The article “The Analysis and Selection of Variables in Linear Regression” (Biometrics [...

The article “The Analysis and Selection of Variables in Linear Regression” (Biometrics [1976]: 1– 49) reports on an analysis of data taken from issues of Motor Trend magazine. The dependent variable y was gas mileage; there were n = 32 observations; and the independent variables were x₁ = engine type (1 = straight, 0 = V), x₂ = number of cylinders, x₃ = transmission type (1 manual, 0 automatic), x₄ = number of transmission speeds, x₅ = engine size, x₆ = horsepower, x₇ = number of carburetor barrels, x₈ final drive ratio, x₉ weight, and x₁₀ quarter-mile time. The R² and adjusted R² values are given in the accompanying table for the best model using k predictors for k = 1, . . . , 10. Which model would you select? Explain your choice and the criteria used to reach your decision.