,985.55
33. 33. MEDIUM DIAMOND Certified by GIA (Carat=.71, Color=E, Clarity=VS1) FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(.0790909) - 2.10368(.006255370) + 0.44273(1) + 0.31905(1) => PREDICTION=> exp(PREDICTION): $6,742.68
34. 34. FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(-.0509091) - 2.10368(.002591736) + 0.19683(1) + 0.14267(1) => PREDICTION=> exp(PREDICTION): $3,010.30 FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(.3990909) - 2.10368(.159273546) => PREDICTION=> exp(PREDICTION): $5,985.55 FITTED MODEL LOG(PRICE) = 7.8292 + 3.01427(.0790909) - 2.10368(.006255370) + 0.44273(1) + 0.31905(1) => PREDICTION=> exp(PREDICTION): $6,742.68 CARAT WT MATTERS COLOR MATTERS CLARITY MATTERS
35. 35. HOW TO SHOP? ALL diamonds Sparkle and Shine. Color and Clarity determine how much! Use our FITTED MODEL because STATISTICS tell the TRUTH.