Sand, Silt, and Clay Compositions In An Artic Lake

Obs Sediment
Number		 Percent Sand Percent Silt Percent Clay Water Depth(m) Log Ratio 1 Log Ratio 2 Log(Depth) Axis1 Axis2
1 S1 77.5000 19.5000 3.0000 10.4 3.25167 1.87180 2.34181 12.7500 16.8875
2 S2 71.9000 24.9000 3.2000 11.7 3.11213 2.05172 2.45959 15.6500 21.5640
3 S3 50.7000 36.1000 13.2000 12.8 1.34571 1.00608 2.54945 31.2500 31.2635
4 S4 52.3571 41.0231 6.6199 13.0 2.06801 1.82406 2.56495 27.1314 35.5270
5 S5 70.0000 26.5000 3.5000 15.7 2.99573 2.02438 2.75366 16.7500 22.9497
6 S6 66.5000 32.2000 1.3000 16.3 3.93484 3.20960 2.79117 17.4000 27.8860
7 S7 43.1000 55.3000 1.6000 18.0 3.29352 3.54277 2.89037 29.2500 47.8912
8 S8 53.4000 36.8000 9.8000 18.7 1.69543 1.32312 2.92852 28.2000 31.8697
9 S9 15.5000 54.4000 30.1000 20.7 -0.66369 0.59184 3.03013 57.3000 47.1118
10 S10 31.7000 41.5000 26.8000 22.1 0.16791 0.43729 3.09558 47.5500 35.9401
11 S11 65.7000 27.8000 6.5000 22.4 2.31330 1.45323 3.10906 20.4000 24.0755
12 S12 70.4000 29.0000 0.6000 24.4 4.76502 3.87812 3.19458 15.1000 25.1147
13 S13 17.4000 53.6000 29.0000 25.8 -0.51083 0.61425 3.25037 55.8000 46.4190
14 S14 10.6000 69.8000 19.6000 32.5 -0.61468 1.27010 3.48124 54.5000 60.4486
15 S15 38.2000 43.1000 18.7000 33.6 0.71431 0.83500 3.51453 40.2500 37.3257
16 S16 10.8000 52.7000 36.5000 36.8 -1.21777 0.36730 3.60550 62.8500 45.6395
17 S18 4.6000 47.4000 48.0000 36.9 -2.34514 -0.01258 3.60821 71.7000 41.0496
18 S17 18.4000 50.7000 30.9000 37.8 -0.51841 0.49517 3.63231 56.2500 43.9075
19 S19 15.6000 50.4000 34.0000 42.2 -0.77909 0.39363 3.74242 59.2000 43.6477
20 S20 31.9000 45.1000 23.0000 47.0 0.32711 0.67339 3.85015 45.5500 39.0577
21 S21 9.5000 53.5000 37.0000 47.1 -1.35963 0.36876 3.85227 63.7500 46.3324
22 S22 17.1000 48.0000 34.9000 48.4 -0.71341 0.31871 3.87950 58.9000 41.5692
23 S23 10.5000 55.4000 34.1000 49.4 -1.17792 0.48528 3.89995 61.8000 47.9778
24 S24 4.7761 54.4279 40.7960 49.5 -2.14496 0.28829 3.90197 68.0100 47.1359
25 S25 2.6000 45.2000 52.2000 59.2 -2.99957 -0.14399 4.08092 74.8000 39.1443
26 S26 11.4000 52.7000 35.9000 60.1 -1.14712 0.38388 4.09601 62.2500 45.6395
27 S27 6.7000 46.9000 46.4000 61.7 -1.93519 0.01072 4.12228 69.8500 40.6166
28 S28 6.9000 49.7000 43.4000 62.4 -1.83894 0.13555 4.13357 68.2500 43.0415
29 S29 4.0000 44.9000 51.1000 69.3 -2.54749 -0.12935 4.23844 73.5500 38.8845
30 S30 7.4074 51.6517 40.9409 73.6 -1.70965 0.23239 4.29865 66.7668 44.7316
31 S31 4.8000 49.5000 45.7000 74.4 -2.25348 0.07987 4.30946 70.4500 42.8683
32 S32 4.5000 48.5000 47.0000 78.5 -2.34607 0.03142 4.36310 71.2500 42.0022
33 S33 6.6000 52.1000 41.3000 82.9 -1.83379 0.23230 4.41764 67.3500 45.1199
34 S34 6.7067 47.3473 45.9459 87.7 -1.92436 0.03005 4.47392 69.6196 41.0040
35 S35 7.4074 45.6456 46.9469 88.1 -1.84654 -0.02811 4.47847 69.7698 39.5303
36 S36 6.0000 48.9000 45.1000 90.4 -2.01712 0.08090 4.50424 69.5500 42.3486
37 S37 6.3000 53.8000 39.9000 90.6 -1.84583 0.29890 4.50645 66.8000 46.5922
38 S38 2.5000 48.0000 49.5000 97.7 -2.98568 -0.03077 4.58190 73.5000 41.5692
39 S39 2.0000 47.8000 50.2000 103.7 -3.22287 -0.04899 4.64150 74.1000 41.3960

Sand, Silt, and Clay Compositions In An Artic Lake

Obs Sand Clay Axis1 Axis2 Depth LogDepth Shape Size
1 0 0 50 86.6025 0 0 Pyramid 0.25
2 100 0 0 0.0000 0 0 Pyramid 0.25
3 0 100 100 0.0000 0 0 Pyramid 0.25
4 0 0 50 86.6025 0 0 Pyramid 0.25

Plot of Sand * LogDepth

Plot of Silt * LogDepth

Plot of Clay * LogDepth

VBAR chart of DepthOrder

TEMPLATE GRAPH PRODUCED BY GREPLAY

TEMPLATE GRAPH PRODUCED BY GREPLAY

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure

Number of Observations Read 39
Number of Observations Used 39

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
 
Dependent Variable: Y1 Log Ratio 1

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 132.6376326 132.6376326 104.06 <.0001
Error 37 47.1590967 1.2745702    
Corrected Total 38 179.7967292      

R-Square Coeff Var Root MSE Y1 Mean
0.737709 -303.3498 1.128969 -0.372167

Source DF Type III SS Mean Square F Value Pr > F
LogDepth 1 132.6376326 132.6376326 104.06 <.0001

Parameter Estimate Standard Error t Value Pr > |t|
Intercept 9.697382110 1.00351181 9.66 <.0001
LogDepth -2.742906197 0.26888059 -10.20 <.0001

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
 
Dependent Variable: Y2 Log Ratio 2

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 21.18692678 21.18692678 43.20 <.0001
Error 37 18.14415574 0.49038259    
Corrected Total 38 39.33108253      

R-Square Coeff Var Root MSE Y2 Mean
0.538682 89.70168 0.700273 0.780669

Source DF Type III SS Mean Square F Value Pr > F
LogDepth 1 21.18692678 21.18692678 43.20 <.0001

Parameter Estimate Standard Error t Value Pr > |t|
Intercept 4.805157074 0.62245525 7.72 <.0001
LogDepth -1.096254926 0.16678043 -6.57 <.0001

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for LogDepth
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
Y1 Y2
3.37676362 100.00 0.23660364 -0.19277507
0.00000000 0.00 -0.17202156 0.43040994

MANOVA Test Criteria and Exact F Statistics for
the Hypothesis of No Overall LogDepth Effect
H = Type III SSCP Matrix for LogDepth
E = Error SSCP Matrix

S=1 M=0 N=17
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.22847933 60.78 2 36 <.0001
Pillai's Trace 0.77152067 60.78 2 36 <.0001
Hotelling-Lawley Trace 3.37676362 60.78 2 36 <.0001
Roy's Greatest Root 3.37676362 60.78 2 36 <.0001

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
Multivariate Analysis of Variance

M Matrix Describing Transformed Variables
  Y1 Y2
Y3 1 -1

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for LogDepth
E = Error SSCP Matrix

Variables have been transformed by the M Matrix
Characteristic Root Percent Characteristic Vector
V'EV=1
Y3
3.28232484 100.00 0.26203948

MANOVA Test Criteria and Exact F Statistics for
the Hypothesis of No Overall LogDepth Effect
on the Variables Defined by the M Matrix Transformation
H = Type III SSCP Matrix for LogDepth
E = Error SSCP Matrix

S=1 M=-0.5 N=17.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.23351802 121.45 1 37 <.0001
Pillai's Trace 0.76648198 121.45 1 37 <.0001
Hotelling-Lawley Trace 3.28232484 121.45 1 37 <.0001
Roy's Greatest Root 3.28232484 121.45 1 37 <.0001

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

The GLM Procedure
Multivariate Analysis of Variance
 
Dependent Variable: Y3

Source DF Type III SS Mean Square F Value Pr > F
LogDepth 1 47.80222567 47.80222567 121.45 <.0001
Error 37 14.56352675 0.39360883    

Sand, Silt, and Clay Compositions In An Artic Lake
Compositional Data Multivariate Regression Model

Obs Sand SandHAT Silt SiltHAT Clay ClayHAT TotalHAT
1 77.5000 71.8033 19.5000 25.4787 3.0000 2.7180 100
2 71.9000 67.4274 24.9000 29.0469 3.2000 3.5257 100
3 50.7000 63.8411 36.1000 31.8877 13.2000 4.2712 100
4 52.3571 63.2027 41.0231 32.3851 6.6199 4.4122 100
5 70.0000 55.0575 26.5000 38.4928 3.5000 6.4497 100
6 66.5000 53.3757 32.2000 39.6942 1.3000 6.9301 100
7 43.1000 48.8737 55.3000 42.7962 1.6000 8.3301 100
8 53.4000 47.1327 36.8000 43.9477 9.8000 8.9196 100
9 15.5000 42.5113 54.4000 46.8578 30.1000 10.6309 100
10 31.7000 39.5741 41.5000 48.5837 26.8000 11.8422 100
11 65.7000 38.9751 27.8000 48.9225 6.5000 12.1024 100
12 70.4000 35.2404 29.0000 50.9239 0.6000 13.8357 100
13 17.4000 32.8772 53.6000 52.0804 29.0000 15.0424 100
14 10.6000 23.9315 69.8000 55.4431 19.6000 20.6255 100
15 38.2000 22.7712 43.1000 55.7272 18.7000 21.5016 100
16 10.8000 19.7839 52.7000 56.2407 36.5000 23.9754 100
17 4.6000 19.6990 47.4000 56.2501 48.0000 24.0509 100
18 18.4000 18.9559 50.7000 56.3192 30.9000 24.7250 100
19 15.6000 15.8079 50.4000 56.3030 34.0000 27.8891 100
20 31.9000 13.1169 45.1000 55.7861 23.0000 31.0970 100
21 9.5000 13.0676 53.5000 55.7712 37.0000 31.1612 100
22 17.1000 12.4484 48.0000 55.5650 34.9000 31.9866 100
23 10.5000 11.9987 55.4000 55.3916 34.1000 32.6097 100
24 4.7761 11.9549 54.4279 55.3736 40.7960 32.6715 100
25 2.6000 8.5588 45.2000 53.2285 52.2000 38.2127 100
26 11.4000 8.3133 52.7000 53.0020 35.9000 38.6847 100
27 6.7000 7.8998 46.9000 52.5926 46.4000 39.5076 100
28 6.9000 7.7276 49.7000 52.4112 43.4000 39.8612 100
29 4.0000 6.2741 44.9000 50.5747 51.1000 43.1512 100
30 7.4074 5.5515 51.6517 49.4126 40.9409 45.0359 100
31 4.8000 5.4297 49.5000 49.1967 45.7000 45.3736 100
32 4.5000 4.8594 48.5000 48.0957 47.0000 47.0449 100
33 6.6000 4.3345 52.1000 46.9313 41.3000 48.7342 100
34 6.7067 3.8463 47.3473 45.6894 45.9459 50.4644 100
35 7.4074 3.8090 45.6456 45.5874 46.9469 50.6036 100
36 6.0000 3.6042 48.9000 45.0060 45.1000 51.3898 100
37 6.3000 3.5871 53.8000 44.9559 39.9000 51.4570 100
38 2.5000 3.0457 48.0000 43.2194 49.5000 53.7350 100
39 2.0000 2.6716 47.8000 41.8211 50.2000 55.5073 100

TEMPLATE GRAPH PRODUCED BY GREPLAY