Take Home Section
252y0333TH11/18/03ECO252 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 .
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)
1
Sales of ‘Whee’ Cereal
Shelf
Row 1 2 3 4
1 336 440 464 354
2 417 277 479 423
3 208 374 492 321
4 420 421 456 424
5 366 481 338 518
6 227 349 413 451
7 357 328 383 311
8 353 449 554 462
9 518 462 497 339
10 388 373 510 202
Sum of shelf 1 = 3590.0
Sum of squares of shelf 1 = 1362860
Sum of shelf 2 = 3954.0
Sum of squares of shelf 2 = 1602366
Sum of shelf 3 = 4586.0
Sum of squares of shelf 3 = 2140264
1
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.
1
Row Ad Sales
1 77 85
2 110 103
3 110 102
4 93 109
5 90 85
6 95 103
7 100 110
8 85 86
9 96 92
10 83 87
11 100 98
12 95 108
Sum of Ad = 1134.0
Sum of squares of Ad = 108258
Sum of Sales = 1168.0
Sum of 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.
1
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 to predict the ‘Sales’ on the basis of ‘Ad’. (2)
b. Compute. (2)
c. Compute . (2)
d. Compute and do a significance test on (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)
————— 11/22/20034:04:56 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
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 451 6------0
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 55058 18353 2.91 0.048
Error 36 227003 6306
Total 39 282061
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.50 92.42 (------*------)
------+------+------+------
Pooled StDev = 79.41 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 55058 18353 2.91 0.048
Error 36 227003 6306
Total 39 282061
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.50 92.42 (------*------)
------+------+------+------
Pooled StDev = 79.41 360 420 480
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 -158.9
-3.9 32.5
4 -117.2 -80.8 -17.6
74.2 110.6 173.8
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62914 6990 1.15 0.364
C11 3 55058 18353 3.02 0.047
Error 27 164090 6077
Total 39 282061
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 452 6------1
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 55022 18341 2.91 0.048
Error 36 227145 6310
Total 39 282168
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.60 92.51 (------*------)
------+------+------+------
Pooled StDev = 79.43 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 55022 18341 2.91 0.048
Error 36 227145 6310
Total 39 282168
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.60 92.51 (------*------)
------+------+------+------
Pooled StDev = 79.43 360 420 480
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 -158.9
-3.9 32.5
4 -117.3 -80.9 -17.7
74.1 110.5 173.7
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62837 6982 1.15 0.366
C11 3 55022 18341 3.01 0.047
Error 27 164308 6085
Total 39 282168
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 453 6------2
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54987 18329 2.90 0.048
Error 36 227289 6314
Total 39 282276
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.70 92.59 (------*------)
------+------+------+------
Pooled StDev = 79.46 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54987 18329 2.90 0.048
Error 36 227289 6314
Total 39 282276
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.70 92.59 (------*------)
------+------+------+------
Pooled StDev = 79.46 360 420 480
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 -158.9
-3.9 32.5
4 -117.4 -81.0 -17.8
74.0 110.4 173.6
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62761 6973 1.14 0.368
C11 3 54987 18329 3.01 0.048
Error 27 164528 6094
Total 39 282276
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 454 6------3
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54952 18317 2.90 0.048
Error 36 227434 6318
Total 39 282386
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.80 92.68 (------*------)
------+------+------+------
Pooled StDev = 79.48 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54952 18317 2.90 0.048
Error 36 227434 6318
Total 39 282386
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.80 92.68 (------*------)
------+------+------+------
Pooled StDev = 79.48 360 420 480
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 -132.2
59.4
3 -195.4 -159.0
-3.8 32.6
4 -117.6 -81.2 -18.0
74.0 110.4 173.6
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62685 6965 1.14 0.369
C11 3 54952 18317 3.00 0.048
Error 27 164749 6102
Total 39 282386
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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.
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 455 6------4
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54916 18305 2.90 0.048
Error 36 227582 6322
Total 39 282498
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.90 92.77 (------*------)
------+------+------+------
Pooled StDev = 79.51 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54916 18305 2.90 0.048
Error 36 227582 6322
Total 39 282498
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 380.90 92.77 (------*------)
------+------+------+------
Pooled StDev = 79.51 360 420 480
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 -132.2
59.4
3 -195.4 -159.0
-3.8 32.6
4 -117.7 -81.3 -18.1
73.9 110.3 173.5
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62610 6957 1.14 0.371
C11 3 54916 18305 3.00 0.048
Error 27 164971 6110
Total 39 282498
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
MTB > Save "C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\2x0333-04.mtw";
SUBC> Replace.
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 456 6------5
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54881 18294 2.89 0.049
Error 36 227731 6326
Total 39 282612
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.00 92.86 (------*------)
------+------+------+------
Pooled StDev = 79.54 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54881 18294 2.89 0.049
Error 36 227731 6326
Total 39 282612
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.00 92.86 (------*------)
------+------+------+------
Pooled StDev = 79.54 360 420 480
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 -132.2
59.4
3 -195.4 -159.0
-3.8 32.6
4 -117.8 -81.4 -18.2
73.8 110.2 173.4
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62536 6948 1.14 0.373
C11 3 54881 18294 2.99 0.048
Error 27 165195 6118
Total 39 282612
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 457 6------6
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54846 18282 2.89 0.049
Error 36 227882 6330
Total 39 282728
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.10 92.95 (------*------)
------+------+------+------
Pooled StDev = 79.56 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54846 18282 2.89 0.049
Error 36 227882 6330
Total 39 282728
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.10 92.95 (------*------)
------+------+------+------
Pooled StDev = 79.56 360 420 480
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 -132.3
59.5
3 -195.5 -159.1
-3.7 32.7
4 -118.0 -81.6 -18.4
73.8 110.2 173.4
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62461 6940 1.13 0.375
C11 3 54846 18282 2.98 0.049
Error 27 165420 6127
Total 39 282728
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 459 6------7
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54777 18259 2.88 0.049
Error 36 228189 6339
Total 39 282966
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.30 93.13 (------*------)
------+------+------+------
Pooled StDev = 79.62 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54777 18259 2.88 0.049
Error 36 228189 6339
Total 39 282966
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.30 93.13 (------*------)
------+------+------+------
Pooled StDev = 79.62 360 420 480
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 -132.3
59.5
3 -195.5 -159.1
-3.7 32.7
4 -118.2 -81.8 -18.6
73.6 110.0 173.2
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62314 6924 1.13 0.378
C11 3 54777 18259 2.97 0.049
Error 27 165875 6144
Total 39 282966
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 459 6------8
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54777 18259 2.88 0.049
Error 36 228189 6339
Total 39 282966
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.30 93.13 (------*------)
------+------+------+------
Pooled StDev = 79.62 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54777 18259 2.88 0.049
Error 36 228189 6339
Total 39 282966
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.30 93.13 (------*------)
------+------+------+------
Pooled StDev = 79.62 360 420 480
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 -132.3
59.5
3 -195.5 -159.1
-3.7 32.7
4 -118.2 -81.8 -18.6
73.6 110.0 173.2
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62314 6924 1.13 0.378
C11 3 54777 18259 2.97 0.049
Error 27 165875 6144
Total 39 282966
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
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 C12
1 354 1
2 423 2
3 321 3
4 424 4
5 518 5
6 460 6------9
7 311 7
8 462 8
9 339 9
10 202 10
11 1
12 2
13 3
14 4
15 5
16 6
17 7
18 8
19 9
20 10
21 1
22 2
23 3
24 4
25 5
26 6
27 7
28 8
29 9
30 10
31 1
32 2
33 3
34 4
35 5
36 6
37 7
38 8
39 9
40 10
One-way ANOVA: 1, 2, 3, 4
Analysis of Variance
Source DF SS MS F P
Factor 3 54742 18247 2.88 0.049
Error 36 228345 6343
Total 39 283088
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.40 93.22 (------*------)
------+------+------+------
Pooled StDev = 79.64 360 420 480
One-way ANOVA: C10 versus C11
Analysis of Variance for C10
Source DF SS MS F P
C11 3 54742 18247 2.88 0.049
Error 36 228345 6343
Total 39 283088
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+------+------+------
1 10 359.00 90.71 (------*------)
2 10 395.40 65.79 (------*------)
3 10 458.60 64.23 (------*------)
4 10 381.40 93.22 (------*------)
------+------+------+------
Pooled StDev = 79.64 360 420 480
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 -132.4
59.6
3 -195.6 -159.2
-3.6 32.8
4 -118.4 -82.0 -18.8
73.6 110.0 173.2
Two-way ANOVA: C10 versus C12, C11
Analysis of Variance for C10
Source DF SS MS F P
C12 9 62241 6916 1.12 0.380
C11 3 54742 18247 2.97 0.050
Error 27 166104 6152
Total 39 283088
Friedman Test: C10 versus C11, C12
Friedman test for C10 by C11 blocked by C12
S = 8.76 DF = 3 P = 0.033
Est Sum of
C11 N Median Ranks
1 10 377.63 19.0
2 10 414.75 22.0
3 10 474.13 35.0
4 10 396.50 24.0
Grand median = 415.75
MTB >
————— 11/22/20036:18:36 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 Coef SE Coef T P
Constant 35.71 22.22 1.61 0.139
Ad 0.6521 0.2339 2.79 0.019
S = 7.740 R-Sq = 43.7% R-Sq(adj) = 38.1%
Analysis of Variance
Source DF SS MS F P
Regression 1 465.57 465.57 7.77 0.019
Residual Error 10 599.10 59.91
Total 11 1064.67
Predicted Values for New Observations
New Obs Fit SE Fit 95.0% CI 95.0% PI
1 107.44 4.26 ( 97.95, 116.93) ( 87.76, 127.12)
Values of Predictors for New Observations
New Obs Ad
1 110
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 Coef SE Coef T P
Constant 29.23 23.52 1.24 0.242
Sales 0.6706 0.2406 2.79 0.019
S = 7.850 R-Sq = 43.7% R-Sq(adj) = 38.1%
Analysis of Variance
Source DF SS MS F P
Regression 1 478.83 478.83 7.77 0.019
Residual Error 10 616.17 61.62
Total 11 1095.00
Data Display
Row Ad Sales C3 exec C5
1 77 85 7225 6545 5929
2 110 103 10609 11330 12100
3 110 102 10404 11220 12100
4 93 109 11881 10137 8649
5 90 85 7225 7650 8100
6 95 103 10609 9785 9025
7 100 110 12100 11000 10000
8 85 86 7396 7310 7225
9 96 92 8464 8832 9216
10 83 87 7569 7221 6889
11 100 98 9604 9800 10000
12 95 108 11664 10260 9025
Data Display
sumy 1134.00
sumx 1168.00
smxsq 114750
smxy 111090