General Linear Models
General Linear Models
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Number of dependent variables: 1
Number of categorical factors: 3
Number of quantitative factors: 0
Analysis of Variance for kwiatostany_2008
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Source Sum of Squares Df Mean Square F-Ratio P-Value
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Model 12104,0 13 931,077 2,00 0,0733
Residual 10239,4 22 465,428
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Total (Corr.) 22343,4 35
Type III Sums of Squares
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Source Sum of Squares Df Mean Square F-Ratio P-Value
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powt2 1327,98 2 663,988 1,43 0,2615
podkladka 7022,41 5 1404,48 3,02 0,0319
root_pruning 976,563 1 976,563 2,10 0,1616
podkladka*root_pruning 2777,05 5 555,411 1,19 0,3446
Residual 10239,4 22 465,428
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Total (corrected) 22343,4 35
All F-ratios are based on the residual mean square error.
R-Squared = 54,1726 percent
R-Squared (adjusted for d.f.) = 27,0927 percent
Standard Error of Est. = 21,5738
Mean absolute error = 13,1389
Durbin-Watson statistic = 2,07215
Residual Analysis
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Estimation Validation
n 36
MSE 465,428
MAE 13,1389
MAPE 20,6682
ME 1,38161E-15
MPE -5,66444
The StatAdvisor
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This pane summarizes the results of fitting a general linear
statistical model relating kwiatostany_2008 to 3 predictive factors.
Since the P-value in the first ANOVA table for kwiatostany_2008 is
less than 0.10, there is a statistically significant relationship
between kwiatostany_2008 and the predictor variables at the 90%
confidence level.
The second ANOVA table for kwiatostany_2008 tests the statistical
significance of each of the factors as it was entered into the model.
Notice that the highest P-value is 0,3446, belonging to B*C. Since
the P-value is greater or equal to 0.10, that term is not
statistically significant at the 90% or higher confidence level.
Consequently, you should consider removing B*C from the model.
The R-Squared statistic indicates that the model as fitted explains
54,1726% of the variability in kwiatostany_2008. The adjusted
R-squared statistic, which is more suitable for comparing models with
different numbers of independent variables, is 27,0927%. The standard
error of the estimate shows the standard deviation of the residuals to
be 21,5738. This value can be used to construct prediction limits for
new observations by selecting the Reports option from the text menu.
The mean absolute error (MAE) of 13,1389 is the average value of the
residuals. The Durbin-Watson (DW) statistic tests the residuals to
determine if there is any significant correlation based on the order
in which they occur in your data file. Since the DW value is greater
than 1.4, there is probably not any serious autocorrelation in the
residuals.
The output also summarizes the performance of the model in fitting
the data, and in predicting any values withheld from the fitting
process. It displays:
(1) the mean squared error (MSE)
(2) the mean absolute error (MAE)
(3) the mean absolute percentage error (MAPE)
(4) the mean error (ME)
(5) the mean percentage error (MPE)
Each of the statistics is based on the residuals. The first three
statistics measure the magnitude of the errors. A better model will
give a smaller value. The last two statistics measure bias. A better
model will give a value close to 0.0.
Table of Least Squares Means for kwiatostany_2008
with 95,0 Percent Confidence Intervals
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Stnd. Lower Upper
Level Count Mean Error Limit Limit
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GRAND MEAN 36 70,1806 3,59563 62,7237 77,6375
powt2
I 12 68,6944 6,22781 55,7787 81,6102
II 12 63,5972 6,22781 50,6815 76,5129
III 12 78,25 6,22781 65,3343 91,1657
podkladka
1 6 65,8333 8,80746 47,5677 84,0989
2 6 60,5556 8,80746 42,29 78,8211
3 6 89,2222 8,80746 70,9566 107,488
4 6 55,4722 8,80746 37,2066 73,7378
5 6 60,2778 8,80746 42,0122 78,5434
6 6 89,7222 8,80746 71,4566 107,988
root_pruning
+ 18 64,9722 5,08499 54,4266 75,5179
- 18 75,3889 5,08499 64,8432 85,9345
podkladka by root_pruning
1 + 3 44,0 12,4556 18,1686 69,8314
1 - 3 87,6667 12,4556 61,8352 113,498
2 + 3 54,4444 12,4556 28,613 80,2759
2 - 3 66,6667 12,4556 40,8352 92,4981
3 + 3 84,5556 12,4556 58,7241 110,387
3 - 3 93,8889 12,4556 68,0574 119,72
4 + 3 58,1667 12,4556 32,3352 83,9981
4 - 3 52,7778 12,4556 26,9463 78,6092
5 + 3 53,2222 12,4556 27,3908 79,0537
5 - 3 67,3333 12,4556 41,5019 93,1648
6 + 3 95,4444 12,4556 69,613 121,276
6 - 3 84,0 12,4556 58,1686 109,831
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The StatAdvisor
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This table shows the mean kwiatostany_2008 for each level of the
factors. It also shows the standard error of each mean, which is a
measure of its sampling variability. The rightmost two columns show
95,0% confidence intervals for each of the means. You can display
these means and intervals by selecting Means Plot from the list of
Graphical Options.
Multiple Comparisons for kwiatostany_2008 by podkladka
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Method: 95,0 percent Student-Newman-Keuls
podkladka Count LS Mean Homogeneous Groups
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4 6 55,4722 X
5 6 60,2778 X
2 6 60,5556 X
1 6 65,8333 X
3 6 89,2222 X
6 6 89,7222 X
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Contrast Difference
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1 - 2 5,27778
1 - 3 -23,3889
1 - 4 10,3611
1 - 5 5,55556
1 - 6 -23,8889
2 - 3 -28,6667
2 - 4 5,08333
2 - 5 0,277778
2 - 6 -29,1667
3 - 4 33,75
3 - 5 28,9444
3 - 6 -0,5
4 - 5 -4,80556
4 - 6 -34,25
5 - 6 -29,4444
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* denotes a statistically significant difference.
The StatAdvisor
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This table applies a multiple comparison procedure to determine
which means are significantly different from which others. The bottom
half of the output shows the estimated difference between each pair of
means. There are no statistically significant differences between any
pair of means at the 95,0% confidence level. At the top of the page,
one homogenous group is identified by a column of X's. Within each
column, the levels containing X's form a group of means within which
there are no statistically significant differences. The method
currently being used to discriminate among the means is the
Student-Newman-Keuls multiple comparison procedure. With this method,
there is a 5,0% risk of calling one or more pairs significantly
different when their actual difference equals 0.