A lead inspector at ElectroTech, an electronics assembly shop, wants to convince
ID: 3060740 • Letter: A
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 from the last 25 devices. The data are shown in the accompanying table.
Number of Components
on Device
http://lectures.mhhe.com/connect/0078020557/Ch16/Static/Ch16_Q10_Data_File.xlsx
a.
A scatterplot of the above data is shown below. Does the lead inspector’s claim seem credible?
Number of Components
on Device
Inspection Time (seconds) 32 84 13 49 9 30 17 60 15 51 11 41 24 71 42 99 7 22 12 42 19 63 8 26 30 80 12 48 10 31 19 62 16 52 19 60 25 72 44 102 16 59 13 44 21 67 12 46 23 70 * - 86% (40) Mon 11:00 AM 9 0 i Firefox File Edit View History Bookmarks Tools Window Help Ch. 16 HW C Chegg Study | Guided Solution x + -) C 0 ezto.mheducation.com/hm.tpx e *** V * Q Search lille S 0 = Time (sec) 8 8 8 * & - ODOS A B D P - E O Q8 - TE FI Number of components O Yes O No b-1. Estimate the linear, quadratic, and cubic regression models. Report the Adjusted R for each model. (Round your answers to 4 decimal places.) Linear model Quadratic model Cubic model Adjusted R2 0.9106 0.9572 0.9614 b-2. Which model has the best fit?Explanation / Answer
a)
Yes
b-1)
Linear Model
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.968
R Square
0.936
Adjusted R Square
0.933
Standard Error
5.368
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
1
9723.87
9723.87
337.49
0.00
Residual
23
662.69
28.81
Total
24
10386.56
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
18.59
2.36
7.87
0.00
13.70
23.47
Number of Components (x)
2.06
0.11
18.37
0.00
1.83
2.29
Quadratic Model
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.99
R Square
0.98
Adjusted R Square
0.98
Standard Error
3.21
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
2
10159.81
5079.90
492.86
0.00
Residual
22
226.75
10.31
Total
24
10386.56
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
0.09
3.18
0.03
0.98
-6.49
6.68
Number of Components (x)
3.96
0.30
13.21
0.00
3.34
4.58
x^2
-0.04
0.01
-6.50
0.00
-0.05
-0.03
Cubic Model
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.99
R Square
0.99
Adjusted R Square
0.99
Standard Error
2.35
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
3
10270.93
3423.64
621.79
0.00
Residual
21
115.63
5.51
Total
24
10386.56
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-21.85
5.41
-4.04
0.00
-33.09
-10.60
Number of Components (x)
7.56
0.83
9.10
0.00
5.83
9.29
x^2
-0.21
0.04
-5.49
0.00
-0.29
-0.13
x^3
0.00
0.00
4.49
0.00
0.00
0.00
Model
Adj r^2
Linear Model
0.933
Quadratic Model
0.98
Cubic Model
0.99
b-2)
Cubic model has the best fit.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.968
R Square
0.936
Adjusted R Square
0.933
Standard Error
5.368
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
1
9723.87
9723.87
337.49
0.00
Residual
23
662.69
28.81
Total
24
10386.56
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
18.59
2.36
7.87
0.00
13.70
23.47
Number of Components (x)
2.06
0.11
18.37
0.00
1.83
2.29
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