Question

A lead inspector at ElectroTech, an electronics assembly shop, wants to convince management that it takes longer, on a per-component basis, to inspect large devices with many components than it does to inspect small devices because it is difficult to keep track of which components have already been inspected. To prove her point, she has collected data on the inspection time (Time in seconds) and the number of components per device (Components) from the last 25 devices. A portion of the data is shown in the accompanying table.

Components	Inspection Time
31	83
13	50
9	30
17	59
15	51
11	40
24	71
43	98
8	21
11	42
18	62
7	25
30	79
12	49
10	32
19	63
17	53
18	60
24	71
44	102
17	58
14	44
21	68
13	46
23	69

a-1. Estimate the linear, quadratic, and cubic regression models with Time as the response variable. Report the Adjusted R² for each model. (Round answers to 4 decimal places.)

a-2. Based on adjusted-R² only, which model has the best fit?

• Cubic model

• Linear model

• Quadratic model

b. Use the best model to predict the time required to inspect a device with 38 components. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

LINEAR MODEL

QUADRATIC MODEL

CUBIC MODEL

Summary of fitting of The Linear, Quadratic and Cubic regression model respectively.

Adjusted R^2 values of LInear is 0.922, Quadratic is 0.9691 and Cubic is 0.9786.

Cubic has the highest value. Hence, Cubic model has the best fit.

For X = 38 components, Y(time) = ?

Our Regression equation is

Y = -20.898 + 7.3675X -0.1978X2 + 0.002124X3

substituting X = 38 we will get, Y(time) as 89.992