A and I
Estimating Concrete Compressive Strength from Use Materials and the Concrete Age (ECCS from UM and CA)
Abstract
This project uses Prof. I-Cheng Yeh’s dataset of (Concrete Data.xls) that contains more than 1000 observations with nine variables. The variable of Concrete Compressive Strength (MPa) is related to Cement, Blast Furnace Slag, Fly Ash, Water, Superplasticizer, Coarse Aggregate, Fine Aggregate, and age of samples. An acceptable model is needed to be found to have an equation to estimate Concrete Compressive Strength utilizing eight independent variables from dataset. The dataset is scaled. Subset Selection Methods and Stepwise Regression are used resulting in using all regressors obtaining higher Adjusted R squared and lower Root Mean Square Error. The 3 order of Multivariate Polynomial Regression with eight regressors has fitted utilizing 1005 observations that are not duplicated. The fitted model is significant and has 0.909 of an adjusted R squared and 62.17 of F-statistic.
Introduction
Concrete Compressive Strength is one of the main tests of concrete samples. This test, used for Compressing Concrete samples for education purposes, research purposes, or measuring quality, determines how strong hardened concrete samples are. It is known that the ratio of cement water plays a role in increasing or decreasing the strength of concrete. Choosing the appropriate ratio of water to cement is considered essential for making concrete whose compressive strength is significant. Every decreasing in the weight ratio of cement water leads to an increase in the compressive strength of concrete. The low ratio of cement weight to water weight in concrete mixtures causes poor workability, which means it is hard to be mixed (concrete mixtures). Plasticizers are used to improve the workability of a concrete mixture that is desired to contain less amount of water for raising a compressive Strength. Fly ash and slag cement (Class F) are used in a mixture of concrete to protect the concrete from Alkali-Silica Reaction and sulfate attack (IS-11). This The dataset that is used in this project belongs to Prof. I-Cheng Yeh’s. This data, about component of concrete, contains nine variables and 1030 records of each variable. This dataset has eight regressors or/and independent variables which are cement (kg in a m3 mixture), Blast Furnace Slag (kg in a m3 mixture), Fly Ash (kg in a m3 mixture), Water(kg in a m3 mixture), Superplasticizer (kg in a m3 mixture), Coarse Aggregate (kg in a m3 mixture), Fine Aggregate (kg in a m3 mixture), Age (1 ~ 365 days). These quantitative independent variables control of concrete compressive strength (MPa). It is a chance to find a good model of this dataset and obtain an equation from which the researcher can learn how use materials and the age of concrete: - how many days concrete samples since it has been made, determine the strength of concrete samples or the concrete.
The researcher looks for answers of these questions:
1-what regressors that are suggested to be on the model ?
2- What is type of the model that have a good fit the dataset?
Methods
Data Exploration
The matrix of scatterplots for the data was examined
Matrix of scatterplots of Y, X1, X5, and X8
Column
Motivation
I know that the ratio of water to cement has an impact on the compressive strength of concrete.
My motivation is that
I want to know that the effects of each independent variable, including water and cement in this model how concrete compressive strength will got affacted by regressor coefficients.
Information
1- Cement is the main element of concrete. Its job is to glue other concrete parts such as sand and aggregate to gather them after mixing with water.
2- Fine aggregates are aggregates that are passing through a 4.76 mm sieve.
3- And remained aggregates are not passing the sieve, are called Coarse Aggregate.
4- Water is no need to be defined.
5- Super-plasticizers are used to maintain high workability while at the same time maintaining strength ( Ruwan Rajapakse).
6- “Fly ash is the finely divided residue that results from the combustion of pulverized coal and is transported from the combustion chamber by exhaust gases” (Fly Ash Facts for Highway Engineers)
7- "Blast Furnace Slag is formed when iron ore or iron pellets, coke and a flux (either limestone or dolomite) are melted together in a blast furnace. When the metallurgical smelting process is complete, the lime in the flux has been chemically combined with the aluminates and silicatesof the ore and coke ash to form a non-metallic product called blast furnace slag (National Slag Association).
8- Age of concrete
Variables
X1 : Cement (kg in a m3 mixture)
X2 : Blast Furnace Slag (kg in a m3 mixture)
X3 : Fly Ash (kg in a m3 mixture)
X4 : Water (kg in a m3 mixture)
X5 : Superplasticizer (kg in a m3 mixture)
X6 : Coarse Aggregate (kg in a m3 mixture)
X7 : Fine Aggregate (kg in a m3 mixture)
X8 : Age (Day (1~365))
Y : Concrete compressive strength (MPa)
First
The scatterplot for X1 vs X8 shows a potential curve relationship between X1 and X8 because of existing points in the middle of X8 = 2 and 5.
First S
Call:
lm(formula = X1 ~ X8, data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.7580 -0.8266 -0.1605 0.6146 2.5629
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.742e-16 3.144e-02 0.000 1.00000
X8 8.635e-02 3.146e-02 2.745 0.00616 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9968 on 1003 degrees of freedom
Multiple R-squared: 0.007456, Adjusted R-squared: 0.006466
F-statistic: 7.534 on 1 and 1003 DF, p-value: 0.006161
Call:
lm(formula = X1 ~ poly(X8, degree = 3, raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.8372 -0.8332 -0.1308 0.6053 2.5795
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.551e-16 3.121e-02 0.000 1.00000
poly(X8, degree = 3, raw = F)1 2.736e+00 9.893e-01 2.766 0.00579 **
poly(X8, degree = 3, raw = F)2 8.601e-01 9.893e-01 0.869 0.38485
poly(X8, degree = 3, raw = F)3 -4.006e+00 9.893e-01 -4.049 5.54e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9893 on 1001 degrees of freedom
Multiple R-squared: 0.02417, Adjusted R-squared: 0.02125
F-statistic: 8.266 on 3 and 1001 DF, p-value: 1.956e-05Second
The scatterplot for X5 vs X1 shows a potential curve relationship between X5 and X1.
Second S
Call:
lm(formula = X5 ~ X1, data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.1717 -0.9954 0.0417 0.6944 4.3090
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.595e-16 3.150e-02 0.000 1.0000
X1 6.091e-02 3.152e-02 1.932 0.0536 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9986 on 1003 degrees of freedom
Multiple R-squared: 0.003709, Adjusted R-squared: 0.002716
F-statistic: 3.734 on 1 and 1003 DF, p-value: 0.05358
Call:
lm(formula = X5 ~ poly(X1, degree = 3, raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.2049 -0.9705 0.0642 0.6993 4.2449
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.484e-16 3.147e-02 0.000 1.0000
poly(X1, degree = 3, raw = F)1 1.930e+00 9.976e-01 1.935 0.0533 .
poly(X1, degree = 3, raw = F)2 7.557e-01 9.976e-01 0.758 0.4489
poly(X1, degree = 3, raw = F)3 -1.883e+00 9.976e-01 -1.887 0.0594 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9976 on 1001 degrees of freedom
Multiple R-squared: 0.007809, Adjusted R-squared: 0.004835
F-statistic: 2.626 on 3 and 1001 DF, p-value: 0.04918Third
Third S
Call:
lm(formula = Y ~ X8, data = df_new)
Residuals:
Min 1Q Median 3Q Max
-2.31385 -0.67123 -0.08051 0.55588 2.94992
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6.147e-16 2.971e-02 0.00 1
X8 3.374e-01 2.972e-02 11.35 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9418 on 1003 degrees of freedom
Multiple R-squared: 0.1138, Adjusted R-squared: 0.1129
F-statistic: 128.8 on 1 and 1003 DF, p-value: < 2.2e-16
Call:
lm(formula = Y ~ poly(X8, degree = 3, raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.7943 -0.5954 -0.1437 0.4930 2.8486
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.416e-16 2.599e-02 0.000 1
poly(X8, degree = 3, raw = F)1 1.069e+01 8.239e-01 12.975 <2e-16 ***
poly(X8, degree = 3, raw = F)2 -1.217e+01 8.239e-01 -14.772 <2e-16 ***
poly(X8, degree = 3, raw = F)3 7.888e+00 8.239e-01 9.574 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8239 on 1001 degrees of freedom
Multiple R-squared: 0.3233, Adjusted R-squared: 0.3213
F-statistic: 159.4 on 3 and 1001 DF, p-value: < 2.2e-16Fourth
Fourth S
Call:
lm(formula = X1 ~ X8, data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.7580 -0.8266 -0.1605 0.6146 2.5629
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.742e-16 3.144e-02 0.000 1.00000
X8 8.635e-02 3.146e-02 2.745 0.00616 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9968 on 1003 degrees of freedom
Multiple R-squared: 0.007456, Adjusted R-squared: 0.006466
F-statistic: 7.534 on 1 and 1003 DF, p-value: 0.006161
Call:
lm(formula = X1 ~ poly(X8, degree = 3, raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.8372 -0.8332 -0.1308 0.6053 2.5795
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.551e-16 3.121e-02 0.000 1.00000
poly(X8, degree = 3, raw = F)1 2.736e+00 9.893e-01 2.766 0.00579 **
poly(X8, degree = 3, raw = F)2 8.601e-01 9.893e-01 0.869 0.38485
poly(X8, degree = 3, raw = F)3 -4.006e+00 9.893e-01 -4.049 5.54e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9893 on 1001 degrees of freedom
Multiple R-squared: 0.02417, Adjusted R-squared: 0.02125
F-statistic: 8.266 on 3 and 1001 DF, p-value: 1.956e-05Fifth
Fifth S
Call:
lm(formula = X5 ~ X8, data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.1557 -1.0735 -0.0254 0.6217 4.5576
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.908e-16 3.096e-02 0.000 1
X8 -1.941e-01 3.098e-02 -6.266 5.51e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9815 on 1003 degrees of freedom
Multiple R-squared: 0.03767, Adjusted R-squared: 0.03671
F-statistic: 39.26 on 1 and 1003 DF, p-value: 5.505e-10
Call:
lm(formula = X5 ~ poly(X8, degree = 3, raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.2462 -0.9436 -0.0146 0.5903 4.5494
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.990e-16 3.027e-02 0.000 1.00000
poly(X8, degree = 3, raw = F)1 -6.149e+00 9.595e-01 -6.409 2.25e-10 ***
poly(X8, degree = 3, raw = F)2 -2.924e+00 9.595e-01 -3.047 0.00237 **
poly(X8, degree = 3, raw = F)3 6.010e+00 9.595e-01 6.263 5.58e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9595 on 1001 degrees of freedom
Multiple R-squared: 0.08215, Adjusted R-squared: 0.0794
F-statistic: 29.86 on 3 and 1001 DF, p-value: < 2.2e-16
D and A
Column
Data and Analytic Methods
Data management
- All column names are modified to be X1, X2, X3 ~ X8, and Y
The dataset was checked from any missing value and Null value. There was no missing value and no null value on the dataset.
Duplicate values were deleted, and there were 25 duplicate observations
The data was scaled
c. Analytic Methods —
- Matrix of scatterplots for the data was examined
Correlation of regressors were examined
Subset Selection Methods and Stepwise Regression were used to determine what variables should be used.
The 3 order of Multivariate Polynomial Regression with eight regressors model was made.
F statistical and adjusted R squared was checked.
Investigation of model adequacy was done
Column
Correlation
The correlation of regressors matrices show that X5 vs X4 high correlation of -0.64694605. This is an indication of collinearity issue.
X1 X2 X3 X4 X5
X1 1.00000000 -0.30332393 -0.38560975 -0.05662462 0.06090565
X2 -0.30332393 1.00000000 -0.31235235 0.13026211 0.01980022
X3 -0.38560975 -0.31235235 1.00000000 -0.28331366 0.41421276
X4 -0.05662462 0.13026211 -0.28331366 1.00000000 -0.64694605
X5 0.06090565 0.01980022 0.41421276 -0.64694605 1.00000000
X6 -0.08620530 -0.27755887 -0.02646847 -0.21247975 -0.24172051
X7 -0.24537545 -0.28968490 0.09026178 -0.44491471 0.20799292
X8 0.08634782 -0.04275925 -0.15894045 0.27928351 -0.19407633
X6 X7 X8
X1 -0.086205301 -0.24537545 0.086347817
X2 -0.277558868 -0.28968490 -0.042759251
X3 -0.026468472 0.09026178 -0.158940454
X4 -0.212479752 -0.44491471 0.279283512
X5 -0.241720507 0.20799292 -0.194076334
X6 1.000000000 -0.16218697 -0.005263596
X7 -0.162186974 1.00000000 -0.156572492
X8 -0.005263596 -0.15657249 1.000000000
Stepwise Regression
Stepwise Regression suggests having 8 regressors on the model because this model has the lowest Root Mean Square Error (RMSE = 0.6339170), the highest Coefficient of determination (R-squared = 0.5973950), and lowest Mean Absolute Error (MAE = 0.5039133).
nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
1 1 0.8704813 0.2458884 0.7151686 0.07288146 0.08200000 0.05992693
2 2 0.8129049 0.3413771 0.6651493 0.06214243 0.07415486 0.05382460
3 3 0.7260136 0.4738393 0.5798846 0.06588871 0.07705157 0.05824140
4 4 0.6783065 0.5387098 0.5483010 0.05508152 0.08051937 0.04727427
5 5 0.6358125 0.5950898 0.5071442 0.04549369 0.05452078 0.04171870
6 6 0.7564071 0.4281821 0.6111919 0.04863825 0.06022739 0.04317181
7 7 0.6986066 0.5099107 0.5576974 0.08976091 0.09666554 0.07866024
8 8 0.6339170 0.5973950 0.5039133 0.04596748 0.05467927 0.04467015
Subset selection
We can choose wanted variables in the model if the R Squared and RMSE are chosen from Stepwise Regression
Subset selection object
Call: regsubsets.formula(Y ~ ., data = df_new, nvmax = 8)
8 Variables (and intercept)
Forced in Forced out
X1 FALSE FALSE
X2 FALSE FALSE
X3 FALSE FALSE
X4 FALSE FALSE
X5 FALSE FALSE
X6 FALSE FALSE
X7 FALSE FALSE
X8 FALSE FALSE
1 subsets of each size up to 8
Selection Algorithm: exhaustive
X1 X2 X3 X4 X5 X6 X7 X8
1 ( 1 ) "*" " " " " " " " " " " " " " "
2 ( 1 ) "*" " " " " " " "*" " " " " " "
3 ( 1 ) "*" " " " " " " "*" " " " " "*"
4 ( 1 ) "*" "*" " " "*" " " " " " " "*"
5 ( 1 ) "*" "*" "*" "*" " " " " " " "*"
6 ( 1 ) "*" "*" "*" "*" "*" " " " " "*"
7 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*"
8 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*"Polynomial Model
# polynomial Model Summary
Row
Call:
lm(formula = Y ~ polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3,
raw = F), data = df_new)
Residuals:
Min 1Q Median 3Q Max
-1.17395 -0.17114 -0.00948 0.16854 0.91701
Coefficients:
Estimate
(Intercept) -2.343e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.0 -1.583e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.0 -2.374e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)3.0.0.0.0.0.0.0 -1.533e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.0 -1.440e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.0 -2.284e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.1.0.0.0.0.0.0 -1.425e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.0 -2.640e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.2.0.0.0.0.0.0 -9.087e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.3.0.0.0.0.0.0 -4.779e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.0 -2.244e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.0 -2.273e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.1.0.0.0.0.0 -2.250e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.0 -2.409e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.1.0.0.0.0.0 -1.059e+05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.1.0.0.0.0.0 -1.142e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.0 -1.937e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.2.0.0.0.0.0 -1.223e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.2.0.0.0.0.0 -1.013e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.3.0.0.0.0.0 -7.183e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.0 -7.539e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.0 -3.473e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.1.0.0.0.0 -3.360e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.0 -4.745e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.1.0.0.0.0 -1.867e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.1.0.0.0.0 -2.557e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.0 -5.959e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.1.0.0.0.0 -5.153e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.1.0.0.0.0 -3.688e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.1.0.0.0.0 -6.701e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.0 -4.441e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.2.0.0.0.0 1.509e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.2.0.0.0.0 -2.254e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.2.0.0.0.0 -3.090e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.3.0.0.0.0 2.432e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.0 5.070e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.0 4.519e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.1.0.0.0 6.661e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.0 3.324e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.1.0.0.0 2.750e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.1.0.0.0 3.955e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.0 1.758e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.1.0.0.0 1.457e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.1.0.0.0 9.122e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.1.0.0.0 -3.431e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.0 -3.559e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.1.0.0.0 3.412e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.1.0.0.0 1.947e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.1.0.0.0 2.328e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.1.0.0.0 4.429e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.0 -2.482e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.2.0.0.0 3.470e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.2.0.0.0 1.252e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.2.0.0.0 4.253e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.2.0.0.0 -2.165e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.3.0.0.0 -9.884e-01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.0 -1.053e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.0 -5.365e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.1.0.0 -9.376e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.0 -5.119e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.1.0.0 -3.530e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.1.0.0 -1.000e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.0 -7.211e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.1.0.0 -8.472e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.1.0.0 -5.244e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.1.0.0 -8.770e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.0 -2.535e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.1.0.0 -1.355e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.1.0.0 1.967e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.1.0.0 -3.377e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.1.0.0 -1.795e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.0 -5.163e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.1.0.0 2.691e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.1.0.0 1.980e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.1.0.0 6.473e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.1.0.0 1.802e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.1.0.0 1.757e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.0 1.223e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.2.0.0 -6.781e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.2.0.0 -2.684e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.2.0.0 -1.177e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.2.0.0 -4.602e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.2.0.0 3.393e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.3.0.0 -6.895e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.0 -1.763e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.0 -9.728e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.1.0 -1.482e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.0 -1.592e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.1.0 -8.176e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.1.0 -9.332e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.0 -1.189e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.1.0 -1.316e+05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.1.0 -1.145e+05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.1.0 -1.482e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.0 -4.110e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.1.0 -2.665e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.1.0 -2.433e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.1.0 -6.334e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.1.0 -1.001e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.0 -9.774e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.1.0 4.455e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.1.0 3.369e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.1.0 1.962e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.1.0 3.612e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.1.0 3.619e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.0 -1.913e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.1.0 -5.027e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.1.0 -3.213e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.1.0 -9.364e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.1.0 -1.522e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.1.0 3.636e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.1.0 -5.865e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.0 -1.868e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.2.0 -1.449e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.2.0 -1.440e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.2.0 -2.586e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.2.0 -3.290e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.2.0 1.058e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.2.0 -7.240e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.3.0 -8.308e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.1 -2.870e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.1 -5.949e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.1 -2.274e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.1 -5.471e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.1 -1.039e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.1 -2.488e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.1 -7.757e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.1 1.530e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.1 1.592e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.1 2.395e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.1 -2.803e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.1 -4.167e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.1 -1.258e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.1 5.726e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.1 1.121e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.1 -7.462e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.1 -3.058e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.1 -2.221e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.1 -1.303e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.1 -1.631e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.1 8.636e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.1 -3.481e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.1 -1.493e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.1 -3.137e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.1 1.215e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.1 8.492e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.1 -2.018e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.1 5.964e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.1 -3.676e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.1 -7.057e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.1 -1.476e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.1 6.586e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.1 -7.647e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.1 -2.056e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.1 -2.880e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.1 -3.093e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.2 -4.014e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.2 -8.277e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.2 -1.067e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.2 -2.395e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.2 2.854e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.2 -7.374e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.2 1.620e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.2 -5.069e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.3 5.066e+00
Std. Error
(Intercept) 7.748e-01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.0 6.969e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.0 8.254e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)3.0.0.0.0.0.0.0 7.767e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.0 6.614e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.0 7.722e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.1.0.0.0.0.0.0 6.383e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.0 1.330e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.2.0.0.0.0.0.0 5.084e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.3.0.0.0.0.0.0 5.339e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.0 5.573e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.0 5.145e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.1.0.0.0.0.0 5.428e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.0 6.600e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.1.0.0.0.0.0 2.867e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.1.0.0.0.0.0 4.101e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.0 7.872e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.2.0.0.0.0.0 3.315e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.2.0.0.0.0.0 3.167e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.3.0.0.0.0.0 2.548e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.0 5.001e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.0 2.799e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.1.0.0.0.0 3.866e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.0 4.006e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.1.0.0.0.0 2.061e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.1.0.0.0.0 3.082e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.0 2.560e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.1.0.0.0.0 1.418e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.1.0.0.0.0 1.400e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.1.0.0.0.0 1.654e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.0 6.154e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.2.0.0.0.0 4.338e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.2.0.0.0.0 4.509e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.2.0.0.0.0 3.377e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.3.0.0.0.0 7.646e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.0 4.532e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.0 3.268e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.1.0.0.0 3.237e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.0 3.979e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.1.0.0.0 1.753e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.1.0.0.0 2.619e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.0 2.652e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.1.0.0.0 1.651e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.1.0.0.0 1.693e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.1.0.0.0 1.814e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.0 3.206e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.1.0.0.0 1.387e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.1.0.0.0 1.426e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.1.0.0.0 1.366e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.1.0.0.0 3.565e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.0 1.234e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.2.0.0.0 2.950e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.2.0.0.0 2.840e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.2.0.0.0 2.637e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.2.0.0.0 3.470e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.3.0.0.0 3.762e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.0 5.723e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.0 2.841e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.1.0.0 5.033e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.0 3.838e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.1.0.0 2.595e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.1.0.0 3.670e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.0 2.987e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.1.0.0 2.252e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.1.0.0 2.016e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.1.0.0 2.575e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.0 2.285e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.1.0.0 1.894e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.1.0.0 1.753e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.1.0.0 1.337e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.1.0.0 4.376e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.0 2.550e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.1.0.0 1.522e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.1.0.0 1.513e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.1.0.0 1.375e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.1.0.0 1.424e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.1.0.0 2.917e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.0 4.908e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.2.0.0 4.118e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.2.0.0 3.733e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.2.0.0 3.403e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.2.0.0 3.353e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.2.0.0 2.907e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.3.0.0 3.987e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.0 7.733e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.0 2.994e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.1.0 6.353e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.0 4.063e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.1.0 3.325e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.1.0 4.644e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.0 3.342e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.1.0 2.849e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.1.0 2.648e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.1.0 3.210e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.0 2.892e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.1.0 2.325e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.1.0 2.177e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.1.0 1.620e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.1.0 5.042e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.0 2.517e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.1.0 1.774e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.1.0 1.790e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.1.0 1.640e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.1.0 1.524e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.1.0 2.909e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.0 3.539e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.1.0 2.846e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.1.0 2.600e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.1.0 2.257e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.1.0 2.189e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.1.0 1.641e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.1.0 4.503e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.0 7.388e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.2.0 8.345e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.2.0 7.655e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.2.0 6.510e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.2.0 6.140e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.2.0 4.110e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.2.0 7.184e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.3.0 1.367e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.1 2.312e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.1 2.449e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.1 2.203e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.1 2.456e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.1 1.093e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.1 1.497e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.1 2.921e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.1 1.084e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.1 9.863e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.1 1.389e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.1 1.628e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.1 5.977e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.1 5.972e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.1 7.534e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.1 1.518e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.1 2.247e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.1 9.106e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.1 8.082e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.1 7.641e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.1 6.002e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.1 1.287e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.1 1.667e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.1 7.669e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.1 6.425e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.1 9.104e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.1 5.996e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.1 7.827e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.1 1.375e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.1 2.099e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.1 1.055e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.1 9.366e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.1 1.008e+04
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.1 6.962e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.1 7.966e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.1 7.573e+03
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.1 2.217e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.2 2.671e+00
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.2 9.035e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.2 7.393e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.2 1.326e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.2 6.553e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.2 1.059e+02
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.2 3.888e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.2 7.262e+01
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.3 4.947e-01
t value
(Intercept) -3.025
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.0 -2.271
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.0 -2.876
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)3.0.0.0.0.0.0.0 -1.974
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.0 -2.177
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.0 -2.958
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.1.0.0.0.0.0.0 -2.232
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.0 -1.985
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.2.0.0.0.0.0.0 -1.787
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.3.0.0.0.0.0.0 -0.895
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.0 -4.026
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.0 -4.419
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.1.0.0.0.0.0 -4.145
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.0 -3.650
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.1.0.0.0.0.0 -3.695
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.1.0.0.0.0.0 -2.785
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.0 -2.461
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.2.0.0.0.0.0 -3.690
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.2.0.0.0.0.0 -3.199
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.3.0.0.0.0.0 -2.819
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.0 -1.508
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.0 -1.241
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.1.0.0.0.0 -0.869
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.0 -1.184
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.1.0.0.0.0 -0.906
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.1.0.0.0.0 -0.083
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.0 -2.328
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.1.0.0.0.0 -3.633
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.1.0.0.0.0 -2.634
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.1.0.0.0.0 -4.052
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.0 -0.722
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.2.0.0.0.0 0.348
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.2.0.0.0.0 -0.005
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.2.0.0.0.0 -0.915
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.3.0.0.0.0 0.318
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.0 1.119
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.0 1.383
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.1.0.0.0 2.058
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.0 0.835
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.1.0.0.0 1.569
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.1.0.0.0 1.510
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.0 0.663
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.1.0.0.0 0.883
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.1.0.0.0 0.539
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.1.0.0.0 -0.189
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.0 -1.110
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.1.0.0.0 2.460
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.1.0.0.0 1.366
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.1.0.0.0 1.703
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.1.0.0.0 1.242
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.0 -2.012
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.2.0.0.0 1.176
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.2.0.0.0 0.441
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.2.0.0.0 1.613
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.2.0.0.0 -0.624
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.3.0.0.0 -0.263
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.0 -1.840
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.0 -1.889
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.1.0.0 -1.863
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.0 -1.334
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.1.0.0 -1.360
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.1.0.0 -0.273
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.0 -2.414
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.1.0.0 -3.761
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.1.0.0 -2.601
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.1.0.0 -3.406
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.0 -1.109
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.1.0.0 -0.715
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.1.0.0 0.112
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.1.0.0 -2.527
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.1.0.0 -0.410
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.0 -0.202
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.1.0.0 1.768
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.1.0.0 1.309
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.1.0.0 0.471
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.1.0.0 1.266
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.1.0.0 0.602
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.0 0.249
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.2.0.0 -1.647
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.2.0.0 -0.072
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.2.0.0 -3.458
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.2.0.0 -1.372
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.2.0.0 1.167
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.3.0.0 -1.730
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.0 -2.280
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.0 -3.249
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.1.0 -2.333
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.0 -3.918
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.1.0 -2.459
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.1.0 -2.009
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.0 -3.558
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.1.0 -4.620
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.1.0 -4.322
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.1.0 -4.616
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.0 -1.421
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.1.0 -1.146
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.1.0 -1.118
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.1.0 -3.910
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.1.0 -0.199
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.0 -0.388
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.1.0 2.511
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.1.0 1.882
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.1.0 1.196
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.1.0 2.370
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.1.0 1.244
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.0 -0.540
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.1.0 -1.766
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.1.0 -1.236
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.1.0 -4.149
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.1.0 -0.695
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.1.0 2.216
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.1.0 -1.302
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.0 -2.528
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.2.0 -1.736
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.2.0 -1.881
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.2.0 -3.972
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.2.0 -0.536
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.2.0 2.575
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.2.0 -1.008
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.3.0 -0.608
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.1 -1.242
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.1 -2.429
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.1 -0.103
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.1 -2.228
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.1 -0.951
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.1 -1.663
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.1 -2.656
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.1 1.411
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.1 0.161
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.1 1.724
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.1 -1.722
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.1 -0.697
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.1 -2.107
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.1 0.760
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.1 0.739
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.1 -3.322
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.1 -3.359
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.1 -2.748
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.1 -1.706
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.1 -0.272
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.1 0.671
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.1 -2.089
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.1 -0.195
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.1 -0.488
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.1 1.334
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.1 0.142
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.1 -2.579
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.1 0.434
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.1 -1.751
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.1 -0.669
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.1 -1.576
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.1 0.653
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.1 -1.098
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.1 -2.581
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.1 -0.380
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.1 -1.395
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.2 -15.027
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.2 -0.916
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.2 -1.443
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.2 -1.806
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.2 0.436
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.2 -6.962
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.2 0.417
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.2 -0.698
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.3 10.242
Pr(>|t|)
(Intercept) 0.002565
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.0 0.023409
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.0 0.004126
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)3.0.0.0.0.0.0.0 0.048733
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.0 0.029738
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.0 0.003188
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.1.0.0.0.0.0.0 0.025870
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.0 0.047502
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.2.0.0.0.0.0.0 0.074227
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.3.0.0.0.0.0.0 0.371031
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.0 6.19e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.0 1.12e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.1.0.0.0.0.0 3.75e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.0 0.000278
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.1.0.0.0.0.0 0.000234
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.1.0.0.0.0.0 0.005477
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.0 0.014069
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.2.0.0.0.0.0 0.000238
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.2.0.0.0.0.0 0.001429
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.3.0.0.0.0.0 0.004933
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.0 0.132045
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.0 0.214946
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.1.0.0.0.0 0.385022
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.0 0.236614
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.1.0.0.0.0 0.365186
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.1.0.0.0.0 0.933918
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.0 0.020138
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.1.0.0.0.0 0.000298
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.1.0.0.0.0 0.008593
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.1.0.0.0.0 5.55e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.0 0.470745
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.2.0.0.0.0 0.728110
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.2.0.0.0.0 0.996013
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.2.0.0.0.0 0.360424
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.3.0.0.0.0 0.750497
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.0 0.263590
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.0 0.167172
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.1.0.0.0 0.039934
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.0 0.403701
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.1.0.0.0 0.117116
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.1.0.0.0 0.131424
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.0 0.507551
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.1.0.0.0 0.377736
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.1.0.0.0 0.590161
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.1.0.0.0 0.850008
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.0 0.267316
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.1.0.0.0 0.014077
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.1.0.0.0 0.172399
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.1.0.0.0 0.088853
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.1.0.0.0 0.214474
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.0 0.044544
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.2.0.0.0 0.239876
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.2.0.0.0 0.659494
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.2.0.0.0 0.107184
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.2.0.0.0 0.532808
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.3.0.0.0 0.792817
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.0 0.066050
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.0 0.059298
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.1.0.0 0.062804
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.0 0.182602
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.1.0.0 0.174131
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.1.0.0 0.785226
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.0 0.016009
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.1.0.0 0.000181
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.1.0.0 0.009456
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.1.0.0 0.000691
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.0 0.267589
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.1.0.0 0.474651
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.1.0.0 0.910679
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.1.0.0 0.011700
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.1.0.0 0.681687
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.0 0.839624
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.1.0.0 0.077489
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.1.0.0 0.190961
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.1.0.0 0.638011
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.1.0.0 0.206016
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.1.0.0 0.547165
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.0 0.803231
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.2.0.0 0.100017
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.2.0.0 0.942710
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.2.0.0 0.000572
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.2.0.0 0.170304
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.2.0.0 0.243487
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.3.0.0 0.084083
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.0 0.022854
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.0 0.001202
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.1.0 0.019884
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.0 9.64e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.1.0 0.014139
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.1.0 0.044809
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.0 0.000394
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.1.0 4.43e-06
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.1.0 1.73e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.1.0 4.53e-06
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.0 0.155678
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.1.0 0.252141
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.1.0 0.264000
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.1.0 9.98e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.1.0 0.842671
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.0 0.697866
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.1.0 0.012241
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.1.0 0.060202
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.1.0 0.231889
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.1.0 0.018034
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.1.0 0.213787
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.0 0.588998
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.1.0 0.077725
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.1.0 0.216875
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.1.0 3.68e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.1.0 0.487098
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.1.0 0.026976
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.1.0 0.193131
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.0 0.011664
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.2.0 0.082861
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.2.0 0.060255
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.2.0 7.73e-05
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.2.0 0.592220
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.2.0 0.010192
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.2.0 0.313847
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.3.0 0.543415
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.1 0.214721
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.1 0.015364
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.1 0.917806
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.1 0.026156
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.1 0.342023
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.1 0.096784
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.1 0.008064
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.1 0.158646
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.1 0.871852
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.1 0.085039
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.1 0.085487
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.1 0.485915
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.1 0.035424
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.1 0.447475
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.1 0.460376
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.1 0.000933
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.1 0.000819
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.1 0.006121
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.1 0.088410
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.1 0.785860
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.1 0.502265
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.1 0.037042
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.1 0.845697
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.1 0.625452
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.1 0.182530
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.1 0.887413
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.1 0.010085
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.1 0.664468
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.1 0.080299
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.1 0.503882
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.1 0.115509
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.1 0.513750
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.1 0.272338
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.1 0.010029
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.1 0.703833
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.1 0.163406
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.2 < 2e-16
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.2 0.359861
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.2 0.149385
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.2 0.071341
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.2 0.663258
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.2 6.77e-12
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.2 0.677072
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.2 0.485386
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.3 < 2e-16
(Intercept) **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)3.0.0.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.1.0.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.2.0.0.0.0.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.3.0.0.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.1.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.1.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.1.0.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.2.0.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.2.0.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.3.0.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.1.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.1.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.1.0.0.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.1.0.0.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.2.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.2.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.2.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.3.0.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.1.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.1.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.1.0.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.1.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.2.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.2.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.2.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.2.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.3.0.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.1.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.1.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.1.0.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.1.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.1.0.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.1.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.1.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.2.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.2.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.2.0.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.2.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.2.0.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.3.0.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.0 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.1.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.1.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.1.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.1.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.1.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.2.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.2.0 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.2.0 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.2.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.2.0 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.2.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.3.0
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)2.0.0.0.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.1.0.0.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.2.0.0.0.0.0.1 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.1 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.1.0.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.1.0.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.2.0.0.0.0.1 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.1 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.1.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.1.0.0.0.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.1.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.2.0.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.1 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.1.0.0.1 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.1.0.0.1 **
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.1.0.0.1 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.1.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.2.0.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.1.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.1.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.1.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.1.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.1.0.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.2.0.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.1 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.1.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.1.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.1.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.1.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.1.1 *
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.1.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.2.1
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.2 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)1.0.0.0.0.0.0.2
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.1.0.0.0.0.0.2
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.1.0.0.0.0.2 .
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.1.0.0.0.2
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.1.0.0.2 ***
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.1.0.2
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.1.2
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F)0.0.0.0.0.0.0.3 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3016 on 840 degrees of freedom
Multiple R-squared: 0.9239, Adjusted R-squared: 0.909
F-statistic: 62.17 on 164 and 840 DF, p-value: < 2.2e-16Polynomial
Adjusted R squared
This section includes the coefficient determination of Adjusted R squared of the third order of Multivariate Polynomial Regression with eight regressors. The Adjusted R Squared is about 91%. About 91% of the total variation in the Concrete compressive strength (MPa) can be explained by the third order polynomial model using the eight regressors.
[1] " [1] is the coefficient determination of 3 order of Multivariate Polynomial Regression with 8 regressors "[1] 0.9090186
F statistic
\(H_0: \beta_i=0, i=1,2,3,4,5,6,7,8\) versus \(H_1:\) at least one of \(\beta_i\neq0, i=1,2,3,4,5,6,7,8\).
Based on the output above, we can find that the F-statistic is 62.166 and the p-value is 2.2e-16 < 0.05= \(\alpha\). We reject \(H_0\) at the level of significance 0.01. We have sufficient evidence that using the polynomial model with Cement (X1, kg in a m3 mixture), Blast Furnace Slag (X2, kg in a m3 mixture), Fly Ash (X3, kg in a m3 mixture), Water (X4, kg in a m3 mixture), Superplasticizer (X5, kg in a m3 mixture), Coarse Aggregate (X6, kg in a m3 mixture), Fine Aggregate (X7, kg in a m3 mixture), Age (X8, Day (1~365)) is better than just using the mean Concrete compressive strength (Y, MPa).
Column
Analysis of Variance Table
Response: Y
Df Sum Sq
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F) 164 927.58
Residuals 840 76.42
Mean Sq F value
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F) 5.6559 62.166
Residuals 0.0910
Pr(>F)
polym(X1, X2, X3, X4, X5, X6, X7, X8, degree = 3, raw = F) < 2.2e-16 ***
Residuals
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Diagnostics
Column
Linearity
Column
Diagnostics
1. Linearity Assumption
We check the linearity assumption: After checking the residual vs fitted value plot, most blue plots locate between 0.5 and -0.5 on residual axes and -2 and 2 on Fitted Value. Thus, there is no particular pattern between the residuals and the fitted values whose shape indicates for a regression relationship.
2. Normality Assumption
Equal Variance Assumption can be checked by the Scale-Location plot in Diagnostics 2 . Based on the Scale-Location plot , the residuals are randomly spread points. There is no pattern.This is an indication that the equal variance assumption is not violated. The histogram of the residuals should be examined to make a decision of tolerating these blue points that are not behind orange line. In addition, examing the histogram of residuals is necessary to to see whether the normality assumption is reasonable or not.
3. Histogram of fitted residuals The residuals follow the normal distribution because the distribution of the residuals is unimodal and about symmetric.
4.Equality Variance Based on the Scale-Location plot, the residuals are randomly spread pints. There is no pattern.This is an indication that the equal variance assumption is not violated.
5. Residuals vs Leverage There is no leverage because all points below leverage 1.0.
Diagnostics 2
Column
2. Normality Assumption
3. Histogram of fitted residuals : the residuals follow the normal distribution because the distribution of the residuals is unimodal and about symmetric.
Column
4.Equality Variance
5. Residuals vs Leverage
R and C
Results and Conclusions — Results The answers of these questions the researcher look for :
1-what regressors that are suggested to be on the model ?
According to Stepwise Regression and Subset selection, using all regressors, use materials [Cement (X1), Blast Furnace Slag(X2),Fly Ash(X3), Water(X4), Superplasticizer(X5), Coarse Aggregate(X6), Fine Aggregate(X7)] and Concrete Age [Age(X8)], is recommended because this model has has the lowest Root Mean Square Error (RMSE = 0.6339170), the highest Coefficient of determination (R-squared = 0.5973950), and lowest Mean Absolute Error (MAE = 0.5039133).
2- What is type of the model that have a good fit the dataset?
According to diagnostics of 3 order of Multivariate Polynomial Regression with 8 regressors, There is no issue to use this model to estimate Concrete compressive strength (MPa), using Cement (kg in a m3 mixture), Blast Furnace Slag (kg in a m3 mixture), fly Ash (kg in a m3 mixture), Water (kg in a m3 mixture), superplasticizer (kg in a m3 mixture), Coarse Aggregate (kg in a m3 mixture), Fine Aggregate (kg in a m3 mixture), and Age (Day (1~365)) in the model. Thus, the type of the model that have a good fit the dataset is Multivariate Polynomial Regression with 8 Regressors.
Discussion / Conclusions Multivariate Polynomial Regression with 8 Regressors has Root Mean Square Error (RMSE = 0.6339170), Coefficient of determination (R-squared = 0.5973950), and Mean Absolute Error (MAE = 0.5039133) using all independent variables in the model.
Future study:
I will remove the problematic points and make compersing the model before and after. In addtion, I check What going to be changed. Study coefficient of liquid regressors of use materials that are in Multivariate Polynomial Regression with 8 Regressors what do they affect on Concrete Compressive Strength?
References
- Fly Ash Facts for Highway Engineers, web: https://www.fhwa.dot.gov/pavement/recycling/fach01.cfm, [Nov 25, 2019]
- IS-11, “Slag Cement and Fly Ash”, Slag cement Association, web: https://www.slagcement.org/aboutslagcement/is-11.aspx, [Nov 26, 2019]
- National Slag Association, " Blast Furnace Slag " , web : http://www.nationalslag.org/blast-furnace-slag, [Nov 27, 2019]
- Ruwan Rajapakse, " Construction Engineering Design Calculations and Rules of Thumb", ScienceDirect, web: https://www.sciencedirect.com/topics/engineering/superplasticizer, [Nov 25, 2019]
-Concrete_Data.xls, “Concrete Compressive Strength Data Set”, Machine learning Repository, the UC Irvine Machine Learning Repository!, web : https://archive.ics.uci.edu/ml/datasets/Concrete+Compressive+Strength [Nov 2, 2019]
-Concrete Compressive Strength Data Set belongs to Original Owner and Donor Prof. I-Cheng Yeh, Department of Information Management, Chung-Hua University, Hsin Chu, Taiwan 30067, R.O.C., e-mail:icyeh@chu.edu.tw, TEL:886-3-5186511, Date Donated: August 3, 2007.