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