summary.lmcal: Summarizing fitted calibration curves
In quantchem: Quantitative chemical analysis: calibration and evaluation of results
Description
Usage
Arguments
Details
Value
Note
Author(s)
See Also
Examples
Description
A 'summary' class for 'lmcal' and 'nlscal' objects.
Usage
1
2
3
4
Arguments
object
an object of class 'lmcal' or 'nlscal'
sort.models
should the tables be sorted by models (TRUE) or variables (FALSE).
...
additional arguments, currently ignored.
Details
The function performs summarizing of fitted calibration models and produces several
tables (see below). The are printed in appropriate form, and their list is returned
invisibly.
Value
A list, consisting of following items:
coefficients
Estimated coefficients, their standard error, significance (t) and p-value
residuals
Quantiles of residuals and Shapiro-Wilk test of their normality
variances
Quantiles of variances (without transform, with log-log, and with Box-Cox on y)
ond Bartlett test for therir heteroscedascity. Calculated only, if there are at least
2 replicates for each x
fit
R-squared, adjusted R-squared, AIC, residual standard error, sum of squared residuals,
sum of pure error and Lack-of-Fit ANOVA test
sensitivity
sensitivity, limit of detection and quantitation, autocorrelation of residuals,
Durbin-Watson test for autocorrelation
Note
The p-value of Durbin-Watson statistic is *only* approximated using normal
transform algorhitm! This is not critical criterion and *always* residual plot
should be visually examined.
Some of values given above are not computed for 'nlscal' models.
Author(s)
Lukasz Komsta, with portion by Achim Zeileis (from dwtest())
See Also
Examples
1
2
3
4
5
6
Example output
Loading required package: MASS
Loading required package: outliers
------------------------------------------
If you use this package, please cite the recent paper containing description of this software:
Komsta, L. Chemometric and statistical evaluation of calibration curves in pharmaceutical analysis
- a short review on trends and recommendations. J. AOAC Int. 2012, 95, 3, 669-672.
------------------------------------------
There were 12 warnings (use warnings() to see them)
Optimal Box-Cox power on x: 0.4737
Optimal Box-Cox power on y: 2.0234
Optimal power of weighting on x: -2.3
Optimal power of weighting on y: -4
Better weighting on y: FALSE
Coefficients:
x0 x1 x2 x3 x4
p1 0.8921822 0.2540093 NA NA NA
p2 0.6234089 0.4152733 -0.0179182 NA NA
p3 0.4910853 0.5529433 -0.0540065 0.0026732 NA
p4 0.4342341 0.6364974 -0.0904238 0.0087029 -3e-04
P1 0.7019934 0.3084108 NA NA NA
P2 0.5445987 0.4703910 -0.0245821 NA NA
P3 0.4563520 0.5925888 -0.0651559 0.0035413 NA
P4 0.3960184 0.6955026 -0.1173771 0.0133395 -6e-04
l1 -0.0030650 0.5037472 NA NA NA
l2 -0.0054354 0.5220794 -0.0198106 NA NA
bx 0.9885017 0.5170598 NA NA NA
by -0.5112502 0.5063314 NA NA NA
r1 1.0262661 0.2317381 NA NA NA
r2 0.6221464 0.4163627 -0.0180644 NA NA
r3 0.4857868 0.5584750 -0.0554785 0.0027792 NA
r4 0.4327170 0.6370596 -0.0899461 0.0085171 -3e-04
R1 1.0644338 0.2277410 NA NA NA
R2 0.7204687 0.3791276 -0.0148678 NA NA
R3 0.4461184 0.5980542 -0.0659036 0.0035650 NA
R4 0.3824829 0.7051641 -0.1190629 0.0133534 -6e-04
Goodness of fit:
R-Sq Adj-R-Sq AIC Sigma
p1 0.97779 0.97720 -75.17266 0.0900
p2 0.99725 0.99710 -156.73694 0.0321
p3 0.99878 0.99868 -187.30302 0.0217
p4 0.99886 0.99872 -187.78518 0.0213
P1 0.97223 0.97150 -49.12746 0.0271
P2 0.99677 0.99660 -133.19178 0.0094
P3 0.99841 0.99828 -159.55685 0.0067
P4 0.99854 0.99837 -160.96813 0.0065
l1 0.99899 0.99896 -311.23094 0.0047
l2 0.99910 0.99905 -313.93331 0.0045
bx 0.99887 0.99884 -194.39086 0.0203
by 0.99836 0.99832 -125.07729 0.0482
r1 NA NA -59.29057 0.0615
r2 NA NA -156.70646 0.0320
r3 NA NA -187.12089 0.0215
r4 NA NA -187.61104 0.0205
R1 NA NA 64.48967 0.0085
R2 NA NA -24.33253 0.0057
R3 NA NA -155.83682 0.0045
R4 NA NA -156.95371 0.0043
Optimal Box-Cox power on x: 0.4737
Optimal Box-Cox power on y: 2.0234
Optimal power of weighting on x: -2.3
Optimal power of weighting on y: -4
Mean relative error:
0.09029114 on x
0.09076084 on y
0.1257794 unweighted
Better weighting on y: FALSE
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x0 P1 0.7020 0.0168 41.7097 < 2.2e-16 ***
x0 P2 0.5446 0.0110 49.3165 < 2.2e-16 ***
x0 P3 0.4564 0.0165 27.7091 < 2.2e-16 ***
x0 P4 0.3960 0.0377 10.4928 2.372e-12 ***
x0 R1 1.0644 0.0046 230.0240 < 2.2e-16 ***
x0 R2 0.7205 0.0054 132.5575 < 2.2e-16 ***
x0 R3 0.4461 0.0119 37.4066 < 2.2e-16 ***
x0 R4 0.3825 0.0269 14.2125 < 2.2e-16 ***
x0 bx 0.9885 0.0065 151.0407 < 2.2e-16 ***
x0 by -0.5113 0.0168 -30.4193 < 2.2e-16 ***
x0 l1 -0.0031 0.0017 -1.8309 0.0749584 .
x0 l2 -0.0054 0.0019 -2.7971 0.0081341 **
x0 p1 0.8922 0.0314 28.4481 < 2.2e-16 ***
x0 p2 0.6234 0.0200 31.1352 < 2.2e-16 ***
x0 p3 0.4911 0.0239 20.5802 < 2.2e-16 ***
x0 p4 0.4342 0.0446 9.7271 1.740e-11 ***
x0 r1 1.0263 0.0226 45.4684 < 2.2e-16 ***
x0 r2 0.6221 0.0225 27.6610 < 2.2e-16 ***
x0 r3 0.4858 0.0259 18.7704 < 2.2e-16 ***
x0 r4 0.4327 0.0492 8.7876 < 2.2e-16 ***
x1 P1 0.3084 0.0085 36.4721 < 2.2e-16 ***
x1 P2 0.4704 0.0101 46.6070 < 2.2e-16 ***
x1 P3 0.5926 0.0213 27.8313 < 2.2e-16 ***
x1 P4 0.6955 0.0619 11.2422 3.633e-13 ***
x1 R1 0.2277 0.0023 97.9542 < 2.2e-16 ***
x1 R2 0.3791 0.0050 76.3223 < 2.2e-16 ***
x1 R3 0.5981 0.0154 38.7879 < 2.2e-16 ***
x1 R4 0.7052 0.0441 15.9854 < 2.2e-16 ***
x1 bx 0.5171 0.0028 183.4632 < 2.2e-16 ***
x1 by 0.5063 0.0033 152.1319 < 2.2e-16 ***
x1 l1 0.5037 0.0026 193.4081 < 2.2e-16 ***
x1 l2 0.5221 0.0089 58.7366 < 2.2e-16 ***
x1 p1 0.2540 0.0062 40.8996 < 2.2e-16 ***
x1 p2 0.4153 0.0102 40.6796 < 2.2e-16 ***
x1 p3 0.5529 0.0216 25.6092 < 2.2e-16 ***
x1 p4 0.6365 0.0597 10.6582 1.558e-12 ***
x1 r1 0.2317 0.0045 51.8462 < 2.2e-16 ***
x1 r2 0.4164 0.0115 36.3088 < 2.2e-16 ***
x1 r3 0.5585 0.0234 23.8481 < 2.2e-16 ***
x1 r4 0.6371 0.0659 9.6711 < 2.2e-16 ***
x2 P2 -0.0246 0.0015 -16.7676 < 2.2e-16 ***
x2 P3 -0.0652 0.0067 -9.6712 1.506e-11 ***
x2 P4 -0.1174 0.0303 -3.8738 0.0004490 ***
x2 R2 -0.0149 0.0007 -20.6049 < 2.2e-16 ***
x2 R3 -0.0659 0.0049 -13.5086 < 2.2e-16 ***
x2 R4 -0.1191 0.0216 -5.5108 3.572e-08 ***
x2 l2 -0.0198 0.0092 -2.1484 0.0382946 *
x2 p2 -0.0179 0.0011 -16.1825 < 2.2e-16 ***
x2 p3 -0.0540 0.0054 -9.9718 6.700e-12 ***
x2 p4 -0.0904 0.0249 -3.6308 0.0008948 ***
x2 r2 -0.0181 0.0012 -14.5236 < 2.2e-16 ***
x2 r3 -0.0555 0.0059 -9.4446 < 2.2e-16 ***
x2 r4 -0.0899 0.0275 -3.2742 0.0010595 **
x3 P3 0.0035 0.0006 6.0959 5.175e-07 ***
x3 P4 0.0133 0.0056 2.3908 0.0223237 *
x3 R3 0.0036 0.0004 8.4746 < 2.2e-16 ***
x3 R4 0.0134 0.0040 3.3564 0.0007896 ***
x3 p3 0.0027 0.0004 6.7277 7.494e-08 ***
x3 p4 0.0087 0.0040 2.1504 0.0385083 *
x3 r3 0.0028 0.0004 6.4489 1.127e-10 ***
x3 r4 0.0085 0.0045 1.9079 0.0564016 .
x4 P4 -0.0006 0.0003 -1.7652 0.0862588 .
x4 R4 -0.0006 0.0002 -2.4375 0.0147881 *
x4 p4 -0.0003 0.0002 -1.4969 0.1433852
x4 r4 -0.0003 0.0002 -1.2974 0.1944866
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residuals:
0% 25% 50% 75% 100% W Pr(<W)
p1 -0.1743 -0.0630 0.0173 0.0661 0.1220 0.9128 0.0045977 **
p2 -0.0536 -0.0314 0.0034 0.0268 0.0545 0.9524 0.0918667 .
p3 -0.0320 -0.0173 -0.0036 0.0182 0.0493 0.9600 0.1678323
p4 -0.0297 -0.0140 -0.0034 0.0147 0.0418 0.9504 0.0783601 .
P1 -0.3743 -0.1468 -0.0242 0.0817 0.1189 0.8853 0.0007354 ***
P2 -0.0677 -0.0242 -0.0053 0.0232 0.1185 0.9368 0.0269511 *
P3 -0.0453 -0.0133 -0.0017 0.0131 0.0551 0.9827 0.7879913
P4 -0.0367 -0.0153 -0.0031 0.0146 0.0349 0.9484 0.0668441 .
l1 -0.0093 -0.0035 -0.0014 0.0037 0.0088 0.9440 0.0472662 *
l2 -0.0070 -0.0034 -0.0005 0.0033 0.0107 0.9686 0.3246200
bx -0.0312 -0.0158 -0.0013 0.0136 0.0408 0.9527 0.0936788 .
by -0.0841 -0.0335 -0.0038 0.0267 0.1096 0.9655 0.2562434
r1 -0.2861 -0.0694 -0.0091 0.0337 0.0774 0.8121 1.220e-05 ***
r2 -0.0536 -0.0310 0.0026 0.0265 0.0561 0.9539 0.1031173
r3 -0.0310 -0.0162 -0.0038 0.0200 0.0516 0.9626 0.2060758
r4 -0.0296 -0.0130 -0.0029 0.0150 0.0444 0.9548 0.1110577
R1 -0.3203 -0.0852 -0.0220 0.0177 0.0592 0.7953 5.422e-06 ***
R2 -0.1129 -0.0249 -0.0043 0.0158 0.0510 0.8993 0.0018284 **
R3 -0.0431 -0.0123 0.0013 0.0152 0.0556 0.9847 0.8550521
R4 -0.0351 -0.0136 -0.0005 0.0152 0.0365 0.9506 0.0794619 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Variances:
Min Median Max K Pr(>K)
Pure 0.0002 0.0004 0.0008 3.1911 0.86678
Log 0.0000 0.0000 0.0000 1.5023 0.98223
Box-Cox 0.0002 0.0021 0.0058 14.4723 0.04339 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Goodness of fit:
R-Sq Adj-R-Sq AIC Sigma SSR SSPE F Pr(>F)
p1 0.97779 0.97720 -75.17266 0.0900 0.3078 0.0149 104.68406 < 2.2e-16
p2 0.99725 0.99710 -156.73694 0.0321 0.0381 0.0149 9.94387 8.267e-06
p3 0.99878 0.99868 -187.30302 0.0217 0.0169 0.0149 1.05072 0.396727
p4 0.99886 0.99872 -187.78518 0.0213 0.0159 0.0149 0.67488 0.573800
P1 0.97223 0.97150 -49.12746 0.0271 0.0280 0.0149 4.67027 0.001624
P2 0.99677 0.99660 -133.19178 0.0094 0.0033 0.0149 NA NA
P3 0.99841 0.99828 -159.55685 0.0067 0.0016 0.0149 NA NA
P4 0.99854 0.99837 -160.96813 0.0065 0.0015 0.0149 NA NA
l1 0.99899 0.99896 -311.23094 0.0047 0.0008 0.0007 1.02249 0.428657
l2 0.99910 0.99905 -313.93331 0.0045 0.0007 0.0007 0.38106 0.857990
bx 0.99887 0.99884 -194.39086 0.0203 0.0156 0.0149 0.25222 0.954790
by 0.99836 0.99832 -125.07729 0.0482 0.0884 0.0851 0.20616 0.972329
r1 NA NA -59.29057 0.0615 0.4578 0.0149 NA NA
r2 NA NA -156.70646 0.0320 0.0381 0.0149 NA NA
r3 NA NA -187.12089 0.0215 0.0170 0.0149 NA NA
r4 NA NA -187.61104 0.0205 0.0159 0.0149 NA NA
R1 NA NA 64.48967 0.0085 0.4792 0.0149 NA NA
R2 NA NA -24.33253 0.0057 0.0495 0.0149 NA NA
R3 NA NA -155.83682 0.0045 0.0018 0.0149 NA NA
R4 NA NA -156.95371 0.0043 0.0016 0.0149 NA NA
p1 ***
p2 ***
p3
p4
P1 **
P2
P3
P4
l1
l2
bx
by
r1
r2
r3
r4
R1
R2
R3
R4
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sensitivity and autocorrelation:
Sens LOD LOQ Auto DW Pr(<DW)
p1 0.3543 1.1692 3.5432 0.5100 0.86374 8.822e-05 ***
p2 0.0773 0.2550 0.7728 -0.0259 1.91823 0.3247223
p3 0.0392 0.1292 0.3916 0.0324 1.87568 0.2780457
p4 0.0334 0.1104 0.3345 0.0524 1.82833 0.2365706
P1 0.0880 0.2904 0.8800 0.5840 0.73389 1.520e-05 ***
P2 0.0199 0.0658 0.1994 0.2005 1.42637 0.0213064 *
P3 0.0113 0.0371 0.1126 0.0391 1.90373 0.3083886
P4 0.0093 0.0308 0.0932 0.0547 1.81244 0.2217909
l1 NA NA NA 0.0518 1.78172 0.2204653
l2 NA NA NA 0.0329 1.83520 0.2465011
bx NA NA NA 0.0692 1.78306 0.2196654
by NA NA NA 0.0962 1.72460 0.1667593
r1 0.2654 0.8759 2.6542 0.4137 0.99185 0.0004245 ***
r2 0.0768 0.2535 0.7682 -0.0361 1.93427 0.3433829
r3 0.0384 0.1268 0.3842 0.0393 1.86204 0.2638388
r4 0.0322 0.1061 0.3215 0.0570 1.81606 0.2251145
R1 0.0374 0.1233 0.3738 0.4592 0.89922 0.0001385 ***
R2 0.0150 0.0494 0.1498 -0.0470 1.87082 0.2722074
R3 0.0076 0.0251 0.0759 0.0263 1.93379 0.3424243
R4 0.0060 0.0200 0.0605 0.0553 1.82233 0.2309266
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
quantchem documentation built on May 30, 2017, 5:28 a.m.
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Description Usage Arguments Details Value Note Author(s) See Also Examples
Description
A 'summary' class for 'lmcal' and 'nlscal' objects.
Usage
1 2 3 4 |
Arguments
object |
an object of class 'lmcal' or 'nlscal' |
sort.models |
should the tables be sorted by models (TRUE) or variables (FALSE). |
... |
additional arguments, currently ignored. |
Details
The function performs summarizing of fitted calibration models and produces several tables (see below). The are printed in appropriate form, and their list is returned invisibly.
Value
A list, consisting of following items:
coefficients |
Estimated coefficients, their standard error, significance (t) and p-value |
residuals |
Quantiles of residuals and Shapiro-Wilk test of their normality |
variances |
Quantiles of variances (without transform, with log-log, and with Box-Cox on y) ond Bartlett test for therir heteroscedascity. Calculated only, if there are at least 2 replicates for each x |
fit |
R-squared, adjusted R-squared, AIC, residual standard error, sum of squared residuals, sum of pure error and Lack-of-Fit ANOVA test |
sensitivity |
sensitivity, limit of detection and quantitation, autocorrelation of residuals, Durbin-Watson test for autocorrelation |
Note
The p-value of Durbin-Watson statistic is *only* approximated using normal transform algorhitm! This is not critical criterion and *always* residual plot should be visually examined.
Some of values given above are not computed for 'nlscal' models.
Author(s)
Lukasz Komsta, with portion by Achim Zeileis (from dwtest())
See Also
Examples
1 2 3 4 5 6 |
Example output
Loading required package: MASS
Loading required package: outliers
------------------------------------------
If you use this package, please cite the recent paper containing description of this software:
Komsta, L. Chemometric and statistical evaluation of calibration curves in pharmaceutical analysis
- a short review on trends and recommendations. J. AOAC Int. 2012, 95, 3, 669-672.
------------------------------------------
There were 12 warnings (use warnings() to see them)
Optimal Box-Cox power on x: 0.4737
Optimal Box-Cox power on y: 2.0234
Optimal power of weighting on x: -2.3
Optimal power of weighting on y: -4
Better weighting on y: FALSE
Coefficients:
x0 x1 x2 x3 x4
p1 0.8921822 0.2540093 NA NA NA
p2 0.6234089 0.4152733 -0.0179182 NA NA
p3 0.4910853 0.5529433 -0.0540065 0.0026732 NA
p4 0.4342341 0.6364974 -0.0904238 0.0087029 -3e-04
P1 0.7019934 0.3084108 NA NA NA
P2 0.5445987 0.4703910 -0.0245821 NA NA
P3 0.4563520 0.5925888 -0.0651559 0.0035413 NA
P4 0.3960184 0.6955026 -0.1173771 0.0133395 -6e-04
l1 -0.0030650 0.5037472 NA NA NA
l2 -0.0054354 0.5220794 -0.0198106 NA NA
bx 0.9885017 0.5170598 NA NA NA
by -0.5112502 0.5063314 NA NA NA
r1 1.0262661 0.2317381 NA NA NA
r2 0.6221464 0.4163627 -0.0180644 NA NA
r3 0.4857868 0.5584750 -0.0554785 0.0027792 NA
r4 0.4327170 0.6370596 -0.0899461 0.0085171 -3e-04
R1 1.0644338 0.2277410 NA NA NA
R2 0.7204687 0.3791276 -0.0148678 NA NA
R3 0.4461184 0.5980542 -0.0659036 0.0035650 NA
R4 0.3824829 0.7051641 -0.1190629 0.0133534 -6e-04
Goodness of fit:
R-Sq Adj-R-Sq AIC Sigma
p1 0.97779 0.97720 -75.17266 0.0900
p2 0.99725 0.99710 -156.73694 0.0321
p3 0.99878 0.99868 -187.30302 0.0217
p4 0.99886 0.99872 -187.78518 0.0213
P1 0.97223 0.97150 -49.12746 0.0271
P2 0.99677 0.99660 -133.19178 0.0094
P3 0.99841 0.99828 -159.55685 0.0067
P4 0.99854 0.99837 -160.96813 0.0065
l1 0.99899 0.99896 -311.23094 0.0047
l2 0.99910 0.99905 -313.93331 0.0045
bx 0.99887 0.99884 -194.39086 0.0203
by 0.99836 0.99832 -125.07729 0.0482
r1 NA NA -59.29057 0.0615
r2 NA NA -156.70646 0.0320
r3 NA NA -187.12089 0.0215
r4 NA NA -187.61104 0.0205
R1 NA NA 64.48967 0.0085
R2 NA NA -24.33253 0.0057
R3 NA NA -155.83682 0.0045
R4 NA NA -156.95371 0.0043
Optimal Box-Cox power on x: 0.4737
Optimal Box-Cox power on y: 2.0234
Optimal power of weighting on x: -2.3
Optimal power of weighting on y: -4
Mean relative error:
0.09029114 on x
0.09076084 on y
0.1257794 unweighted
Better weighting on y: FALSE
Coefficients:
Estimate Std. Error t value Pr(>|t|)
x0 P1 0.7020 0.0168 41.7097 < 2.2e-16 ***
x0 P2 0.5446 0.0110 49.3165 < 2.2e-16 ***
x0 P3 0.4564 0.0165 27.7091 < 2.2e-16 ***
x0 P4 0.3960 0.0377 10.4928 2.372e-12 ***
x0 R1 1.0644 0.0046 230.0240 < 2.2e-16 ***
x0 R2 0.7205 0.0054 132.5575 < 2.2e-16 ***
x0 R3 0.4461 0.0119 37.4066 < 2.2e-16 ***
x0 R4 0.3825 0.0269 14.2125 < 2.2e-16 ***
x0 bx 0.9885 0.0065 151.0407 < 2.2e-16 ***
x0 by -0.5113 0.0168 -30.4193 < 2.2e-16 ***
x0 l1 -0.0031 0.0017 -1.8309 0.0749584 .
x0 l2 -0.0054 0.0019 -2.7971 0.0081341 **
x0 p1 0.8922 0.0314 28.4481 < 2.2e-16 ***
x0 p2 0.6234 0.0200 31.1352 < 2.2e-16 ***
x0 p3 0.4911 0.0239 20.5802 < 2.2e-16 ***
x0 p4 0.4342 0.0446 9.7271 1.740e-11 ***
x0 r1 1.0263 0.0226 45.4684 < 2.2e-16 ***
x0 r2 0.6221 0.0225 27.6610 < 2.2e-16 ***
x0 r3 0.4858 0.0259 18.7704 < 2.2e-16 ***
x0 r4 0.4327 0.0492 8.7876 < 2.2e-16 ***
x1 P1 0.3084 0.0085 36.4721 < 2.2e-16 ***
x1 P2 0.4704 0.0101 46.6070 < 2.2e-16 ***
x1 P3 0.5926 0.0213 27.8313 < 2.2e-16 ***
x1 P4 0.6955 0.0619 11.2422 3.633e-13 ***
x1 R1 0.2277 0.0023 97.9542 < 2.2e-16 ***
x1 R2 0.3791 0.0050 76.3223 < 2.2e-16 ***
x1 R3 0.5981 0.0154 38.7879 < 2.2e-16 ***
x1 R4 0.7052 0.0441 15.9854 < 2.2e-16 ***
x1 bx 0.5171 0.0028 183.4632 < 2.2e-16 ***
x1 by 0.5063 0.0033 152.1319 < 2.2e-16 ***
x1 l1 0.5037 0.0026 193.4081 < 2.2e-16 ***
x1 l2 0.5221 0.0089 58.7366 < 2.2e-16 ***
x1 p1 0.2540 0.0062 40.8996 < 2.2e-16 ***
x1 p2 0.4153 0.0102 40.6796 < 2.2e-16 ***
x1 p3 0.5529 0.0216 25.6092 < 2.2e-16 ***
x1 p4 0.6365 0.0597 10.6582 1.558e-12 ***
x1 r1 0.2317 0.0045 51.8462 < 2.2e-16 ***
x1 r2 0.4164 0.0115 36.3088 < 2.2e-16 ***
x1 r3 0.5585 0.0234 23.8481 < 2.2e-16 ***
x1 r4 0.6371 0.0659 9.6711 < 2.2e-16 ***
x2 P2 -0.0246 0.0015 -16.7676 < 2.2e-16 ***
x2 P3 -0.0652 0.0067 -9.6712 1.506e-11 ***
x2 P4 -0.1174 0.0303 -3.8738 0.0004490 ***
x2 R2 -0.0149 0.0007 -20.6049 < 2.2e-16 ***
x2 R3 -0.0659 0.0049 -13.5086 < 2.2e-16 ***
x2 R4 -0.1191 0.0216 -5.5108 3.572e-08 ***
x2 l2 -0.0198 0.0092 -2.1484 0.0382946 *
x2 p2 -0.0179 0.0011 -16.1825 < 2.2e-16 ***
x2 p3 -0.0540 0.0054 -9.9718 6.700e-12 ***
x2 p4 -0.0904 0.0249 -3.6308 0.0008948 ***
x2 r2 -0.0181 0.0012 -14.5236 < 2.2e-16 ***
x2 r3 -0.0555 0.0059 -9.4446 < 2.2e-16 ***
x2 r4 -0.0899 0.0275 -3.2742 0.0010595 **
x3 P3 0.0035 0.0006 6.0959 5.175e-07 ***
x3 P4 0.0133 0.0056 2.3908 0.0223237 *
x3 R3 0.0036 0.0004 8.4746 < 2.2e-16 ***
x3 R4 0.0134 0.0040 3.3564 0.0007896 ***
x3 p3 0.0027 0.0004 6.7277 7.494e-08 ***
x3 p4 0.0087 0.0040 2.1504 0.0385083 *
x3 r3 0.0028 0.0004 6.4489 1.127e-10 ***
x3 r4 0.0085 0.0045 1.9079 0.0564016 .
x4 P4 -0.0006 0.0003 -1.7652 0.0862588 .
x4 R4 -0.0006 0.0002 -2.4375 0.0147881 *
x4 p4 -0.0003 0.0002 -1.4969 0.1433852
x4 r4 -0.0003 0.0002 -1.2974 0.1944866
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residuals:
0% 25% 50% 75% 100% W Pr(<W)
p1 -0.1743 -0.0630 0.0173 0.0661 0.1220 0.9128 0.0045977 **
p2 -0.0536 -0.0314 0.0034 0.0268 0.0545 0.9524 0.0918667 .
p3 -0.0320 -0.0173 -0.0036 0.0182 0.0493 0.9600 0.1678323
p4 -0.0297 -0.0140 -0.0034 0.0147 0.0418 0.9504 0.0783601 .
P1 -0.3743 -0.1468 -0.0242 0.0817 0.1189 0.8853 0.0007354 ***
P2 -0.0677 -0.0242 -0.0053 0.0232 0.1185 0.9368 0.0269511 *
P3 -0.0453 -0.0133 -0.0017 0.0131 0.0551 0.9827 0.7879913
P4 -0.0367 -0.0153 -0.0031 0.0146 0.0349 0.9484 0.0668441 .
l1 -0.0093 -0.0035 -0.0014 0.0037 0.0088 0.9440 0.0472662 *
l2 -0.0070 -0.0034 -0.0005 0.0033 0.0107 0.9686 0.3246200
bx -0.0312 -0.0158 -0.0013 0.0136 0.0408 0.9527 0.0936788 .
by -0.0841 -0.0335 -0.0038 0.0267 0.1096 0.9655 0.2562434
r1 -0.2861 -0.0694 -0.0091 0.0337 0.0774 0.8121 1.220e-05 ***
r2 -0.0536 -0.0310 0.0026 0.0265 0.0561 0.9539 0.1031173
r3 -0.0310 -0.0162 -0.0038 0.0200 0.0516 0.9626 0.2060758
r4 -0.0296 -0.0130 -0.0029 0.0150 0.0444 0.9548 0.1110577
R1 -0.3203 -0.0852 -0.0220 0.0177 0.0592 0.7953 5.422e-06 ***
R2 -0.1129 -0.0249 -0.0043 0.0158 0.0510 0.8993 0.0018284 **
R3 -0.0431 -0.0123 0.0013 0.0152 0.0556 0.9847 0.8550521
R4 -0.0351 -0.0136 -0.0005 0.0152 0.0365 0.9506 0.0794619 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Variances:
Min Median Max K Pr(>K)
Pure 0.0002 0.0004 0.0008 3.1911 0.86678
Log 0.0000 0.0000 0.0000 1.5023 0.98223
Box-Cox 0.0002 0.0021 0.0058 14.4723 0.04339 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Goodness of fit:
R-Sq Adj-R-Sq AIC Sigma SSR SSPE F Pr(>F)
p1 0.97779 0.97720 -75.17266 0.0900 0.3078 0.0149 104.68406 < 2.2e-16
p2 0.99725 0.99710 -156.73694 0.0321 0.0381 0.0149 9.94387 8.267e-06
p3 0.99878 0.99868 -187.30302 0.0217 0.0169 0.0149 1.05072 0.396727
p4 0.99886 0.99872 -187.78518 0.0213 0.0159 0.0149 0.67488 0.573800
P1 0.97223 0.97150 -49.12746 0.0271 0.0280 0.0149 4.67027 0.001624
P2 0.99677 0.99660 -133.19178 0.0094 0.0033 0.0149 NA NA
P3 0.99841 0.99828 -159.55685 0.0067 0.0016 0.0149 NA NA
P4 0.99854 0.99837 -160.96813 0.0065 0.0015 0.0149 NA NA
l1 0.99899 0.99896 -311.23094 0.0047 0.0008 0.0007 1.02249 0.428657
l2 0.99910 0.99905 -313.93331 0.0045 0.0007 0.0007 0.38106 0.857990
bx 0.99887 0.99884 -194.39086 0.0203 0.0156 0.0149 0.25222 0.954790
by 0.99836 0.99832 -125.07729 0.0482 0.0884 0.0851 0.20616 0.972329
r1 NA NA -59.29057 0.0615 0.4578 0.0149 NA NA
r2 NA NA -156.70646 0.0320 0.0381 0.0149 NA NA
r3 NA NA -187.12089 0.0215 0.0170 0.0149 NA NA
r4 NA NA -187.61104 0.0205 0.0159 0.0149 NA NA
R1 NA NA 64.48967 0.0085 0.4792 0.0149 NA NA
R2 NA NA -24.33253 0.0057 0.0495 0.0149 NA NA
R3 NA NA -155.83682 0.0045 0.0018 0.0149 NA NA
R4 NA NA -156.95371 0.0043 0.0016 0.0149 NA NA
p1 ***
p2 ***
p3
p4
P1 **
P2
P3
P4
l1
l2
bx
by
r1
r2
r3
r4
R1
R2
R3
R4
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sensitivity and autocorrelation:
Sens LOD LOQ Auto DW Pr(<DW)
p1 0.3543 1.1692 3.5432 0.5100 0.86374 8.822e-05 ***
p2 0.0773 0.2550 0.7728 -0.0259 1.91823 0.3247223
p3 0.0392 0.1292 0.3916 0.0324 1.87568 0.2780457
p4 0.0334 0.1104 0.3345 0.0524 1.82833 0.2365706
P1 0.0880 0.2904 0.8800 0.5840 0.73389 1.520e-05 ***
P2 0.0199 0.0658 0.1994 0.2005 1.42637 0.0213064 *
P3 0.0113 0.0371 0.1126 0.0391 1.90373 0.3083886
P4 0.0093 0.0308 0.0932 0.0547 1.81244 0.2217909
l1 NA NA NA 0.0518 1.78172 0.2204653
l2 NA NA NA 0.0329 1.83520 0.2465011
bx NA NA NA 0.0692 1.78306 0.2196654
by NA NA NA 0.0962 1.72460 0.1667593
r1 0.2654 0.8759 2.6542 0.4137 0.99185 0.0004245 ***
r2 0.0768 0.2535 0.7682 -0.0361 1.93427 0.3433829
r3 0.0384 0.1268 0.3842 0.0393 1.86204 0.2638388
r4 0.0322 0.1061 0.3215 0.0570 1.81606 0.2251145
R1 0.0374 0.1233 0.3738 0.4592 0.89922 0.0001385 ***
R2 0.0150 0.0494 0.1498 -0.0470 1.87082 0.2722074
R3 0.0076 0.0251 0.0759 0.0263 1.93379 0.3424243
R4 0.0060 0.0200 0.0605 0.0553 1.82233 0.2309266
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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