final regression on diamond pricing
TRANSCRIPT
- 1. DIAMONDS
- 2. Bruce Pollard ..
- 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. THE IMPORTANCE OF Diamonds Social: Marriage, Feminism, Class, Values Economic: Globalization, Investment, Market, Advertisement... Political: Colonialism, Environmental, Conflict & War (Blood Diamond)
- 5. The 4 Cs Carat Color Clarity Cut factors for pricing a Diamond
- 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. 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. Which Diamond Costs More?
- 9. Data File: DIAMONDS (1st ten observations)
- 10. Scatter Plot Matrix VISUAL (relation among all variables) Non-linearity between price and carat No interaction among other predictors
- 11. Correlation Matrix STATISTICAL (relation among all variables) Strong correlation: price * carat No interaction among other predictors
- 12. Partial Plots VISUAL (inspection of residuals) Price * Predictors (intercept, carat, colors D, E, F, G) All plots indicate linear relation
- 13. Partial Plots (continued) Price * Predictors (color: H, clarity: IF, VVS1, VVS2, VS1, VS2, certification: GIA) All plots, except GIA, indicate linear relation
- 14. Partial Plots (continued) Predictors * Price (certification: IGI) Plot does not indicate linear relation exists
- 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. Normal Plot VISUAL relation between (price * carat) Consistent with scatter plot Issue with the normality assumption
- 17. Residual Plot Initial Model All Variables VISUAL (inspection) Non-linearity issue (curvilinear clearly reflected in plot) Issue with the constant variance assumption
- 18. Normal Plot Initial Model All Variables VISUAL (inspection) Inconsistent data with the expected line - low to high Issue with the normality assumption
- 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. Normal Plot Transformation All Variables (log Price) VISUAL (inspection) Improvement but more correction needed Issue with the normality assumptionstill
- 21. Residual Plot Difference (Carat Diff + Square) VISUAL (inspection) Regression is linear Constant Variance assumption satisfied
- 22. Further improvement but close enough? Assumption of normality satisfied Normal Plot Difference (Carat Diff + Square) VISUAL (inspection)
- 23. BEST *5* MODELS (GIA removed from highlighted number one choice)
- 24. STEPWISE Summary Selection (GIA removed)
- 25. PARAMETERS Tolerance, VIF, CLimits
- 26. REGRESSION SIGNIFICANT (P-value < .0001 and Adj R-Sq = .9947)
- 27. INFLUENTIAL POINTS (no remedial action required)
- 28. Diagnostic Analysis ASSUMPTIONS Normality: YES! Linearity: YES! Homoscedasticity: YES! Independence: YES!
- 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. ORIGINAL QUESTION: Which Diamond Costs More?
- 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. 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. 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. 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. HOW TO SHOP? ALL diamonds Sparkle and Shine. Color and Clarity determine how much! Use our FITTED MODEL because STATISTICS tell the TRUTH.