The
SAS System
Obs Region Product Subsidiary Stores
Sales Inventory Returns
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 Central America/Caribbean Boot
17 Central America/Caribbean Boot
18 Central America/Caribbean Boot
19 Central America/Caribbean Boot
20
21
22
23
24
25
26
27 Pacific Boot
28 Pacific Boot
29 Pacific Boot
30 Pacific Boot
31 Pacific Boot
32 Pacific Boot
33
34
35
36
37
38
39
40 United States Boot
41 United States Boot
42 United States Boot
43 United States Boot
44 United States Boot
45
46
47
48
49
50
51
52
The
SAS System
Plot of
Sales*Inventory. Legend: A = 1 obs, B = 2 obs, etc.
$300,000 ˆ
‚
‚
A
‚
‚
‚
‚
$250,000 ˆ
‚
‚
‚
‚
‚
‚
$200,000 ˆ
‚
T
‚
o ‚
t ‚
a ‚
l ‚
$150,000 ˆ
S
‚
a ‚
l ‚
e ‚
s ‚ A
‚
$100,000 ˆ A A
‚ A
‚ A B
‚ AA
‚ A A
‚ A AAA
‚ B A
$50,000 ˆ
‚ B A
‚ A AAA A A
‚ A A
A
‚ A AAB
‚ DBB
‚ AB A
$0 ˆ CA
Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000
Total Inventory
The
SAS System
The
REG Procedure
Model: MODEL1
Dependent
Variable: Sales Total Sales
Analysis
of Variance
Sum of Mean
Source DF Squares Square
F Value Pr > F
Model 1 95804378965 95804378965 446.30
<.0001
Error 50 10733238966 214664779
Corrected Total 51
1.065376E11
Root MSE 14651 R-Square
0.8993
Dependent Mean 45203 Adj R-Sq 0.8972
Coeff
Var
32.41272
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value
Pr > |t|
Intercept Intercept 1
-1863.51988 3015.25264 -0.62
0.5394
Inventory Total Inventory 1
0.25167 0.01191 21.13
<.0001
The
SAS System
The
REG Procedure
Model: MODEL1
Dependent
Variable: Sales Total Sales
Output
Statistics
Dep Var Predicted Std Error
Obs Sales
Value Mean
Predict 95% CL Mean 95% CL Predict Residual
1
29761 46413 2033 42330
50495 16703 76123
-16652
2
21297 16694 2439 11795
21593 -13139 46527 4603
3
4846 2909 2852 -2820 8639
-27071 32890 1937
4
8365 6444 2738
945.9895 11943 -23493
36382 1921
5
19282 24655 2253 20131
29180 -5119 54429
-5373
6
13921 15939 2459 11000
20878 -13901 45779
-2018
7
6081 11116 2595 5905
16327 -18770 41002
-5035
8
16282 14751 2491 9748
19755 -15099 44602 1531
9
1996 546.5095 2932 -5343 6436
-29465 30558 1449
10
60712 38553 2056 34423
42682 8836 68269
22159
11
17720 14062 2510 9021
19104 -15795 43919 3658
12
40213 58571 2128 54297
62846 28834 88309
-18358
13
7892 5224 2777 -352.8020 10801
-24728 35176 2668
14
33291 35666 2081 31485
39846 5942 65389
-2375
15
286497 220133 8526 203008
237258 186085 254181
66364
16
102372 97139 3189 90733
103545 67021 127256 5233
17
34660 38916 2053 34791
43040 9200 68632
-4256
18
20819 18269 2399 13451
23087 -11551 48089 2550
19
32892 32190 2123 27926
36455 2455 61926
701.7740
20
74102 78047 2558 72908
83185 48173 107920
-3945
21
67476 81089 2648 75770
86409 51184 110994
-13613
22
86215 84039 2740 78536 89543
54101 113978 2176
23
78992 89584 2923 83714
95454 59576 119592
-10592
24
15062 9376 2647 4060
14691 -20529 39280 5686
25
90972 99626 3281 93036
106216 69469 129783
-8654
26
65248 54050 2074 49883
58216 24328 83771
11198
27
20141 22780 2292 18176
27384 -7006
52566 -2639
28
32640 45561 2032 41480
49642 15851 75271
-12921
29
11975 10883 2601 5657
16108 -19006 40771 1092
30
25796 34142
2098 29927 38356 4413
63870 -8346
31
31503 25866 2228 21390
30342 -3901 55632 5637
32
1520 -1769 3012 -7819 4280
-31813 28274
3289
33
15312 7148 2715 1694
12602 -22782 37077 8164
34
17027 8025 2688 2626
13424 -21894 37944 9002
35
63697 75528 2488
70532 80525 45679
105378 -11831
36
36309 23459 2278 18885
28034 -6322 53241
12850
37
53703 36039 2078 31866
40212 6316 65762
17664
38
14907 8008 2689 2608
13408 -21912 37927 6899
39
44720 41822 2038 37728
45915 12110 71533 2898
40
82483 74912 2471 69949
79876 45068 104756 7571
41
85932 85531 2788 79931
91130 55574 115487
401.2492
42
111940 153039 5494 142004
164074 121610 184468
-41099
43
97151 122836 4199 114402
131270 92223 153449
-25685
44
70790 55185 2086 50996
59375 25460 84910
15605
45
1663 -691.4745 2974
-6666 5283 -30720
29337 2354
46
41341 41180 2041 37081
45279 11468 70893
160.7300
47
65610 74086 2449 69167
79005 44250 103923
-8476
48
76349 84187 2745 78674
89699 54246 114127
-7838
49
54449 71003 2371 66241
75764 41192 100814
-16554
50
1179 -1605 3006 -7643
4433 -31646 28436 2784
51
19196 8582 2671 3218
13947 -21331 38496
10614
52
36244 50805 2049 46689
54920 21090 80519
-14561
Sum of Residuals 0
Sum of Squared
Residuals 10733238966
Predicted Residual
SS (PRESS) 17326290516
The SAS System
Plot
of res*pred. Legend: A = 1 obs,
B = 2 obs, etc.
80000 ˆ
‚
‚
‚
‚
‚
A
‚
60000 ˆ
‚
‚
‚
‚
‚
‚
40000 ˆ
‚
‚
R ‚
e ‚
s ‚
i ‚ A
d
20000 ˆ
u ‚ A
a ‚ A
l ‚ A A A
‚ B A
‚ AA A A A
‚ DBA BA A A
0 ˆ A A A A
‚ A A AA
A
‚ A A
‚ A A A A
‚ A A
‚ AA A
‚ A A A
-20000 ˆ
‚
‚
A
‚
‚
‚
‚
-40000 ˆ A
Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ
-50000 0 50000 100000 150000 200000 250000
Predicted Value of
Sales
The
SAS System
The
UNIVARIATE Procedure
Variable: res (Residual)
Moments
N 52 Sum Weights 52
Mean 0 Sum Observations 0
Std
Deviation 14507.0902 Variance 210455666
Skewness 1.36886588 Kurtosis 8.56047016
Uncorrected SS 1.07332E10 Corrected SS 1.07332E10
Coeff Variation . Std Error Mean 2011.77144
Basic
Statistical Measures
Location Variability
Mean 0.000
Std
Deviation 14507
Median 1490.127
Variance 210455666
Mode . Range 107463
Tests for
Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 0
Pr > |t| 1.0000
Sign M 5
Pr >= |M| 0.2116
Signed Rank S
-5 Pr >= |S| 0.9642
Quantiles (Definition 5)
Quantile
Estimate
100% Max 66363.99
99% 66363.99
95% 17664.18
90% 11198.38
75%
Q3 5435.19
50%
Median 1490.13
25%
Q1 -8091.63
10% -14560.53
5% -18358.44
1% -41099.01
0%
Min -41099.01
The
SAS System
The
UNIVARIATE Procedure
Variable: res
(Residual)
Extreme
Observations
------Lowest----- -----Highest-----
Value Obs Value Obs
-41099.0 42 12849.6 36
-25684.6 43 15604.6 44
-18358.4 12 17664.2 37
-16651.8 1 22159.5 10
-16553.9 49 66364.0 15
Stem Leaf # Boxplot
6 6
1 *
6
5
5
4
4
3
3
2
2 2
1 |
1 68 2 |
1 113 3 |
0 55667889 8 +-----+
0
0011122222333334 16 *--+--*
-0 44322 5 | |
-0 988855 6 +-----+
-1 4321 4 |
-1 8775 4 |
-2 |
-2 6 1 |
-3
-3
-4 1 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**+4
The
SAS System
The UNIVARIATE
Procedure
Variable: res
(Residual)
Normal Probability Plot
67500+ *
|
|
|
|
|
|
+
|
++++
| +++
| ++++ *
| +++ **
12500+ ++++***
| ++******
| *********
| ***++
| ****+
| ****++
| ** *++
| ++++
| +*+
| ++++
|+
-42500+ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The
SAS System
Plot of
Sales*Inventory. Legend: A = 1 obs, B = 2 obs, etc.
$120,000 ˆ
‚
‚
‚ A
‚
‚
‚
A
$100,000 ˆ
‚
A
‚
‚
A
‚
‚ AA
‚ A
$80,000 ˆ A
‚ A
T ‚ A
o ‚ A
t ‚ A
a ‚ A A
l ‚ A
$60,000 ˆ A
S ‚
a ‚ A A
l ‚
e ‚
s ‚ A
‚
$40,000 ˆ A A
‚ A A
‚ A AA
‚ A A
‚ A
‚ A
‚
$20,000 ˆ A
AA AA
‚ A B
‚ AB A
‚ A
‚
AA
‚
A A
‚ AB
$0 ˆ A
Šƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒ
$0 $100,000 $200,000
$300,000 $400,000 $500,000
$600,000 $700,000
Total Inventory
The
SAS System
The REG Procedure
Model: MODEL1
Dependent
Variable: Sales Total Sales
Analysis
of Variance
Sum of Mean
Source DF Squares Square F Value
Pr > F
Model 1 43099093239 43099093239 518.38
<.0001
Error 49 4073983824 83142527
Corrected Total 50
47173077063
Root MSE 9118.25241 R-Square
0.9136
Dependent Mean 40471 Adj R-Sq 0.9119
Coeff
Var
22.53006
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error
t Value Pr > |t|
Intercept Intercept 1
4830.25907 2020.09361 2.39
0.0207
Inventory Total Inventory 1
0.20556 0.00903 22.77
<.0001
The SAS System
The
REG Procedure
Model: MODEL1
Dependent
Variable: Sales Total Sales
Output
Statistics
Dep Var Predicted Std Error
Obs Sales
Value Mean
Predict 95% CL Mean 95% CL Predict Residual
1
29761 44261 1288 41674
46849 25756 62767
-14500
2
21297 19988 1562 16849
23127 1397 38579 1309
3
4846 8729 1891 4930
12528 -9985 27442
-3883
4
8365 11616 1799 8001
15231 -7061 30293
-3251
5
19282 26490 1417 23643
29338 7947 45034
-7208
6
13921 19371 1578 16200
22541 774.8258 37967
-5450
7
6081 15432 1685 12045
18818 -3203 34066
-9351
8
16282 18401 1603 15179
21622 -203.9923 37006
-2119
9
1996 6799 1954 2872
10725 -11941 25538
-4803
10
60712 37841 1282 35265
40418 19337 56345
22871
11
17720 17838 1618 14586
21090 -771.8813 36448
-118.2374
12
40213 54192 1412 51355
57030 35650 72735
-13979
13
7892 10619 1830 6942
14297 -8070 29309
-2727
14
33291 35483 1295 32880
38087 16975 53991
-2192
15
102372 85694 2361 80948
90439 66765 104622
16678
16
34660 38138 1281 35564
40712 19634 56642
-3478
17
20819 21274 1530 18199
24349 2694 39854 -455.0047
18
32892 32645 1322 29987
35302 14129 51160
247.3202
19
74102 70099 1823 66436
73763 51413 88786 4003
20
67476 72584 1903 68761
76408 53866 91303
-5108
21
86215 74994 1982 71010
78977 56242 93746
11221
22
78992 79523 2138 75226
83820 60702 98344 -530.9424
23
15062 14010 1727 10541
17480 -4639 32660 1052
24
90972 87725 2437 82828
92622 68758 106692 3247
25
65248 50499 1351 47785
53213 31975 69023
14749
26
20141 24959 1447 22050
27867 6406 43512
-4818
27 32640 43566 1284 40985
46146 25061 62070
-10926
28
11975 15241 1691 11843
18638 -3395 33877
-3266
29
25796 34239 1306 31614
36863 15728
52749 -8443
30
31503 27479 1399 24668
30289 8941 46017 4024
31
1520 4907 2017
852.8654 8961 -13860
23674 -3387
32
15312 12190 1781 8611
15770 -6480 30861 3122
33
17027 12907 1760 9371
16443 -5755 31569 4120
34
63697 68042 1760 64506
71579 49381
86704 -4345
35
36309 25514 1436 22628
28399 6964 44063
10795
36
53703 35788 1293 33189
38387 17281 54295
17915
37
14907 12893 1760 9356
16430 -5769 31555 2014
38
44720 40511 1277 37945
43077 22009 59014 4209
39
82483 67539 1745 64033
71045 48883 86195
14944
40
85932 76212 2023 72146
80278 57443 94982 9720
41
111940 131352 4191 122930
139773 111185 151518
-19412
42
97151 106682 3176
100300 113064 87278
126086 -9531
43
70790 51427 1364 48685
54169 32899 69955
19363
44
1663 5788 1988 1793 9782
-12967 24542 -4125
45
41341 39988 1277 37421
42554 21485 58490 1353
46
65610 66865 1725 63399
70330 48216 85513
-1255
47
76349 75114 1986 71123
79106 56361 93868 1235
48
54449 64346 1652 61026
67666 45724 82968
-9897
49
1179 5041 2013
996.2638 9086 -13724
23806 -3862
50
19196 13362 1746 9854
16871 -5294 32019 5834
51
36244 47848 1317 45201
50496 29334 66363
-11604
Sum of Residuals 0
Sum of Squared
Residuals 4073983824
Predicted Residual
SS (PRESS) 4555469404
The
SAS System
Plot
of res*pred. Legend: A = 1 obs,
B = 2 obs, etc.
‚
‚
30000 ˆ
‚
‚
‚
‚
‚ A
‚
20000 ˆ A
‚ A
‚
A
‚
‚ A A
‚
R ‚ A A
e
10000 ˆ
A
s ‚
i ‚
d ‚ A
u ‚ A A A A
a ‚ A A
l ‚
B A A A
0 ˆ A A A A
‚ A A
‚
A AA
A A A
‚
BAA A A
‚ A A
‚ A
‚ A
-10000 ˆ A A
A
‚ A A
‚
‚ A A
‚
‚
‚
-20000 ˆ
A
‚
Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒ
0 20000 40000 60000 80000 100000 120000 140000
Predicted Value of Sales