Professor Proposes

3118 Words Oct 24th, 2012 13 Pages

Case Overview
Characteristics of a Diamond * The Four C’s (Color, Carat, Cut and Clarity) * Symmetry and Polish * Certification
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
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….βk are coefficients of the ‘k’ predictor variables (k = 7 in this model). The coefficients indicate how the price changes by a unit change in any variable, keeping rest of the variables constant.
The output shows that cut, polish and certification have t-stats and corresponding p-values that are considerably greater than 0.05 (significance level). A stepwise regression drops these variables, indicating that they are not a good fit for the model (Appendix).
One reason might be that the scatterplot of price vs. carat shows observations being clumped; representing the three different wholesalers (Appendix). Making inferences on this scatterplot shows that wholesaler 3 carries diamonds in the range of $160 to $665, significantly lower than the total range. These observations might lead to inaccurate prediction of the effect of predictor variables on price. Also, it can be seen from the scatterplot that wholesaler 1 deals in diamonds falling under a very small interval of $3000 to $3091, while the ones from wholesaler 2 fall in the range of $1856 to $3145.
As a result, this paper makes an assumption that only data from wholesalers 1 and 2 will fit the model best, in terms of finding the correct diamond for the professor.
2. Partial Level – Level Model (Carat):
Considering the assumption made above, the next model regresses price on all the variables, but only for diamonds from wholesalers 1 and 2. It can be seen from the scatterplot of price vs. carat