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.

Variable Intercept Coeff Carat Weight 1.200301 0.011365 SE(Coeff) t-ratio P-Value 2.437903 0.014834 164.349