| Chapter 9 : Relationship of WingSize size to selected variables |
| Raw data Listing |
| Obs | continent | latitude | females | seF | males | seM | ratio | seR |
|---|---|---|---|---|---|---|---|---|
| 1 | na | 35.5 | 901 | 2.5 | 797 | 3.8 | 0.831 | 0.010 |
| 2 | na | 37.0 | 896 | 3.5 | 806 | 3.0 | 0.834 | 0.014 |
| 3 | na | 38.6 | 906 | 3.0 | 812 | 3.2 | 0.836 | 0.012 |
| 4 | na | 40.7 | 907 | 3.5 | 807 | 3.2 | 0.833 | 0.013 |
| 5 | na | 40.9 | 898 | 3.6 | 818 | 2.7 | 0.830 | 0.012 |
| 6 | na | 42.4 | 893 | 3.4 | 809 | 3.3 | 0.828 | 0.015 |
| 7 | na | 45.0 | 913 | 4.3 | 810 | 4.3 | 0.834 | 0.024 |
| 8 | na | 46.8 | 915 | 3.8 | 819 | 3.3 | 0.825 | 0.014 |
| 9 | na | 48.8 | 927 | 2.0 | 800 | 4.9 | 0.832 | 0.009 |
| 10 | na | 49.8 | 924 | 4.5 | 823 | 2.2 | 0.824 | 0.011 |
| 11 | na | 50.8 | 930 | 3.4 | 814 | 4.1 | 0.826 | 0.013 |
| 12 | eu | 36.4 | 905 | 6.1 | 789 | 5.9 | 0.822 | 0.016 |
| 13 | eu | 39.3 | 889 | 4.7 | 803 | 3.5 | 0.809 | 0.021 |
| 14 | eu | 41.3 | 915 | 2.1 | 812 | 3.7 | 0.821 | 0.007 |
| 15 | eu | 43.4 | 930 | 2.6 | 820 | 3.1 | 0.831 | 0.016 |
| 16 | eu | 45.5 | 895 | 4.4 | 808 | 2.9 | 0.821 | 0.017 |
| 17 | eu | 47.3 | 926 | 3.2 | 815 | 6.2 | 0.826 | 0.010 |
| 18 | eu | 48.5 | 944 | 4.8 | 855 | 3.1 | 0.825 | 0.032 |
| 19 | eu | 50.4 | 925 | 3.2 | 842 | 4.3 | 0.820 | 0.013 |
| 20 | eu | 52.1 | 920 | 3.9 | 819 | 3.1 | 0.834 | 0.019 |
| 21 | eu | 56.1 | 934 | 4.2 | 839 | 4.4 | 0.825 | 0.012 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Processed data Listing |
| Obs | continent | latitude | sex | Wingsize | se | ID | group1 | group2 | group3 | group4 | X1 | X2 | X3 | X4 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | eu | 39.3 | Female | 889 | 4.7 | F | 1 | 0 | 0 | 0 | 39.3 | 0.0 | 0.0 | 0.0 |
| 2 | eu | 45.5 | Female | 895 | 4.4 | F | 1 | 0 | 0 | 0 | 45.5 | 0.0 | 0.0 | 0.0 |
| 3 | eu | 36.4 | Female | 905 | 6.1 | F | 1 | 0 | 0 | 0 | 36.4 | 0.0 | 0.0 | 0.0 |
| 4 | eu | 41.3 | Female | 915 | 2.1 | F | 1 | 0 | 0 | 0 | 41.3 | 0.0 | 0.0 | 0.0 |
| 5 | eu | 52.1 | Female | 920 | 3.9 | F | 1 | 0 | 0 | 0 | 52.1 | 0.0 | 0.0 | 0.0 |
| 6 | eu | 50.4 | Female | 925 | 3.2 | F | 1 | 0 | 0 | 0 | 50.4 | 0.0 | 0.0 | 0.0 |
| 7 | eu | 47.3 | Female | 926 | 3.2 | F | 1 | 0 | 0 | 0 | 47.3 | 0.0 | 0.0 | 0.0 |
| 8 | eu | 43.4 | Female | 930 | 2.6 | F | 1 | 0 | 0 | 0 | 43.4 | 0.0 | 0.0 | 0.0 |
| 9 | eu | 56.1 | Female | 934 | 4.2 | F | 1 | 0 | 0 | 0 | 56.1 | 0.0 | 0.0 | 0.0 |
| 10 | eu | 48.5 | Female | 944 | 4.8 | F | 1 | 0 | 0 | 0 | 48.5 | 0.0 | 0.0 | 0.0 |
| 11 | eu | 36.4 | Male | 789 | 5.9 | M | 0 | 1 | 0 | 0 | 0.0 | 36.4 | 0.0 | 0.0 |
| 12 | eu | 39.3 | Male | 803 | 3.5 | M | 0 | 1 | 0 | 0 | 0.0 | 39.3 | 0.0 | 0.0 |
| 13 | eu | 45.5 | Male | 808 | 2.9 | M | 0 | 1 | 0 | 0 | 0.0 | 45.5 | 0.0 | 0.0 |
| 14 | eu | 41.3 | Male | 812 | 3.7 | M | 0 | 1 | 0 | 0 | 0.0 | 41.3 | 0.0 | 0.0 |
| 15 | eu | 47.3 | Male | 815 | 6.2 | M | 0 | 1 | 0 | 0 | 0.0 | 47.3 | 0.0 | 0.0 |
| 16 | eu | 52.1 | Male | 819 | 3.1 | M | 0 | 1 | 0 | 0 | 0.0 | 52.1 | 0.0 | 0.0 |
| 17 | eu | 43.4 | Male | 820 | 3.1 | M | 0 | 1 | 0 | 0 | 0.0 | 43.4 | 0.0 | 0.0 |
| 18 | eu | 56.1 | Male | 839 | 4.4 | M | 0 | 1 | 0 | 0 | 0.0 | 56.1 | 0.0 | 0.0 |
| 19 | eu | 50.4 | Male | 842 | 4.3 | M | 0 | 1 | 0 | 0 | 0.0 | 50.4 | 0.0 | 0.0 |
| 20 | eu | 48.5 | Male | 855 | 3.1 | M | 0 | 1 | 0 | 0 | 0.0 | 48.5 | 0.0 | 0.0 |
| 21 | na | 42.4 | Female | 893 | 3.4 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 42.4 | 0.0 |
| 22 | na | 37.0 | Female | 896 | 3.5 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 37.0 | 0.0 |
| 23 | na | 40.9 | Female | 898 | 3.6 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 40.9 | 0.0 |
| 24 | na | 35.5 | Female | 901 | 2.5 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 35.5 | 0.0 |
| 25 | na | 38.6 | Female | 906 | 3.0 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 38.6 | 0.0 |
| 26 | na | 40.7 | Female | 907 | 3.5 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 40.7 | 0.0 |
| 27 | na | 45.0 | Female | 913 | 4.3 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 45.0 | 0.0 |
| 28 | na | 46.8 | Female | 915 | 3.8 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 46.8 | 0.0 |
| 29 | na | 49.8 | Female | 924 | 4.5 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 49.8 | 0.0 |
| 30 | na | 48.8 | Female | 927 | 2.0 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 48.8 | 0.0 |
| 31 | na | 50.8 | Female | 930 | 3.4 | f | 0 | 0 | 1 | 0 | 0.0 | 0.0 | 50.8 | 0.0 |
| 32 | na | 35.5 | Male | 797 | 3.8 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 35.5 |
| 33 | na | 48.8 | Male | 800 | 4.9 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 48.8 |
| 34 | na | 37.0 | Male | 806 | 3.0 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 37.0 |
| 35 | na | 40.7 | Male | 807 | 3.2 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 40.7 |
| 36 | na | 42.4 | Male | 809 | 3.3 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 42.4 |
| 37 | na | 45.0 | Male | 810 | 4.3 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 45.0 |
| 38 | na | 38.6 | Male | 812 | 3.2 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 38.6 |
| 39 | na | 50.8 | Male | 814 | 4.1 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 50.8 |
| 40 | na | 40.9 | Male | 818 | 2.7 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 40.9 |
| 41 | na | 46.8 | Male | 819 | 3.3 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 46.8 |
| 42 | na | 49.8 | Male | 823 | 2.2 | m | 0 | 0 | 0 | 1 | 0.0 | 0.0 | 0.0 | 49.8 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Plot of the raw data with ID variable |
Plot of Wingsize*latitude. Symbol is value of ID.
Wingsize |
|
960 +
|
|
|
| F
940 +
| F
| F f
| F f
| f F
920 + F
| F f
| f
| f f
| F
900 + f f
| f F
| f
| F
|
880 +
|
|
|
|
860 +
| M
|
|
| M
840 + M
|
|
|
| m
820 + m M m M
| M m
| m M m
| m m m M
| M
800 + m
| m
|
| M
|
780 +
|
-+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-
34 36 38 40 42 44 46 48 50 52 54 56 58
latitude
|
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on Latitude one line |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 4621.44765 | 4621.44765 | 1.72 | 0.1971 |
| Error | 40 | 107425 | 2685.62571 | ||
| Corrected Total | 41 | 112046 | |||
| Root MSE | 51.82302 | R-Square | 0.0412 |
|---|---|---|---|
| Dependent Mean | 864.52381 | Adj R-Sq | 0.0173 |
| Coeff Var | 5.99440 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 780.53173 | 64.52572 | 12.10 | <.0001 |
| latitude | 1 | 1.88323 | 1.43561 | 1.31 | 0.1971 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on Latitude separate intercepts |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 4 | 107409 | 26852 | 214.22 | <.0001 |
| Error | 37 | 4637.94684 | 125.34991 | ||
| Corrected Total | 41 | 112046 | |||
| Root MSE | 11.19598 | R-Square | 0.9586 |
|---|---|---|---|
| Dependent Mean | 864.52381 | Adj R-Sq | 0.9541 |
| Coeff Var | 1.29505 |
| Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased. |
| The following parameters have been set to 0, since the variables are a linear combination of other variables as shown. |
| group4 = | Intercept - group1 - group2 - group3 |
|---|
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | B | 732.83456 | 14.25644 | 51.40 | <.0001 |
| latitude | 1 | 1.79261 | 0.31988 | 5.60 | <.0001 |
| group1 | B | 102.95163 | 4.96921 | 20.72 | <.0001 |
| group2 | B | 4.85163 | 4.96921 | 0.98 | 0.3352 |
| group3 | B | 99.54545 | 4.77398 | 20.85 | <.0001 |
| group4 | 0 | 0 | . | . | . |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on Latitude separate slopes and intercepts |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 7 | 107913 | 15416 | 126.80 | <.0001 |
| Error | 34 | 4133.68477 | 121.57896 | ||
| Corrected Total | 41 | 112046 | |||
| Root MSE | 11.02629 | R-Square | 0.9631 |
|---|---|---|---|
| Dependent Mean | 864.52381 | Adj R-Sq | 0.9555 |
| Coeff Var | 1.27542 |
| Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased. |
| The following parameters have been set to 0, since the variables are a linear combination of other variables as shown. |
| group4 = | Intercept - group1 - group2 - group3 |
|---|---|
| X4 = | latitude - X1 - X2 - X3 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | B | 779.86417 | 28.73352 | 27.14 | <.0001 |
| latitude | B | 0.70648 | 0.65913 | 1.07 | 0.2913 |
| group1 | B | 56.32623 | 40.15128 | 1.40 | 0.1697 |
| group2 | B | -72.93864 | 40.15128 | -1.82 | 0.0781 |
| group3 | B | 39.43235 | 40.63533 | 0.97 | 0.3387 |
| group4 | 0 | 0 | . | . | . |
| X1 | B | 1.07735 | 0.89439 | 1.20 | 0.2367 |
| X2 | B | 1.75441 | 0.89439 | 1.96 | 0.0580 |
| X3 | B | 1.38829 | 0.93216 | 1.49 | 0.1456 |
| X4 | 0 | 0 | . | . | . |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on indicator variables with GLM |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| ID | 4 | F M f m |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on indicator variables with GLM |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 7 | 107912.7914 | 15416.1131 | 126.80 | <.0001 |
| Error | 34 | 4133.6848 | 121.5790 | ||
| Corrected Total | 41 | 112046.4762 |
| R-Square | Coeff Var | Root MSE | Wingsize Mean |
|---|---|---|---|
| 0.963107 | 1.275417 | 11.02629 | 864.5238 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 4621.4476 | 4621.4476 | 38.01 | <.0001 |
| ID | 3 | 102787.0817 | 34262.3606 | 281.81 | <.0001 |
| latitude*ID | 3 | 504.2621 | 168.0874 | 1.38 | 0.2647 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 3772.720501 | 3772.720501 | 31.03 | <.0001 |
| ID | 3 | 1524.400042 | 508.133347 | 4.18 | 0.0127 |
| latitude*ID | 3 | 504.262074 | 168.087358 | 1.38 | 0.2647 |
| Parameter | Estimate | Standard Error | t Value | Pr > |t| | |
|---|---|---|---|---|---|
| Intercept | 779.8641724 | B | 28.73352016 | 27.14 | <.0001 |
| latitude | 0.7064751 | B | 0.65913492 | 1.07 | 0.2913 |
| ID F | 56.3262256 | B | 40.15127904 | 1.40 | 0.1697 |
| ID M | -72.9386446 | B | 40.15127904 | -1.82 | 0.0781 |
| ID f | 39.4323542 | B | 40.63533390 | 0.97 | 0.3387 |
| ID m | 0.0000000 | B | . | . | . |
| latitude*ID F | 1.0773529 | B | 0.89438968 | 1.20 | 0.2367 |
| latitude*ID M | 1.7544085 | B | 0.89438968 | 1.96 | 0.0580 |
| latitude*ID f | 1.3882933 | B | 0.93215755 | 1.49 | 0.1456 |
| latitude*ID m | 0.0000000 | B | . | . | . |
| The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| sex | 2 | Female Male |
| continent | 2 | eu na |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 7 | 107912.7914 | 15416.1131 | 126.80 | <.0001 |
| Error | 34 | 4133.6848 | 121.5790 | ||
| Corrected Total | 41 | 112046.4762 |
| R-Square | Coeff Var | Root MSE | Wingsize Mean |
|---|---|---|---|
| 0.963107 | 1.275417 | 11.02629 | 864.5238 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 4621.4476 | 4621.4476 | 38.01 | <.0001 |
| sex | 1 | 102613.7143 | 102613.7143 | 844.01 | <.0001 |
| continent | 1 | 167.8953 | 167.8953 | 1.38 | 0.2481 |
| sex*continent | 1 | 5.4721 | 5.4721 | 0.05 | 0.8333 |
| latitude*sex | 1 | 21.7609 | 21.7609 | 0.18 | 0.6749 |
| latitude*continent | 1 | 158.3395 | 158.3395 | 1.30 | 0.2618 |
| latitud*sex*continen | 1 | 324.1617 | 324.1617 | 2.67 | 0.1117 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 3772.720501 | 3772.720501 | 31.03 | <.0001 |
| sex | 1 | 1073.113225 | 1073.113225 | 8.83 | 0.0054 |
| continent | 1 | 118.440410 | 118.440410 | 0.97 | 0.3306 |
| sex*continent | 1 | 304.296390 | 304.296390 | 2.50 | 0.1229 |
| latitude*sex | 1 | 38.441861 | 38.441861 | 0.32 | 0.5776 |
| latitude*continent | 1 | 158.339480 | 158.339480 | 1.30 | 0.2618 |
| latitud*sex*continen | 1 | 324.161738 | 324.161738 | 2.67 | 0.1117 |
| Parameter | Estimate | Standard Error | t Value | Pr > |t| | |
|---|---|---|---|---|---|
| Intercept | 779.8641724 | B | 28.73352016 | 27.14 | <.0001 |
| latitude | 0.7064751 | B | 0.65913492 | 1.07 | 0.2913 |
| sex Female | 39.4323542 | B | 40.63533390 | 0.97 | 0.3387 |
| sex Male | 0.0000000 | B | . | . | . |
| continent eu | -72.9386446 | B | 40.15127904 | -1.82 | 0.0781 |
| continent na | 0.0000000 | B | . | . | . |
| sex*continent Female eu | 89.8325160 | B | 56.78248337 | 1.58 | 0.1229 |
| sex*continent Female na | 0.0000000 | B | . | . | . |
| sex*continent Male eu | 0.0000000 | B | . | . | . |
| sex*continent Male na | 0.0000000 | B | . | . | . |
| latitude*sex Female | 1.3882933 | B | 0.93215755 | 1.49 | 0.1456 |
| latitude*sex Male | 0.0000000 | B | . | . | . |
| latitude*continent eu | 1.7544085 | B | 0.89438968 | 1.96 | 0.0580 |
| latitude*continent na | 0.0000000 | B | . | . | . |
| latitud*sex*continen Female eu | -2.0653489 | B | 1.26485802 | -1.63 | 0.1117 |
| latitud*sex*continen Female na | 0.0000000 | B | . | . | . |
| latitud*sex*continen Male eu | 0.0000000 | B | . | . | . |
| latitud*sex*continen Male na | 0.0000000 | B | . | . | . |
| The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM model reordered |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| sex | 2 | Female Male |
| continent | 2 | eu na |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM model reordered |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 7 | 107912.7914 | 15416.1131 | 126.80 | <.0001 |
| Error | 34 | 4133.6848 | 121.5790 | ||
| Corrected Total | 41 | 112046.4762 |
| R-Square | Coeff Var | Root MSE | Wingsize Mean |
|---|---|---|---|
| 0.963107 | 1.275417 | 11.02629 | 864.5238 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 4621.4476 | 4621.4476 | 38.01 | <.0001 |
| sex | 1 | 102613.7143 | 102613.7143 | 844.01 | <.0001 |
| latitude*sex | 1 | 15.6052 | 15.6052 | 0.13 | 0.7224 |
| continent | 1 | 167.8953 | 167.8953 | 1.38 | 0.2481 |
| latitude*continent | 1 | 158.3395 | 158.3395 | 1.30 | 0.2618 |
| sex*continent | 1 | 11.6278 | 11.6278 | 0.10 | 0.7590 |
| latitud*sex*continen | 1 | 324.1617 | 324.1617 | 2.67 | 0.1117 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 3772.720501 | 3772.720501 | 31.03 | <.0001 |
| sex | 1 | 1073.113225 | 1073.113225 | 8.83 | 0.0054 |
| latitude*sex | 1 | 38.441861 | 38.441861 | 0.32 | 0.5776 |
| continent | 1 | 118.440410 | 118.440410 | 0.97 | 0.3306 |
| latitude*continent | 1 | 158.339480 | 158.339480 | 1.30 | 0.2618 |
| sex*continent | 1 | 304.296390 | 304.296390 | 2.50 | 0.1229 |
| latitud*sex*continen | 1 | 324.161738 | 324.161738 | 2.67 | 0.1117 |
| Parameter | Estimate | Standard Error | t Value | Pr > |t| | |
|---|---|---|---|---|---|
| Intercept | 779.8641724 | B | 28.73352016 | 27.14 | <.0001 |
| latitude | 0.7064751 | B | 0.65913492 | 1.07 | 0.2913 |
| sex Female | 39.4323542 | B | 40.63533390 | 0.97 | 0.3387 |
| sex Male | 0.0000000 | B | . | . | . |
| latitude*sex Female | 1.3882933 | B | 0.93215755 | 1.49 | 0.1456 |
| latitude*sex Male | 0.0000000 | B | . | . | . |
| continent eu | -72.9386446 | B | 40.15127904 | -1.82 | 0.0781 |
| continent na | 0.0000000 | B | . | . | . |
| latitude*continent eu | 1.7544085 | B | 0.89438968 | 1.96 | 0.0580 |
| latitude*continent na | 0.0000000 | B | . | . | . |
| sex*continent Female eu | 89.8325160 | B | 56.78248337 | 1.58 | 0.1229 |
| sex*continent Female na | 0.0000000 | B | . | . | . |
| sex*continent Male eu | 0.0000000 | B | . | . | . |
| sex*continent Male na | 0.0000000 | B | . | . | . |
| latitud*sex*continen Female eu | -2.0653489 | B | 1.26485802 | -1.63 | 0.1117 |
| latitud*sex*continen Female na | 0.0000000 | B | . | . | . |
| latitud*sex*continen Male eu | 0.0000000 | B | . | . | . |
| latitud*sex*continen Male na | 0.0000000 | B | . | . | . |
| The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize - best model? |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| sex | 2 | Female Male |
| continent | 2 | eu na |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize - best model? |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 2 | 107235.1619 | 53617.5810 | 434.62 | <.0001 |
| Error | 39 | 4811.3143 | 123.3670 | ||
| Corrected Total | 41 | 112046.4762 |
| R-Square | Coeff Var | Root MSE | Wingsize Mean |
|---|---|---|---|
| 0.957060 | 1.284762 | 11.10707 | 864.5238 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 4621.4476 | 4621.4476 | 37.46 | <.0001 |
| sex | 1 | 102613.7143 | 102613.7143 | 831.78 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| latitude | 1 | 4621.4476 | 4621.4476 | 37.46 | <.0001 |
| sex | 1 | 102613.7143 | 102613.7143 | 831.78 | <.0001 |
| Parameter | Estimate | Standard Error | t Value | Pr > |t| | |
|---|---|---|---|---|---|
| Intercept | 731.1031578 | B | 13.93539338 | 52.46 | <.0001 |
| latitude | 1.8832305 | 0.30769045 | 6.12 | <.0001 | |
| sex Female | 98.8571429 | B | 3.42771661 | 28.84 | <.0001 |
| sex Male | 0.0000000 | B | . | . | . |
| The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Residual plot with sex ID variable |
Plot of resid*latitude. Symbol is value of sex.
resid |
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40 +
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| M
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30 +
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| F
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20 +
| F
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| M
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10 + M
| M
| F F M F
| M F
| F F
| F M M
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0 + F M F F
| M M M M F M F
| F
| F
| M M
|
| F M F
-10 + M M
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| M
| F
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| F
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-20 + F
|
| M
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|
|
|
-30 +
|
---+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
34 36 38 40 42 44 46 48 50 52 54 56 58
latitude
|
| Chapter 9 : Relationship of WingSize size to selected variables |
| Residual plot with sex ID variable |
| Moments | |||
|---|---|---|---|
| N | 42 | Sum Weights | 42 |
| Mean | 0 | Sum Observations | 0 |
| Std Deviation | 10.8327803 | Variance | 117.349128 |
| Skewness | 0.48361594 | Kurtosis | 1.3897594 |
| Uncorrected SS | 4811.31426 | Corrected SS | 4811.31426 |
| Coeff Variation | . | Std Error Mean | 1.67153428 |
| Basic Statistical Measures | |||
|---|---|---|---|
| Location | Variability | ||
| Mean | 0.00000 | Std Deviation | 10.83278 |
| Median | -0.49449 | Variance | 117.34913 |
| Mode | . | Range | 55.56497 |
| Interquartile Range | 11.06584 | ||
| Tests for Location: Mu0=0 | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Student's t | t | 0 | Pr > |t| | 1.0000 |
| Sign | M | -1 | Pr >= |M| | 0.8776 |
| Signed Rank | S | -14.5 | Pr >= |S| | 0.8587 |
| Tests for Normality | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Shapiro-Wilk | W | 0.966654 | Pr < W | 0.2539 |
| Kolmogorov-Smirnov | D | 0.108445 | Pr > D | >0.1500 |
| Cramer-von Mises | W-Sq | 0.084476 | Pr > W-Sq | 0.1825 |
| Anderson-Darling | A-Sq | 0.505494 | Pr > A-Sq | 0.2004 |
| Quantiles (Definition 5) | |
|---|---|
| Quantile | Estimate |
| 100% Max | 32.560163 |
| 99% | 32.560163 |
| 95% | 18.307496 |
| 90% | 9.872715 |
| 75% Q3 | 5.217314 |
| 50% Median | -0.494492 |
| 25% Q1 | -5.848530 |
| 10% | -12.771267 |
| 5% | -16.809274 |
| 1% | -23.004806 |
| 0% Min | -23.004806 |
| Extreme Observations | |||
|---|---|---|---|
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -23.0048 | 33 | 9.87271 | 40 |
| -20.6473 | 2 | 15.98203 | 19 |
| -16.8093 | 21 | 18.30750 | 8 |
| -14.9713 | 1 | 22.70302 | 10 |
| -12.7713 | 39 | 32.56016 | 20 |
Stem Leaf # Boxplot Normal Probability Plot
3 3 1 0 32.5+ *
2 | ++
2 3 1 0 | *+++++
1 68 2 | | **+++
1 0 1 | | ++++
0 5567778 7 +-----+ | +*******
0 00023344 8 | + | | +*****
-0 4322222110 10 *-----* | ******
-0 99865 5 +-----+ | ****+
-1 310 3 | | *+***
-1 75 2 | | +++*+
-2 31 2 0 -22.5+ +*+++*
----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2
|
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on Latitude separate slopes and intercepts |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| No intercept in model. R-Square is redefined. |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 8 | 31498772 | 3937347 | 32385.1 | <.0001 |
| Error | 34 | 4133.68477 | 121.57896 | ||
| Uncorrected Total | 42 | 31502906 | |||
| Root MSE | 11.02629 | R-Square | 0.9999 |
|---|---|---|---|
| Dependent Mean | 864.52381 | Adj R-Sq | 0.9998 |
| Coeff Var | 1.27542 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| group1 | 1 | 836.19040 | 28.04479 | 29.82 | <.0001 |
| group2 | 1 | 706.92553 | 28.04479 | 25.21 | <.0001 |
| group3 | 1 | 819.29653 | 28.73352 | 28.51 | <.0001 |
| group4 | 1 | 779.86417 | 28.73352 | 27.14 | <.0001 |
| X1 | 1 | 1.78383 | 0.60454 | 2.95 | 0.0057 |
| X2 | 1 | 2.46088 | 0.60454 | 4.07 | 0.0003 |
| X3 | 1 | 2.09477 | 0.65913 | 3.18 | 0.0032 |
| X4 | 1 | 0.70648 | 0.65913 | 1.07 | 0.2913 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM |
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| sex | 2 | Female Male |
| continent | 2 | eu na |
| Number of Observations Read | 42 |
|---|---|
| Number of Observations Used | 42 |
| Chapter 9 : Relationship of WingSize size to selected variables |
| Fit of WingSize on original variables with GLM |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 8 | 31498772.32 | 3937346.54 | 32385.1 | <.0001 |
| Error | 34 | 4133.68 | 121.58 | ||
| Uncorrected Total | 42 | 31502906.00 |
| R-Square | Coeff Var | Root MSE | Wingsize Mean |
|---|---|---|---|
| 0.963107 | 1.275417 | 11.02629 | 864.5238 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| sex*continent | 4 | 31494331.57 | 7873582.89 | 64761.1 | <.0001 |
| latitud*sex*continen | 4 | 4440.74 | 1110.19 | 9.13 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| sex*continent | 4 | 373743.1513 | 93435.7878 | 768.52 | <.0001 |
| latitud*sex*continen | 4 | 4440.7425 | 1110.1856 | 9.13 | <.0001 |
| Parameter | Estimate | Standard Error | t Value | Pr > |t| |
|---|---|---|---|---|
| sex*continent Female eu | 836.1903980 | 28.04478612 | 29.82 | <.0001 |
| sex*continent Female na | 819.2965266 | 28.73352016 | 28.51 | <.0001 |
| sex*continent Male eu | 706.9255278 | 28.04478612 | 25.21 | <.0001 |
| sex*continent Male na | 779.8641724 | 28.73352016 | 27.14 | <.0001 |
| latitud*sex*continen Female eu | 1.7838280 | 0.60454450 | 2.95 | 0.0057 |
| latitud*sex*continen Female na | 2.0947684 | 0.65913492 | 3.18 | 0.0032 |
| latitud*sex*continen Male eu | 2.4608836 | 0.60454450 | 4.07 | 0.0003 |
| latitud*sex*continen Male na | 0.7064751 | 0.65913492 | 1.07 | 0.2913 |