The President of a Manufacturing Firm Used a Regression Model

Essay

The president of a manufacturing firm used a regression model of the form y = α + β₁x₁ + β₂x₂ + β₃x₃ + e to study the relationship between the variables
y = production cost (in dollars)
x₁ = machine time to produce one unit of the product (in minutes)
x₂ = material and labor costs per unit (in dollars)
x₃ = percentage of defective products produced All of seven of the possible models containing combinations of these three variables were fit resulting in the summary table below ​
a) If n = 20, compute the value of the adjusted R² statistic for each of the 7 models.
b) Which of the single variable models is the best? Explain your choice in a few sentences.
c) Let model A be the model with variables x₁, x₂, and model B be the model with variables x₁, x₂, x₃. Which of these two models appears to be the better model? Explain your choice in a few sentences.
d) Which of the seven models appears to be the best overall model? Explain your choice in a few sentences.