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.

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

• Quadratic model

• Linear model

b. Use the best model to predict the time required to inspect a device with 35 components. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Here is the data:

Components	Inspection Time
31	85
13	48
8	29
18	59
16	52
12	40
24	71
41	98
7	21
12	42
18	63
9	25
30	81
11	48
10	30
18	63
19	53
20	60
25	73
45	101
16	59
14	45
20	67
11	46
23	70

Answer 1

Data

Using Excel

data -> data analysis -> regression

Linear

Quadratic

Cubic

a1

linear - 0.908948
quadratic - 0.954099
cubic - 0.956649

b)

cubic has highest adjusted R^2

b)

y^ = -13.8322 + 6.152273 x -0.13929 x^2 + 0.001333 x^3

= -13.8322 + 6.152273 *35 -0.13929*35^2 + 0.001333 **35^3

= 88.03405