Breakdowns of machines that produce steel cans are very costly. The more breakdowns, the fewer cans produced, and the smaller the company’s profits. To help anticipate profit loss, the owners of a can company would like to find a model that will predict the number of breakdowns on the assembly line. The model proposed by the company’s statisticians is the following:

y = β_o + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + ∈

where y is the number of breakdowns per 8-hour shift,

x₃ is the temperature of the plant (F°), and x₄ is the number of inexperienced personnel working on the assembly line. After the model is fit using the least-squares procedure, the residuals are plotted against ŷ, as shown in the accompanying figure.

a. Do you detect a pattern in the residual plot? What does this suggest about the least-squares assumptions? 

b. Given the nature of the response variable y and the pattern detected in part a, what model adjustments would you recommend?    

Transcribed Image Text:

Si if afternoon shift lo otherwise Si if midnight X2 lo otherwise