In addition to the predictor variables from the last example (For Example: "Regression diagnostics for diamond prices"), we have information on the quality of the Cut (four grades: Good, Very Good, Excellent, and Ideal) and the quality of the Clarity (seven grades: \(V V S 2, V V S 1, V S 2, V S 1, S I 2, S I 1\), and \(I F\) ). A model was fit to predict Log10Price from all the predictors we have available: Carat Weight, Colour, Cut, Clarity, Depth, and Table on all 749 diamonds. A stepwise backward removal of predictors was performed, and the following model was selected:
Response Variable: \(\log _{10}\) Price \(^{2}\)
\(R^{2}=94.46 \%\) Adjusted \(R^{2}=94.37 \%\)
\(s=0.06806\) with \(749-13=736\) degrees of freedom

QUESTION:

Compare this model with the model based only on Carat Weight and Colour from For Example: “Indicator variables for diamond colour” with indicator variables for Colour.

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Variable Intercept Coeff Carat Weight 1.200301 0.011365 SE(Coeff) t-ratio P-Value 2.437903 0.014834 164.349 <0.0001 105.611 <0.0001 ColourD ColourG 0.342888 0.009107 37.649 <0.0001 0.254024 0.008159 31.135 <0.0001 CutGood -0.028884 0.011133 -2.594 0.00966 CutVeryGood Cutideal -0.015374 0.005503 -2.793 0.00535 0.012127 0.010022 -0.237850 0.011736 -20.267 ClaritySI1 ClarityS12 -0.312076 0.012454 -25.058 <0.0001 ClarityVS1 -0.130431 0.012118 -10.764 <0.0001 -15.273 1.210 0.22662 <0.0001 ClarityVS2 -0.178439 0.011684 ClarityVVS1 -0.064518 0.012445 ClarityVVS2 -0.076747 0.011878 -6.461 <0.0001 -5.184 <0.0001 <0.0001