STATISTICS 401D
Spring 2016
Laboratory Assignment 9
1. Data on three variables were collected in an observational study in a semiconductor manufacturing plant. In this plant, the finished semiconductor is wire bonded to a frame. To study
the effect of two variables the wire length, and the height of the die on the pull strength (a
measure of the amount of force required to break the bond), the engineers would like to find
a model relating pull strength to wire length and die height. The data appear below and in
the file wirepull.jmp. You may use JMP to perform as much of the computations needed as
you can.
Obs.
Pull
Wire
Die
No. Strength(y) Length(x1 ) Height(x2 )
1
9.95
2
50
2
24.45
8
110
3
31.75
11
120
4
35
10
550
5
25.02
8
295
6
16.86
4
200
7
14.38
2
375
8
9.6
2
52
9
24.35
9
100
10
27.5
8
300
11
17.08
4
412
12
37
11
400
Obs.
Pull
Wire
Die
No. Strength(y) Length(x1 ) Height(x2 )
13
41.95
12
500
14
11.66
2
360
15
21.65
4
205
16
17.89
4
400
17
69
20
600
18
10.3
1
585
19
34.93
10
540
20
46.59
15
250
21
44.88
15
290
22
54.12
16
510
23
56.63
17
590
24
22.13
6
100
25
21.15
5
400
(a) The first order model
y = β0 + β1 x1 + β2 x2 + was fitted to the data. Using the JMP output, construct an analysis of variance table
and test the hypothesis of H0 : β1 = β2 = 0 vs. Ha : at least one of β1 or β2 6= 0. Give
the R2 value. Should we accept the first order model and not proceed further because
R2 is fairly high? Explain why or why not?
(b) Use the residual plots to evaluate whether the model assumptions are reasonable. By
examining the residual plots, are there reasons to believe that the first order model is
not adequate? Also is there evidence that interaction exists between the two factors? As
a result of your analysis what other terms would you consider adding to the model, if
any. Explain why?
(c) From the residual diagnostics of the above model fit, select one case each that you might
select as a possible x-outlier, a possible y-outlier, or an influential observation. Give a
reason for each of your choices.
(d) Based on the above residual analysis and expertise of the engineers, the model
y = β0 + β1 x1 + β2 x2 + β3 x21 + β4 x1 x2 + β5 x21 x2 + was suggested. Fit this model and use the sums of squares from the JMP output, to
construct an F statistic to test the hypothesis H0 : β4 = β5 = 0. Use a percentile from
the F table to test this hypothesis at α = .05. What does the result of this test tell you ?
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2. In a laboratory experiment, the weight loss in milligrams of a certain machine part due to
friction when specimens were used in a wear-tester with four different lubricants SP51, L43,
Z90, and Blu-Tek, were measured. Lower the weight loss, the better the performance of the
lubricant. The lubricants were assigned to the test runs completely at random. The model
yij = µi + ij , i = 1, . . . , 4; j = 1, . . . , 8 was used to analyze the resulting data:
i
1
2
3
4
Lubricant
SP51
L43
Z907
Blu-Tek
12
8
10
8
11
10
5
5
Weight Loss (in milligrams)
7
10
9
10
5
7
10
9
7
8
9
6
8
7
5
6
12
7
7
6
7
8
5
7
ȳi.
9.75
8.0
7.125
6.5
(a) Construct an analysis of variance using numbers from the JMP output. Test H0 : µ1 =
µ2 = µ3 = µ4 vs. Ha : at least one µi is different from the others, using α = .05. Use the
p-value from the JMP output to make a decision.
(b) Use the lsd procedure to test all possible differences H0 : µi − µj = 0 vs. Ha : µi − µj 6=
0 using α = .05. Report the results using the underlining display. Summarize your
conclusions from this procedure in sentence or two.
(c) Use the Tukey procedure to test all possible differences H0 : µi − µj = 0 vs. Ha :
µi − µj 6= 0 using α = .05. Report the results using the underlining display. Point out
any conclusions that are different from those made using the lsd procedure.
(d) It would be more useful to test pre-planned comparisons than testing pairwise differences
among the 4 lubricant effects. In this experiment it is known that the 4 factors are
Lubricant
1
2
3
4
Formulation
Petroleum Distillate Base with Standard Silicon Additive
Petroleum Distillate Base with a Hi-tech Detergent Additive
Synthetic Oil Base with Standard Silicon Additive
Synthetic Oil Base with a Hi-tech Detergent Additive
Thus the experimenter could have planned to do the following comparisons.
i. compare the average effect of the petroleum distillate based lubricants to the average
effect of the synthetic oil based lubricants,
ii. compare the average effect of the standard silicon additive to the average effect of
the hi-tech detergent additive,
iii. compare the effects of the two petroleum distillate based lubricants, one with the
silicon additive to that with the hi-tech detergent additive, and
iv. compare the effects of the two synthetic oil based lubricants, one with the silicon
additive to that with the hi-tech detergent additive.
Compute appropriate t-statistics to test the comparisons given above both by hand and
using JMP controlling the error rate for each comparison at α = .05. Write a statement
in conclusion in each case.
Write your answers to Problems 1 and 2 on separate sheets extracting numbers from
the JMP output. Remember to turn-in the JMP outputs also.
Due Tuesday, April 26 , 2016 (Turn-in at the end of the lab
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