The article ??The Ball-on-Three-Ball Test for Tensile Strength: Refined Methodology and Results for Three Hohokam Ceramic Types?? (M. Beck, American Antiquity, 2002:558??569) discusses the strength of ancient ceramics. The following table presents measured weights (in g), thicknesses (in mm), and loads (in kg) required to crack the specimen for a collection of specimens dated between A.D. 1100 and 1300 from the Middle Gila River, in Arizona.

a. Fit the model y = β₀ + β₁x₁ + β₂x₂ + ε.

b. Drop the variable whose coefficient has the larger P-value, and refit.

c. Plot the residuals versus the fitted values from the model in part (b). Are there any indications that the model is not appropriate?

Weight (x,) Thickness (x2) Load (y) 12.7 5.69 20 12.9 5.05 16 17.8 6.53 20 18.5 6.51 36 13.4 5.92 27 15.2 5.88 35 13.2 4.09 15 18.3 6.14 18 16.2 5.73 5.47 24 14.7 18.2 21 7.32 30 14.8 4.91 20 17.7 6.72 24 16.0 5.85 23 17.2 6.18 21 14.1 5.13 13 16.1 5.71 21