252y0333TH 11/18/03
ECO252 QBA2
Third EXAM
Nov 25 2003
TAKE HOME SECTION
Name: ______KEY_______________
Social Security Number: _________________________
Please Note: computer problems 2 and 3 should be turned in with the exam. In problem 2, the 2 way
ANOVA table should be completed. The three F tests should be done with a 5% significance level and you
should note whether there was (i) a significant difference between drivers, (ii) a significant difference
between cars and (iii) significant interaction. In problem 3, you should show on your third graph where the
regression line is.
II. Do the following: (23+ points). Assume a 5% significance level. Show your work!
1. Assume that each column below represents a random sample of sales of the popular cereal brand,
‘Whee!’ As it was moved from shelf 1 (lowest) to shelf 4 (highest) of a group of supermarkets. Assume that
the underlying distribution is Normal and test the hypothesis 1   2   3   4 .
a) Before you start add the second to last digit of your social security number to the 451 in column 4 and
find the sample variance of sales from shelf 4. For example, Seymour Butz’s SS number is 123456789 and
he will change 451 to 459. This should not change the results by much. (2)
b) Test the hypothesis (6) Show your work – it is legitimate to check your results by running these problems
on the computer, but I expect to see hand computations for every part of them.
c) Compare means two by two, using any one appropriate statistical method, to find out which shelves are
significantly better than others. (3)
d) (Extra Credit) What if you found out that each row represented one store? If this changes your analysis,
redo the analysis. (5)
e) (Extra Credit) What if you found out that each row represented one store and that the underlying
distribution was not Normal? If this changes your analysis, redo the analysis. (5)
f) I did some subsequent analysis on theis problem. The output, in part said
Levene's Test (any continuous distribution)
Test Statistic: 0.609
P-Value
: 0.613
What was I testing for and what should my conclusion be? (2)
Row
1
1
2
3
4
5
6
7
8
9
10
336
417
208
420
366
227
357
353
518
388
Sales of ‘Whee’ Cereal
Shelf
2
3
4
440
277
374
421
481
349
328
449
462
373
464
479
492
456
338
413
383
554
497
510
354
423
321
424
518
451
311
462
339
202
Sum of
Sum of
1362860
Sum of
Sum of
1602366
Sum of
Sum of
2140264
shelf 1 = 3590.0
squares of shelf 1 =
shelf 2 = 3954.0
squares of shelf 2 =
shelf 3 = 4586.0
squares of shelf 3 =
252x0333 11/18/03
2. A company, operating in 12 regions, gives us its advertising expenses as a percent of those of its leading
competitor, and its sales as a percent of those of its leading competitor.
Row
1
2
3
4
5
6
7
8
9
10
11
12
Ad
77
110
110
93
90
95
100
85
96
83
100
95
Sales
85
103
102
109
85
103
110
86
92
87
98
108
Sum
Sum
Sum
Sum
of
of
of
of
Ad = 1134.0
squares of Ad = 108258
Sales = 1168.0
squares of Sales = 114750
Note that the sum and sum of squares
of sales can’t be used directly, but
they should help you to get the
corrected numbers.
Change the 103 in the ‘sales’ column by adding the second-to-last digit of your Social Security number to it.
For example, Seymour Butz’s SS number is 123456789 and he will change 103 to 112. This should not
change the results by much. The question is whether our relative advertising expenses affect our relative
sales, so ‘Sales’ should be your dependent variable and ‘Ad’ should be your independent variable.
Show your work – it is legitimate to check your results by running the problem on the computer, but I
expect to see hand computations that show clearly where you got your numbers for every part of this
problem.
a. Compute the regression equation Y  b0  b1 x to predict the ‘Sales’ on the basis of ‘Ad’. (2)
b. Compute R 2 . (2)
c. Compute s e . (2)
d. Compute s b0 and do a significance test on b0 (2)
e. Do an ANOVA table for the regression. What conclusion can you draw from this table about the
relationship between advertising expenditures and sales? Why? (2)
f. It is proposed to raise our expenditures to 110% of our competitors’ in every region. Use this
to find a predicted value for sales and to create a confidence interval for sales. Explain the
difference between this and a prediction interval and when the prediction interval would be more
useful. (3)
————— 11/22/2003 4:04:56 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-00.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-00.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-00.mtw
MTB > Execute "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\252AOV3W.MTB" 1.
Executing from file: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\252AOV3W.MTB
Sum of 1
2
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3805.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1524677
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
354
423
321
424
518
451
311
462
339
202
C12
1
2
3
4
5
6---------------------------0
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
3
Analysis of Variance
Source
DF
SS
Factor
3
55058
Error
36
227003
Total
39
282061
Level
1
2
3
4
N
10
10
10
10
MS
18353
6306
Mean
359.00
395.40
458.60
380.50
Pooled StDev =
StDev
90.71
65.79
64.23
92.42
79.41
F
2.91
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
55058
18353
Error
36
227003
6306
Total
39
282061
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.50
Pooled StDev =
StDev
90.71
65.79
64.23
92.42
79.41
F
2.91
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
3
2
-132.1
59.3
3
-195.3
-3.9
-158.9
32.5
4
-117.2
74.2
-80.8
110.6
-17.6
173.8
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62914
C11
3
55058
Error
27
164090
Total
39
282061
MS
6990
18353
6077
F
1.15
3.02
P
0.364
0.047
Friedman Test: C10 versus C11, C12
4
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
5
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-01.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-01.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-01.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3806.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1525580
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
354
423
321
424
518
452
311
462
339
202
C12
1
2
3
4
5
6-------------------------1
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
6
30
31
32
33
34
35
36
37
38
39
40
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
55022
Error
36
227145
Total
39
282168
Level
1
2
3
4
N
10
10
10
10
MS
18341
6310
Mean
359.00
395.40
458.60
380.60
Pooled StDev =
StDev
90.71
65.79
64.23
92.51
79.43
F
2.91
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
55022
18341
Error
36
227145
6310
Total
39
282168
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.60
Pooled StDev =
StDev
90.71
65.79
64.23
92.51
79.43
F
2.91
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.1
59.3
3
-195.3
-3.9
-158.9
32.5
4
-117.3
74.1
-80.9
110.5
3
-17.7
173.7
7
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62837
C11
3
55022
Error
27
164308
Total
39
282168
MS
6982
18341
6085
F
1.15
3.01
P
0.366
0.047
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
8
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-02.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-02.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-02.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3807.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1526485
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
354
423
321
424
518
453
311
462
339
202
C12
1
2
3
4
5
6---------------------------2
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
9
30
31
32
33
34
35
36
37
38
39
40
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54987
Error
36
227289
Total
39
282276
Level
1
2
3
4
N
10
10
10
10
MS
18329
6314
Mean
359.00
395.40
458.60
380.70
Pooled StDev =
StDev
90.71
65.79
64.23
92.59
79.46
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54987
18329
Error
36
227289
6314
Total
39
282276
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.70
Pooled StDev =
StDev
90.71
65.79
64.23
92.59
79.46
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.1
59.3
3
-195.3
-3.9
-158.9
32.5
4
-117.4
74.0
-81.0
110.4
3
-17.8
173.6
10
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62761
C11
3
54987
Error
27
164528
Total
39
282276
MS
6973
18329
6094
F
1.14
3.01
P
0.368
0.048
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
11
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-03.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-03.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-03.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3808.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1527392
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
354
423
321
424
518
454
311
462
339
202
C12
1
2
3
4
5
6------------------------------------3
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
12
29
30
31
32
33
34
35
36
37
38
39
40
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54952
Error
36
227434
Total
39
282386
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.80
Pooled StDev =
MS
18317
6318
StDev
90.71
65.79
64.23
92.68
79.48
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54952
18317
Error
36
227434
6318
Total
39
282386
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.80
Pooled StDev =
StDev
90.71
65.79
64.23
92.68
79.48
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.2
59.4
3
-195.4
-3.8
-159.0
32.6
4
-117.6
74.0
-81.2
110.4
3
-18.0
173.6
13
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62685
C11
3
54952
Error
27
164749
Total
39
282386
MS
6965
18317
6102
F
1.14
3.00
P
0.369
0.048
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-03.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-03.mtw
* NOTE * Existing file replaced.
14
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-04.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-04.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-04.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3809.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1528301
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
354
423
321
424
518
455
311
462
339
202
C12
1
2
3
4
5
6-----------------------------------------------4
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
15
29
30
31
32
33
34
35
36
37
38
39
40
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54916
Error
36
227582
Total
39
282498
Level
1
2
3
4
N
10
10
10
10
MS
18305
6322
Mean
359.00
395.40
458.60
380.90
Pooled StDev =
StDev
90.71
65.79
64.23
92.77
79.51
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54916
18305
Error
36
227582
6322
Total
39
282498
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
380.90
Pooled StDev =
StDev
90.71
65.79
64.23
92.77
79.51
F
2.90
P
0.048
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(-------*--------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.2
59.4
3
-195.4
-3.8
-159.0
32.6
4
-117.7
73.9
-81.3
110.3
3
-18.1
173.5
16
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62610
C11
3
54916
Error
27
164971
Total
39
282498
MS
6957
18305
6110
F
1.14
3.00
P
0.371
0.048
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-04.mtw";
SUBC>
Replace.
17
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-05.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-05.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-05.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3810.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1529212
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
354
423
321
424
518
456
311
462
339
202
C12
1
2
3
4
5
6-----------------------------5
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
18
29
30
31
32
33
34
35
36
37
38
39
40
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54881
Error
36
227731
Total
39
282612
Level
1
2
3
4
N
10
10
10
10
MS
18294
6326
Mean
359.00
395.40
458.60
381.00
Pooled StDev =
StDev
90.71
65.79
64.23
92.86
79.54
F
2.89
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54881
18294
Error
36
227731
6326
Total
39
282612
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.00
Pooled StDev =
StDev
90.71
65.79
64.23
92.86
79.54
F
2.89
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.2
59.4
3
-195.4
-3.8
-159.0
32.6
4
-117.8
73.8
-81.4
110.2
3
-18.2
173.4
19
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62536
C11
3
54881
Error
27
165195
Total
39
282612
MS
6948
18294
6118
F
1.14
2.99
P
0.373
0.048
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
20
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-06.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-06.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-06.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3811.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1530125
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
354
423
321
424
518
457
311
462
339
202
C12
1
2
3
4
5
6---------------------------6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
21
27
28
29
30
31
32
33
34
35
36
37
38
39
40
7
8
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54846
Error
36
227882
Total
39
282728
Level
1
2
3
4
N
10
10
10
10
MS
18282
6330
Mean
359.00
395.40
458.60
381.10
Pooled StDev =
StDev
90.71
65.79
64.23
92.95
79.56
F
2.89
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54846
18282
Error
36
227882
6330
Total
39
282728
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.10
Pooled StDev =
StDev
90.71
65.79
64.23
92.95
79.56
F
2.89
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
-132.3
59.5
3
-195.5
-3.7
2
3
-159.1
32.7
22
4
-118.0
73.8
-81.6
110.2
-18.4
173.4
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62461
C11
3
54846
Error
27
165420
Total
39
282728
MS
6940
18282
6127
F
1.13
2.98
P
0.375
0.049
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
23
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-07.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-07.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-07.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3813.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1531957
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
354
423
321
424
518
459
311
462
339
202
C12
1
2
3
4
5
6-------------------------------7
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
24
31
32
33
34
35
36
37
38
39
40
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54777
Error
36
228189
Total
39
282966
Level
1
2
3
4
N
10
10
10
10
MS
18259
6339
Mean
359.00
395.40
458.60
381.30
Pooled StDev =
StDev
90.71
65.79
64.23
93.13
79.62
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54777
18259
Error
36
228189
6339
Total
39
282966
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.30
Pooled StDev =
StDev
90.71
65.79
64.23
93.13
79.62
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.3
59.5
3
-195.5
-3.7
-159.1
32.7
4
-118.2
73.6
-81.8
110.0
3
-18.6
173.2
25
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62314
C11
3
54777
Error
27
165875
Total
39
282966
MS
6924
18259
6144
F
1.13
2.97
P
0.378
0.049
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
26
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-08.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-08.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-08.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3813.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1531957
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
354
423
321
424
518
459
311
462
339
202
C12
1
2
3
4
5
6----------------------------------8
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
27
29
30
31
32
33
34
35
36
37
38
39
40
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54777
Error
36
228189
Total
39
282966
Level
1
2
3
4
N
10
10
10
10
MS
18259
6339
Mean
359.00
395.40
458.60
381.30
Pooled StDev =
StDev
90.71
65.79
64.23
93.13
79.62
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54777
18259
Error
36
228189
6339
Total
39
282966
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.30
Pooled StDev =
StDev
90.71
65.79
64.23
93.13
79.62
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.3
59.5
3
-195.5
-3.7
-159.1
32.7
4
-118.2
73.6
-81.8
110.0
3
-18.6
173.2
28
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62314
C11
3
54777
Error
27
165875
Total
39
282966
MS
6924
18259
6144
F
1.13
2.97
P
0.378
0.049
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
Grand median
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Sum of
Ranks
19.0
22.0
35.0
24.0
29
252y0333TH 11/18/03
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-09.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-09.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-09.mtw
MTB > exec '252AOV3w'
Executing from file: 252AOV3w.MTB
Sum of 1
Sum of 1 = 3590.0
Sum of Squares of 1
Sum of squares (uncorrected) of 1 = 1362860
Sum of 2
Sum of 2 = 3954.0
Sum of Squares of 2
Sum of squares (uncorrected) of 2 = 1602366
Sum of 3
Sum of 3 = 4586.0
Sum of Squares of 3
Sum of squares (uncorrected) of 3 = 2140264
Sum of 4
Sum of 4 = 3814.0
Sum of Squares of 4
Sum of squares (uncorrected) of 4 = 1532876
Data Display
Row
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
354
423
321
424
518
460
311
462
339
202
C12
1
2
3
4
5
6--------------------------9
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
30
28
29
30
31
32
33
34
35
36
37
38
39
40
8
9
10
1
2
3
4
5
6
7
8
9
10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source
DF
SS
Factor
3
54742
Error
36
228345
Total
39
283088
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.40
Pooled StDev =
MS
18247
6343
StDev
90.71
65.79
64.23
93.22
79.64
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source
DF
SS
MS
C11
3
54742
18247
Error
36
228345
6343
Total
39
283088
Level
1
2
3
4
N
10
10
10
10
Mean
359.00
395.40
458.60
381.40
Pooled StDev =
StDev
90.71
65.79
64.23
93.22
79.64
F
2.88
P
0.049
Individual 95% CIs For Mean
Based on Pooled StDev
---------+---------+---------+------(--------*-------)
(--------*-------)
(-------*--------)
(--------*-------)
---------+---------+---------+------360
420
480
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0107
Critical value = 3.81
Intervals for (column level mean) - (row level mean)
1
2
2
-132.4
59.6
3
-195.6
-3.6
-159.2
32.8
4
-118.4
-82.0
3
-18.8
31
73.6
110.0
173.2
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source
DF
SS
C12
9
62241
C11
3
54742
Error
27
166104
Total
39
283088
MS
6916
18247
6152
F
1.12
2.97
P
0.380
0.050
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76
DF = 3
C11
1
2
3
4
P = 0.033
N
10
10
10
10
Est
Median
377.63
414.75
474.13
396.50
=
415.75
Grand median
Sum of
Ranks
19.0
22.0
35.0
24.0
MTB >
————— 11/22/2003 6:18:36 AM ————————————————————
Results for: 2x0333-10.mtw
MTB > Name c15 = 'CLIM5' c16 = 'CLIM6' c17 = 'PLIM5' c18 = 'PLIM6'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM5'-'CLIM6';
SUBC>
PLimits 'PLIM5'-'PLIM6';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 35.7 + 0.652 Ad
Predictor
Constant
Ad
S = 7.740
Coef
35.71
0.6521
SE Coef
22.22
0.2339
R-Sq = 43.7%
T
1.61
2.79
P
0.139
0.019
R-Sq(adj) = 38.1%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
465.57
599.10
1064.67
MS
465.57
59.91
F
7.77
P
0.019
Predicted Values for New Observations
32
New Obs
1
Fit
107.44
SE Fit
4.26
95.0% CI
97.95, 116.93)
(
95.0% PI
87.76, 127.12)
(
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-10.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-10.mtw
* NOTE * Existing file replaced.
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 29.2 + 0.671 Sales
Predictor
Constant
Sales
Coef
29.23
0.6706
S = 7.850
SE Coef
23.52
0.2406
R-Sq = 43.7%
T
1.24
2.79
P
0.242
0.019
R-Sq(adj) = 38.1%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
478.83
616.17
1095.00
MS
478.83
61.62
F
7.77
P
0.019
Data Display
Row
Ad
Sales
C3
exec
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
103
102
109
85
103
110
86
92
87
98
108
7225
10609
10404
11881
7225
10609
12100
7396
8464
7569
9604
11664
6545
11330
11220
10137
7650
9785
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1168.00
114750
111090
108258
Data Display
n
12.0000
33
SSx
1064.67
SSy
1095.00
Sxy
714.000
xbar
97.3333
ybar
94.5000
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-10.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-10.mtw
* NOTE * Existing file replaced.
34
Results for: 2x0333-11.mtw
MTB > Name c11 = 'CLIM3' c12 = 'CLIM4' c13 = 'PLIM3' c14 = 'PLIM4'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM3'-'CLIM4';
SUBC>
PLimits 'PLIM3'-'PLIM4';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 34.5 + 0.667 Ad
Predictor
Constant
Ad
Coef
34.50
0.6667
S = 7.761
SE Coef
22.28
0.2345
R-Sq = 44.7%
T
1.55
2.84
P
0.152
0.017
R-Sq(adj) = 39.2%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
486.67
602.33
1089.00
MS
486.67
60.23
F
8.08
P
0.017
Predicted Values for New Observations
New Obs
1
Fit
107.83
SE Fit
4.27
(
95.0% CI
98.32, 117.35)
(
95.0% PI
88.10, 127.57)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 29.1 + 0.670 Sales
Predictor
Constant
Sales
Coef
29.14
0.6703
S = 7.782
SE Coef
23.10
0.2358
R-Sq = 44.7%
T
1.26
2.84
P
0.236
0.017
R-Sq(adj) = 39.2%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
489.35
605.65
1095.00
MS
489.35
60.57
F
8.08
P
0.017
Data Display
Row
Ad
Sales
C3
C4
C5
35
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
104
102
109
85
104
110
86
92
87
98
108
7225
10816
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11440
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1170.00
115164
111295
108258
Data Display
n
12.0000
SSx
1089.00
SSy
1095.00
Sxy
730.000
xbar
97.5000
ybar
94.5000
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-11.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-11.mtw
* NOTE * Existing file replaced.
36
Results for: 2x0333-12.mtw
MTB > Name c11 = 'CLIM3' c12 = 'CLIM4' c13 = 'PLIM3' c14 = 'PLIM4'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM3'-'CLIM4';
SUBC>
PLimits 'PLIM3'-'PLIM4';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 33.2 + 0.681 Ad
Predictor
Constant
Ad
Coef
33.25
0.6808
S = 7.716
SE Coef
22.15
0.2332
R-Sq = 46.0%
T
1.50
2.92
P
0.164
0.015
R-Sq(adj) = 40.6%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
507.55
595.36
1102.92
MS
507.55
59.54
F
8.53
P
0.015
Predicted Values for New Observations
New Obs
1
Fit
108.14
SE Fit
4.25
(
95.0% CI
98.68, 117.60)
(
95.0% PI
88.51, 127.76)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 28.5 + 0.676 Sales
Predictor
Constant
Sales
S = 7.688
Coef
28.54
0.6759
SE Coef
22.70
0.2315
R-Sq = 46.0%
T
1.26
2.92
P
0.237
0.015
R-Sq(adj) = 40.6%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
503.91
591.09
1095.00
MS
503.91
59.11
F
8.53
P
0.015
Data Display
37
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
105
102
109
85
104
110
86
92
87
98
108
7225
11025
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11550
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1171.00
115373
111405
108258
Data Display
n
12.0000
SSx
1102.92
SSy
1095.00
Sxy
745.500
xbar
97.5833
ybar
94.5000
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-12.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-12.mtw
* NOTE * Existing file replaced.
38
Results for: 2x0333-13.mtw
MTB > Name c11 = 'CLIM3' c12 = 'CLIM4' c13 = 'PLIM3' c14 = 'PLIM4'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM3'-'CLIM4';
SUBC>
PLimits 'PLIM3'-'PLIM4';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 32.0 + 0.695 Ad
Predictor
Coef
SE Coef
Constant
31.99
22.04
Ad
0.6950
0.2321
S = 7.680
R-Sq = 47.3%
T
1.45
2.99
P
0.177
0.013
R-Sq(adj) = 42.0%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
528.88
589.79
1118.67
MS
528.88
58.98
F
8.97
P
0.013
Predicted Values for New Observations
New Obs
1
Fit
108.44
SE Fit
4.23
95.0% CI
99.02, 117.85)
(
(
95.0% PI
88.91, 127.97)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw
* NOTE * Existing file replaced.
MTB > exec '22sols'
* ERROR * File not found: 22sols.MTB
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw
* NOTE * Existing file replaced.
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 28.1 + 0.680 Sales
Predictor
Constant
Coef
28.06
SE Coef
22.30
T
1.26
P
0.237
39
Sales
0.6803
S = 7.598
0.2272
R-Sq = 47.3%
2.99
0.013
R-Sq(adj) = 42.0%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
517.69
577.31
1095.00
MS
517.69
57.73
F
8.97
P
0.013
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
106
102
109
85
104
110
86
92
87
98
108
7225
11236
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11660
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1172.00
115584
111515
108258
Data Display
n
12.0000
SSx
1118.67
SSy
1095.00
Sxy
761.000
xbar
97.6667
ybar
94.5000
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-13.mtw
* NOTE * Existing file replaced.
40
Results for: 2x0333-14.mtw
MTB > Name c11 = 'CLIM3' c12 = 'CLIM4' c13 = 'PLIM3' c14 = 'PLIM4'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM3'-'CLIM4';
SUBC>
PLimits 'PLIM3'-'PLIM4';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 30.7 + 0.709 Ad
Predictor
Constant
Ad
Coef
30.74
0.7091
S = 7.653
SE Coef
21.97
0.2313
R-Sq = 48.5%
T
1.40
3.07
P
0.192
0.012
R-Sq(adj) = 43.3%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
550.64
585.61
1136.25
MS
550.64
58.56
F
9.40
P
0.012
Predicted Values for New Observations
New Obs
1
Fit
108.74
SE Fit
4.21
95.0% CI
99.36, 118.12)
(
(
95.0% PI
89.28, 128.20)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 27.7 + 0.683 Sales
Predictor
Constant
Sales
S = 7.512
Coef
27.70
0.6834
SE Coef
21.89
0.2229
R-Sq = 48.5%
T
1.27
3.07
P
0.234
0.012
R-Sq(adj) = 43.3%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
530.65
564.35
1095.00
MS
530.65
56.43
F
9.40
P
0.012
41
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
107
102
109
85
104
110
86
92
87
98
108
7225
11449
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11770
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1173.00
115797
111625
108258
Data Display
n
SSx
SSy
Sxy
xbar
ybar
MTB >
12.0000
1136.25
1095.00
776.500
97.7500
94.5000
42
Results for: 2x0333-15.mtw
MTB > Name c11 = 'CLIM3' c12 = 'CLIM4' c13 = 'PLIM3' c14 = 'PLIM4'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM3'-'CLIM4';
SUBC>
PLimits 'PLIM3'-'PLIM4';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 29.5 + 0.723 Ad
Predictor
Constant
Ad
Coef
29.48
0.7233
S = 7.634
SE Coef
21.91
0.2307
R-Sq = 49.6%
T
1.35
3.14
P
0.208
0.011
R-Sq(adj) = 44.5%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
572.84
582.82
1155.67
MS
572.84
58.28
F
9.83
P
0.011
Predicted Values for New Observations
New Obs
1
Fit
109.04
SE Fit
4.20
(
95.0% CI
99.68, 118.40)
(
95.0% PI
89.63, 128.46)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 27.5 + 0.685 Sales
Predictor
Constant
Sales
S = 7.431
Coef
27.45
0.6853
SE Coef
21.49
0.2186
R-Sq = 49.6%
T
1.28
3.14
P
0.230
0.011
R-Sq(adj) = 44.5%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
542.77
552.23
1095.00
MS
542.77
55.22
F
9.83
P
0.011
43
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
108
102
109
85
104
110
86
92
87
98
108
7225
11664
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11880
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1174.00
116012
111735
108258
Data Display
n
12.0000
SSx
1155.67
SSy
1095.00
Sxy
792.000
xbar
97.8333
ybar
94.5000
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-15.mtw";
SUBC>
Replace.
Saving file as: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-15.mtw
* NOTE * Existing file replaced.
44
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-16.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-16.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-16.mtw
MTB > Name c7 = 'CLIM1' c8 = 'CLIM2' c9 = 'PLIM1' c10 = 'PLIM2'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM1'-'CLIM2';
SUBC>
PLimits 'PLIM1'-'PLIM2';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 28.2 + 0.737 Ad
Predictor
Constant
Ad
Coef
28.23
0.7374
S = 7.625
SE Coef
21.89
0.2304
R-Sq = 50.6%
T
1.29
3.20
P
0.226
0.009
R-Sq(adj) = 45.7%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
595.49
581.43
1176.92
MS
595.49
58.14
F
10.24
P
0.009
Predicted Values for New Observations
New Obs
1
Fit
109.35
SE Fit
4.20
95.0% CI
100.00, 118.70)
(
(
95.0% PI
89.96, 128.74)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '22sols'
* ERROR * File not found: 22sols.MTB
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 27.3 + 0.686 Sales
Predictor
Constant
Sales
S = 7.355
Coef
27.32
0.6861
SE Coef
21.10
0.2144
R-Sq = 50.6%
T
1.29
3.20
P
0.225
0.009
R-Sq(adj) = 45.7%
Analysis of Variance
45
Source
Regression
Residual Error
Total
DF
1
10
11
SS
554.04
540.96
1095.00
MS
554.04
54.10
F
10.24
P
0.009
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
109
102
109
85
104
110
86
92
87
98
108
7225
11881
10404
11881
7225
10816
12100
7396
8464
7569
9604
11664
6545
11990
11220
10137
7650
9880
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1175.00
116229
111845
108258
Data Display
n
SSx
SSy
Sxy
xbar
ybar
12.0000
1176.92
1095.00
807.500
97.9167
94.5000
46
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-17.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-17.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-17.mtw
MTB > Name c7 = 'CLIM1' c8 = 'CLIM2' c9 = 'PLIM1' c10 = 'PLIM2'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM1'-'CLIM2';
SUBC>
PLimits 'PLIM1'-'PLIM2';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 27.2 + 0.754 Ad
Predictor
Constant
Ad
Coef
27.22
0.7543
S = 8.258
SE Coef
23.70
0.2496
R-Sq = 47.7%
T
1.15
3.02
P
0.278
0.013
R-Sq(adj) = 42.5%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
623.08
681.92
1305.00
MS
623.08
68.19
F
9.14
P
0.013
Predicted Values for New Observations
New Obs
1
Fit
110.19
SE Fit
4.54
(
95.0% CI
100.07, 120.32)
(
95.0% PI
89.19, 131.19)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 32.2 + 0.633 Sales
Predictor
Constant
Sales
S = 7.564
Coef
32.15
0.6330
SE Coef
20.74
0.2094
R-Sq = 47.7%
T
1.55
3.02
P
0.152
0.013
R-Sq(adj) = 42.5%
Analysis of Variance
Source
Regression
DF
1
SS
522.82
MS
522.82
F
9.14
P
0.013
47
Residual Error
Total
10
11
572.18
1095.00
57.22
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
110
102
109
85
110
110
86
92
87
98
108
7225
12100
10404
11881
7225
12100
12100
7396
8464
7569
9604
11664
6545
12100
11220
10137
7650
10450
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1182.00
117732
112525
108258
Data Display
n
SSx
SSy
Sxy
xbar
ybar
12.0000
1305.00
1095.00
826.000
98.5000
94.5000
48
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-18.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-18.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-18.mtw
MTB > Name c27 = 'CLIM11' c28 = 'CLIM12' c29 = 'PLIM11' c30 = 'PLIM12'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM11'-'CLIM12';
SUBC>
PLimits 'PLIM11'-'PLIM12';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 27.3 + 0.755 Ad
Predictor
Constant
Ad
Coef
27.26
0.7548
S = 8.397
SE Coef
24.10
0.2538
R-Sq = 46.9%
T
1.13
2.97
P
0.285
0.014
R-Sq(adj) = 41.6%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
623.84
705.08
1328.92
MS
623.84
70.51
F
8.85
P
0.014
Predicted Values for New Observations
New Obs
1
Fit
110.28
SE Fit
4.62
95.0% CI
99.99, 120.58)
(
(
95.0% PI
88.93, 131.64)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 33.2 + 0.622 Sales
Predictor
Constant
Sales
S = 7.622
Coef
33.19
0.6219
SE Coef
20.73
0.2091
R-Sq = 46.9%
T
1.60
2.97
P
0.140
0.014
R-Sq(adj) = 41.6%
Analysis of Variance
Source
Regression
DF
1
SS
514.03
MS
514.03
F
8.85
P
0.014
49
Residual Error
Total
10
11
580.97
1095.00
58.10
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
110
102
109
85
111
110
86
92
87
98
108
7225
12100
10404
11881
7225
12321
12100
7396
8464
7569
9604
11664
6545
12100
11220
10137
7650
10545
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1183.00
117953
112620
108258
Data Display
n
SSx
SSy
Sxy
xbar
ybar
12.0000
1328.92
1095.00
826.500
98.5833
94.5000
50
MTB > Retrieve "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive
D\MINITAB\2x0333-19.mtw".
Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My
Documents\Drive D\MINITAB\2x0333-19.mtw
# Worksheet was saved on Sat Nov 22 2003
Results for: 2x0333-19.mtw
MTB > Name c7 = 'CLIM1' c8 = 'CLIM2' c9 = 'PLIM1' c10 = 'PLIM2'
MTB > Regress c2 1 c1;
SUBC>
Constant;
SUBC>
Predict c6;
SUBC>
CLimits 'CLIM1'-'CLIM2';
SUBC>
PLimits 'PLIM1'-'PLIM2';
SUBC>
Brief 2.
Regression Analysis: Sales versus Ad
The regression equation is
Sales = 36.1 + 0.656 Ad
Predictor
Constant
Ad
Coef
36.08
0.6562
S = 8.772
SE Coef
25.18
0.2651
R-Sq = 38.0%
T
1.43
2.48
P
0.182
0.033
R-Sq(adj) = 31.8%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
SS
471.45
769.46
1240.92
MS
471.45
76.95
F
6.13
P
0.033
Predicted Values for New Observations
New Obs
1
Fit
108.25
SE Fit
4.83
95.0% CI
97.50, 119.01)
(
(
95.0% PI
85.95, 130.56)
Values of Predictors for New Observations
New Obs
1
Ad
110
MTB > exec '22solos'
* ERROR * File not found: 22solos.MTB
MTB > exec '252sols'
Executing from file: 252sols.MTB
Regression Analysis: Ad versus Sales
The regression equation is
Ad = 37.7 + 0.579 Sales
Predictor
Constant
Sales
S = 8.240
Coef
37.71
0.5790
SE Coef
23.07
0.2339
R-Sq = 38.0%
T
1.63
2.48
P
0.133
0.033
R-Sq(adj) = 31.8%
Analysis of Variance
51
Source
Regression
Residual Error
Total
DF
1
10
11
SS
416.02
678.98
1095.00
MS
416.02
67.90
F
6.13
P
0.033
Data Display
Row
Ad
Sales
C3
C4
C5
1
2
3
4
5
6
7
8
9
10
11
12
77
110
110
93
90
95
100
85
96
83
100
95
85
103
102
109
85
112
110
86
92
87
98
108
7225
10609
10404
11881
7225
12544
12100
7396
8464
7569
9604
11664
6545
11330
11220
10137
7650
10640
11000
7310
8832
7221
9800
10260
5929
12100
12100
8649
8100
9025
10000
7225
9216
6889
10000
9025
Data Display
sumy
sumx
smxsq
smxy
smysq
1134.00
1177.00
116685
111945
108258
Data Display
n
SSx
SSy
Sxy
xbar
ybar
MTB >
12.0000
1240.92
1095.00
718.500
98.0833
94.5000
52