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
33	85
12	50
9	29
17	59
16	50
12	41
25	72
43	98
7	21
12	41
20	64
7	25
30	80
11	49
11	30
20	63
19	53
19	61
24	73
44	102
17	59
13	45
21	67
11	47
24	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?

• Quadratic model

• Linear model

• Cubic model

b. Use the best model to predict the time required to inspect a device with 40 components. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

Part a)
enter the data in excel

click on insert tab

in that select öther charts

from the drop down menu select all chart types

From the new window of all chart types select "XY scatter"

Click ok

Following scatter plot appears on screen:

.

Once you get the scatterplot

right click on any of the scatter point

A drop down menu appears

from it select "add trendline"

Following window appears on screen:

.

Select the type of model you need , like in this image I have selected Linear

[For quadratic select polynomial of order 2 in the second attempt]

[and for cubic select polynomial of order 3 in the third attempt]

In all three cases make sure to tick mark the box that reads "dispaly R squared on chart"

Click ok following line appears on the chart:

.

For quadratic model following graph is obtained

.

For cubic model following graph is obtained:

.

Thus the three R square values are:

.

Since the cubic model has highest value of R square: 0.9595, hence the best fit model is the cubic model

.

Part b)

The equation of the model can be obtained by the same steps, only when you select polynomial : order 3

tick mark the check box for "display equation on chart "

.

thus the equation obtained is as follows:

.

.