Two other measures of quality of a diamond (see For Example: "Indicator variables for diamond colour") are its Table size and Deptb; both are expressed as percentages. Table size is the ratio of the flat top part (the table) diameter to the diameter of the stone. Depth is the ratio of the distance from table to bottom (culet) to the diameter. The output of the regression of \(\log _{10}\) Price on Carat Weight, Colour D, Colour G, Table, and Depth shows:
Response Variable: \(\log _{10}\) Price
\(R^{2}=85.92 \%\) Adjusted \(R^{2}=85.82 \%\)
\(s=0.1080\) with \(749-6=743\) degrees of freedom

Influence measures can be adversely affected by indicator variables, so Studentized residuals, Cook's Distance, and leverage were all calculated on this model without the indicator variables for Colour.
Here are the histograms and boxplots for these three measures. Several points have unusually high values on one or more measures.

The analyst identified five diamonds that had high leverage (1) or Cook's Distance (4). Two of these also had large Studentized residuals. Indicator variables were created for these five points and a regression was run with these new variables:

QUESTION:

What would you do next?

Transcribed Image Text:

Variable Coeff SE(Coeff) f-ratio P-Value Intercept 3.464326 0.322336 10.748 <0.0001 Carat.Size 1.031627 0.015799 65.295 <0.0001 ColourD ColourG 0.291119 0.213842 0.012760 0.014214 20.481 <0.0001 16.759 <0.0001 Table -0.008497 0.002345 -3.623 0.000311 Depth -0.008638 0.003765 -2.294 0.022043