The operators manager at an electronics company believes that the time required for workers to build a circuit board is not necessarily proportional to the number of parts on the board. He wants to develop a regression model to predict time based on part quantity. He has collected data for the last 25 boards. A portion of this data is shown in the accompanying table.

Time (minutes)..................Parts

30.80................................62

9.8...................................32

⋮.......................................⋮

29.8.................................60

a. Estimate the linear regression model to predict time as a function of number of parts (Parts).

Then estimate the quadratic regression model to predict time as a function of Parts and Parts squared. Provide an intuitive justification for the quadratic term.

b. Evaluate the two models in terms of variable significance (α = 0.05) and adjusted R2.

c. Use the best-fitting model to predict how long it would take to build a circuit board consisting of 48 parts.