library(readr)
ejemplo_regresion <- read_csv("C:/Users/Mario/Desktop/Econometria/ejemplo_regresion.csv")
head(ejemplo_regresion,n=5)## # A tibble: 5 x 3
## X1 X2 Y
## <chr> <dbl> <dbl>
## 1 3.92 7298 0.75
## 2 3.61 6855 0.71
## 3 3.32 6636 0.66
## 4 03.07 6506 0.61
## 5 03.06 6450 0.7library(readxl)
ejemplo_regresion <- read_excel("C:/Users/Mario/Desktop/Econometria/ejemplo_regresion.xlsx")
head(ejemplo_regresion)## # A tibble: 6 x 3
## X1 X2 Y
## <chr> <dbl> <chr>
## 1 3.92 7298 0.75
## 2 3.61 6855 0.71
## 3 3.32 6636 0.66
## 4 45110.0 6506 0.61
## 5 45080.0 6450 0.7
## 6 45233.0 6402 0.72library(stargazer)
Modelo_clase<-lm(formula = Y~X1+X2,data = ejemplo_regresion)
#Usando summary
summary(Modelo_clase)Call: lm(formula = Y ~ X1 + X2, data = ejemplo_regresion)
Residuals: 1 2 3 4 5 6 7 8.117e-18 6.558e-19 6.956e-20 -2.498e-17 -8.731e-18 1.804e-18 -1.163e-17 8 9 10 11 12 13 14 -1.372e-20 3.984e-02 -3.984e-02 2.952e-19 2.820e-19 2.726e-19 4.722e-17 15 16 17 18 19 20 21 -6.986e-18 -4.811e-19 -1.048e-04 -4.742e-20 7.108e-18 1.014e-17 1.048e-04 22 23 24 25 -2.643e-19 -2.643e-19 -2.643e-19 -8.071e-18
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.441e+00 4.483e-01 3.214 0.192 X13.26 -3.295e-02 7.971e-02 -0.413 0.750 X13.32 -8.176e-02 8.185e-02 -0.999 0.500 X13.42 8.816e-02 6.902e-02 1.277 0.423 X13.45 -2.074e-02 7.969e-02 -0.260 0.838 X13.58 1.053e-04 7.968e-02 0.001 0.999 X13.61 -8.692e-03 8.664e-02 -0.100 0.936 X13.66 2.875e-02 8.065e-02 0.357 0.782 X13.78 1.020e-01 8.246e-02 1.237 0.433 X13.82 7.500e-02 8.763e-02 0.856 0.549 X13.92 7.798e-02 1.028e-01 0.759 0.587 X13.97 8.700e-03 9.524e-02 0.091 0.942 X14.25 7.411e-02 1.145e-01 0.647 0.634 X14.41 -5.533e-02 1.351e-01 -0.409 0.753 X14.49 4.216e-02 1.447e-01 0.291 0.819 X14.58 -1.125e-01 1.824e-01 -0.617 0.648 X14.69 1.634e-02 1.998e-01 0.082 0.948 X14.71 -3.848e-03 2.119e-01 -0.018 0.988 X14.78 -1.392e-01 2.209e-01 -0.630 0.642 X145080.0 -6.136e-02 7.989e-02 -0.768 0.583 X145110.0 -1.455e-01 8.026e-02 -1.812 0.321 X145111.0 1.114e-02 1.272e-01 0.088 0.944 X145233.0 -4.642e-02 7.972e-02 -0.582 0.664 X2 -1.053e-04 6.984e-05 -1.509 0.373
Residual standard error: 0.05635 on 1 degrees of freedom Multiple R-squared: 0.9932, Adjusted R-squared: 0.8358 F-statistic: 6.311 on 23 and 1 DF, p-value: 0.3057
#Usando stargazer
stargazer(Modelo_clase,title ="MOdelo de Regresion",type="html",digits = 6)| Dependent variable: | |
| Y | |
| X13.26 | -0.032950 |
| (0.079708) | |
| X13.32 | -0.081765 |
| (0.081853) | |
| X13.42 | 0.088156 |
| (0.069019) | |
| X13.45 | -0.020737 |
| (0.079686) | |
| X13.58 | 0.000105 |
| (0.079684) | |
| X13.61 | -0.008692 |
| (0.086639) | |
| X13.66 | 0.028753 |
| (0.080648) | |
| X13.78 | 0.102028 |
| (0.082464) | |
| X13.82 | 0.074995 |
| (0.087627) | |
| X13.92 | 0.077980 |
| (0.102800) | |
| X13.97 | 0.008700 |
| (0.095242) | |
| X14.25 | 0.074108 |
| (0.114532) | |
| X14.41 | -0.055331 |
| (0.135146) | |
| X14.49 | 0.042158 |
| (0.144671) | |
| X14.58 | -0.112522 |
| (0.182376) | |
| X14.69 | 0.016345 |
| (0.199763) | |
| X14.71 | -0.003848 |
| (0.211867) | |
| X14.78 | -0.139204 |
| (0.220892) | |
| X145080.0 | -0.061361 |
| (0.079890) | |
| X145110.0 | -0.145461 |
| (0.080265) | |
| X145111.0 | 0.011140 |
| (0.127168) | |
| X145233.0 | -0.046418 |
| (0.079720) | |
| X2 | -0.000105 |
| (0.000070) | |
| Constant | 1.440898 |
| (0.448277) | |
| Observations | 25 |
| R2 | 0.993158 |
| Adjusted R2 | 0.835793 |
| Residual Std. Error | 0.056345 (df = 1) |
| F Statistic | 6.311156 (df = 23; 1) |
| Note: | p<0.1; p<0.05; p<0.01 |
mat_x<-model.matrix(Modelo_clase)
# MAtriz X'X
mat_xx<-t(mat_x)%*%mat_x
print(mat_xx)## (Intercept) X13.26 X13.32 X13.42 X13.45 X13.58 X13.61 X13.66 X13.78
## (Intercept) 25 1 1 2 1 1 1 1 1
## X13.26 1 1 0 0 0 0 0 0 0
## X13.32 1 0 1 0 0 0 0 0 0
## X13.42 2 0 0 2 0 0 0 0 0
## X13.45 1 0 0 0 1 0 0 0 0
## X13.58 1 0 0 0 0 1 0 0 0
## X13.61 1 0 0 0 0 0 1 0 0
## X13.66 1 0 0 0 0 0 0 1 0
## X13.78 1 0 0 0 0 0 0 0 1
## X13.82 1 0 0 0 0 0 0 0 0
## X13.92 1 0 0 0 0 0 0 0 0
## X13.97 1 0 0 0 0 0 0 0 0
## X14.25 1 0 0 0 0 0 0 0 0
## X14.41 1 0 0 0 0 0 0 0 0
## X14.49 1 0 0 0 0 0 0 0 0
## X14.58 1 0 0 0 0 0 0 0 0
## X14.69 1 0 0 0 0 0 0 0 0
## X14.71 1 0 0 0 0 0 0 0 0
## X14.78 1 0 0 0 0 0 0 0 0
## X145080.0 1 0 0 0 0 0 0 0 0
## X145110.0 1 0 0 0 0 0 0 0 0
## X145111.0 2 0 0 0 0 0 0 0 0
## X145233.0 1 0 0 0 0 0 0 0 0
## X2 181083 6340 6636 12701 6361 6369 6855 6546 6672
## X13.82 X13.92 X13.97 X14.25 X14.41 X14.49 X14.58 X14.69 X14.71
## (Intercept) 1 1 1 1 1 1 1 1 1
## X13.26 0 0 0 0 0 0 0 0 0
## X13.32 0 0 0 0 0 0 0 0 0
## X13.42 0 0 0 0 0 0 0 0 0
## X13.45 0 0 0 0 0 0 0 0 0
## X13.58 0 0 0 0 0 0 0 0 0
## X13.61 0 0 0 0 0 0 0 0 0
## X13.66 0 0 0 0 0 0 0 0 0
## X13.78 0 0 0 0 0 0 0 0 0
## X13.82 1 0 0 0 0 0 0 0 0
## X13.92 0 1 0 0 0 0 0 0 0
## X13.97 0 0 1 0 0 0 0 0 0
## X14.25 0 0 0 1 0 0 0 0 0
## X14.41 0 0 0 0 1 0 0 0 0
## X14.49 0 0 0 0 0 1 0 0 0
## X14.58 0 0 0 0 0 0 1 0 0
## X14.69 0 0 0 0 0 0 0 1 0
## X14.71 0 0 0 0 0 0 0 0 1
## X14.78 0 0 0 0 0 0 0 0 0
## X145080.0 0 0 0 0 0 0 0 0 0
## X145110.0 0 0 0 0 0 0 0 0 0
## X145111.0 0 0 0 0 0 0 0 0 0
## X145233.0 0 0 0 0 0 0 0 0 0
## X2 6890 7298 7115 7546 7931 8097 8717 8991 9179
## X14.78 X145080.0 X145110.0 X145111.0 X145233.0 X2
## (Intercept) 1 1 1 2 1 181083
## X13.26 0 0 0 0 0 6340
## X13.32 0 0 0 0 0 6636
## X13.42 0 0 0 0 0 12701
## X13.45 0 0 0 0 0 6361
## X13.58 0 0 0 0 0 6369
## X13.61 0 0 0 0 0 6855
## X13.66 0 0 0 0 0 6546
## X13.78 0 0 0 0 0 6672
## X13.82 0 0 0 0 0 6890
## X13.92 0 0 0 0 0 7298
## X13.97 0 0 0 0 0 7115
## X14.25 0 0 0 0 0 7546
## X14.41 0 0 0 0 0 7931
## X14.49 0 0 0 0 0 8097
## X14.58 0 0 0 0 0 8717
## X14.69 0 0 0 0 0 8991
## X14.71 0 0 0 0 0 9179
## X14.78 1 0 0 0 0 9318
## X145080.0 0 1 0 0 0 6450
## X145110.0 0 0 1 0 0 6506
## X145111.0 0 0 0 2 0 15795
## X145233.0 0 0 0 0 1 6402
## X2 9318 6450 6506 15795 6402 1335796275# Matriz A
solve(mat_xx)%*%t(mat_x)-> mat_A
print(mat_A)## 1 2 3 4
## (Intercept) -1.421085e-14 -1.421085e-14 0.000000e+00 -7.105427e-15
## X13.26 1.998401e-15 8.881784e-16 1.332268e-15 1.332268e-15
## X13.32 -4.440892e-16 -1.776357e-15 1.000000e+00 -8.881784e-16
## X13.42 2.026157e-15 9.159340e-16 1.221245e-15 1.221245e-15
## X13.45 7.771561e-16 -4.857226e-16 -1.110223e-16 1.387779e-17
## X13.58 2.602085e-17 -1.177877e-15 -9.159340e-16 -9.332812e-16
## X13.61 8.881784e-16 1.000000e+00 0.000000e+00 0.000000e+00
## X13.66 2.886580e-15 1.554312e-15 1.998401e-15 1.776357e-15
## X13.78 -2.664535e-15 -3.996803e-15 -3.552714e-15 -3.108624e-15
## X13.82 0.000000e+00 -8.881784e-16 0.000000e+00 0.000000e+00
## X13.92 1.000000e+00 -1.776357e-15 -1.776357e-15 0.000000e+00
## X13.97 0.000000e+00 -8.881784e-16 8.881784e-16 0.000000e+00
## X14.25 -1.776357e-15 -3.552714e-15 -3.552714e-15 -1.776357e-15
## X14.41 -3.552714e-15 -3.552714e-15 -3.552714e-15 -3.552714e-15
## X14.49 -3.552714e-15 -7.105427e-15 -3.552714e-15 -7.105427e-15
## X14.58 -3.552714e-15 -7.105427e-15 0.000000e+00 -3.552714e-15
## X14.69 -3.552714e-15 -7.105427e-15 -3.552714e-15 -3.552714e-15
## X14.71 3.552714e-15 0.000000e+00 3.552714e-15 0.000000e+00
## X14.78 0.000000e+00 -3.552714e-15 -3.552714e-15 0.000000e+00
## X145080.0 3.330669e-16 -5.551115e-16 -5.551115e-16 -2.220446e-16
## X145110.0 4.440892e-16 -8.881784e-16 -2.220446e-16 1.000000e+00
## X145111.0 0.000000e+00 -7.105427e-15 -1.776357e-15 -1.776357e-15
## X145233.0 4.996004e-16 -6.106227e-16 -4.440892e-16 -1.665335e-16
## X2 1.734723e-18 1.734723e-18 0.000000e+00 1.734723e-18
## 5 6 7 8
## (Intercept) 0.000000e+00 -1.421085e-14 1.000000e+00 -7.105427e-15
## X13.26 1.498801e-15 1.554312e-15 -1.000000e+00 1.000000e+00
## X13.32 -1.332268e-15 -1.332268e-15 -1.000000e+00 -1.776357e-15
## X13.42 1.526557e-15 1.193490e-15 -1.000000e+00 1.137979e-15
## X13.45 2.359224e-16 4.163336e-17 -1.000000e+00 -9.714451e-17
## X13.58 -8.552187e-16 -9.471590e-16 -1.000000e+00 -1.073794e-15
## X13.61 0.000000e+00 -8.881784e-16 -1.000000e+00 -8.881784e-16
## X13.66 1.998401e-15 1.554312e-15 -1.000000e+00 1.332268e-15
## X13.78 -3.108624e-15 -3.552714e-15 -1.000000e+00 -3.552714e-15
## X13.82 0.000000e+00 0.000000e+00 -1.000000e+00 -8.881784e-16
## X13.92 0.000000e+00 -1.776357e-15 -1.000000e+00 -1.776357e-15
## X13.97 0.000000e+00 -8.881784e-16 -1.000000e+00 -8.881784e-16
## X14.25 -1.776357e-15 -3.552714e-15 -1.000000e+00 -3.552714e-15
## X14.41 -3.552714e-15 -5.329071e-15 -1.000000e+00 -5.329071e-15
## X14.49 -3.552714e-15 -7.105427e-15 -1.000000e+00 -7.105427e-15
## X14.58 -3.552714e-15 -3.552714e-15 -1.000000e+00 -7.105427e-15
## X14.69 -3.552714e-15 -7.105427e-15 -1.000000e+00 -3.552714e-15
## X14.71 3.552714e-15 0.000000e+00 -1.000000e+00 0.000000e+00
## X14.78 0.000000e+00 -3.552714e-15 -1.000000e+00 -3.552714e-15
## X145080.0 1.000000e+00 -2.220446e-16 -1.000000e+00 -4.440892e-16
## X145110.0 0.000000e+00 -2.220446e-16 -1.000000e+00 -6.661338e-16
## X145111.0 -3.552714e-15 -5.329071e-15 -1.000000e+00 -3.552714e-15
## X145233.0 5.551115e-17 1.000000e+00 -1.000000e+00 -4.440892e-16
## X2 1.734723e-18 3.469447e-18 -3.469447e-18 1.734723e-18
## 9 10 11 12
## (Intercept) 1.467405e-02 -1.467405e-02 -7.105427e-15 -7.105427e-15
## X13.26 -6.452158e-05 6.452158e-05 8.881784e-16 1.332268e-15
## X13.32 6.175637e-04 -6.175637e-04 -1.332268e-15 -1.776357e-15
## X13.42 4.999597e-01 5.000403e-01 7.494005e-16 1.082467e-15
## X13.45 -1.613040e-05 1.613040e-05 1.000000e+00 -5.551115e-17
## X13.58 2.304342e-06 -2.304342e-06 -1.464107e-15 1.000000e+00
## X13.61 1.122215e-03 -1.122215e-03 -8.881784e-16 0.000000e+00
## X13.66 4.101729e-04 -4.101729e-04 1.332268e-15 1.554312e-15
## X13.78 7.005200e-04 -7.005200e-04 -3.552714e-15 -3.996803e-15
## X13.82 1.202867e-03 -1.202867e-03 -8.881784e-16 -8.881784e-16
## X13.92 2.143038e-03 -2.143038e-03 -1.776357e-15 -1.776357e-15
## X13.97 1.721344e-03 -1.721344e-03 0.000000e+00 0.000000e+00
## X14.25 2.714515e-03 -2.714515e-03 -1.776357e-15 -3.552714e-15
## X14.41 3.601687e-03 -3.601687e-03 -5.329071e-15 -5.329071e-15
## X14.49 3.984208e-03 -3.984208e-03 -7.105427e-15 -7.105427e-15
## X14.58 5.412900e-03 -5.412900e-03 -3.552714e-15 -7.105427e-15
## X14.69 6.044289e-03 -6.044289e-03 -3.552714e-15 -3.552714e-15
## X14.71 6.477506e-03 -6.477506e-03 3.552714e-15 -3.552714e-15
## X14.78 6.797809e-03 -6.797809e-03 0.000000e+00 -3.552714e-15
## X145080.0 1.889561e-04 -1.889561e-04 -6.661338e-16 -2.220446e-16
## X145110.0 3.179992e-04 -3.179992e-04 -8.881784e-16 -4.440892e-16
## X145111.0 3.524491e-03 -3.524491e-03 -3.552714e-15 -3.552714e-15
## X145233.0 7.834763e-05 -7.834763e-05 -6.106227e-16 -3.330669e-16
## X2 -2.304342e-06 2.304342e-06 1.734723e-18 3.469447e-18
## 13 14 15 16
## (Intercept) -1.421085e-14 0.000000e+00 0.000000e+00 0.000000e+00
## X13.26 1.332268e-15 1.221245e-15 1.776357e-15 1.110223e-15
## X13.32 -1.776357e-15 -1.332268e-15 -8.881784e-16 -1.332268e-15
## X13.42 1.137979e-15 1.193490e-15 1.443290e-15 9.436896e-16
## X13.45 -2.498002e-16 -1.110223e-16 2.636780e-16 4.163336e-17
## X13.58 -1.115427e-15 -7.910339e-16 -8.656270e-16 -1.143183e-15
## X13.61 -8.881784e-16 0.000000e+00 0.000000e+00 -8.881784e-16
## X13.66 1.000000e+00 1.776357e-15 1.998401e-15 1.998401e-15
## X13.78 -3.552714e-15 1.000000e+00 -3.108624e-15 -3.552714e-15
## X13.82 -8.881784e-16 -8.881784e-16 1.000000e+00 0.000000e+00
## X13.92 -1.776357e-15 0.000000e+00 0.000000e+00 0.000000e+00
## X13.97 -8.881784e-16 -8.881784e-16 0.000000e+00 1.000000e+00
## X14.25 -3.552714e-15 -3.552714e-15 -1.776357e-15 -1.776357e-15
## X14.41 -5.329071e-15 -7.105427e-15 -3.552714e-15 -3.552714e-15
## X14.49 -3.552714e-15 -7.105427e-15 -3.552714e-15 -7.105427e-15
## X14.58 -7.105427e-15 -3.552714e-15 0.000000e+00 -3.552714e-15
## X14.69 -3.552714e-15 -3.552714e-15 0.000000e+00 -7.105427e-15
## X14.71 -3.552714e-15 0.000000e+00 3.552714e-15 0.000000e+00
## X14.78 -3.552714e-15 0.000000e+00 0.000000e+00 0.000000e+00
## X145080.0 -4.440892e-16 -3.330669e-16 -1.110223e-16 -1.110223e-16
## X145110.0 -6.661338e-16 -2.220446e-16 -2.220446e-16 -4.440892e-16
## X145111.0 -5.329071e-15 -3.552714e-15 0.000000e+00 -3.552714e-15
## X145233.0 -1.110223e-16 -2.775558e-16 0.000000e+00 -2.775558e-16
## X2 1.734723e-18 1.734723e-18 0.000000e+00 1.734723e-18
## 17 18 19 20
## (Intercept) 5.5810306554 0.000000e+00 -1.421085e-14 -1.421085e-14
## X13.26 -0.0245397077 4.440892e-16 1.998401e-15 2.609024e-15
## X13.32 0.2348800590 -1.776357e-15 -4.440892e-16 -8.881784e-16
## X13.42 -0.0153373173 4.163336e-16 2.192690e-15 2.137179e-15
## X13.45 -0.0061349269 -9.853229e-16 1.193490e-15 3.053113e-16
## X13.58 0.0008764181 -1.460637e-15 4.163336e-16 3.365364e-16
## X13.61 0.4268156296 -1.776357e-15 0.000000e+00 1.776357e-15
## X13.66 0.1560024272 8.881784e-16 2.664535e-15 3.108624e-15
## X13.78 0.2664311117 -3.996803e-15 -2.664535e-15 -2.664535e-15
## X13.82 0.4574902642 -8.881784e-16 0.000000e+00 0.000000e+00
## X13.92 0.8150688614 0.000000e+00 0.000000e+00 -1.776357e-15
## X13.97 0.6546843435 -1.776357e-15 1.776357e-15 1.776357e-15
## X14.25 1.0324205578 1.000000e+00 -1.776357e-15 -1.776357e-15
## X14.41 1.3698415381 -7.105427e-15 1.000000e+00 -3.552714e-15
## X14.49 1.5153269477 -7.105427e-15 -7.105427e-15 1.000000e+00
## X14.58 2.0587061887 -3.552714e-15 0.000000e+00 -3.552714e-15
## X14.69 2.2988447565 -3.552714e-15 -3.552714e-15 0.000000e+00
## X14.71 2.4636113650 0.000000e+00 0.000000e+00 0.000000e+00
## X14.78 2.5854334852 0.000000e+00 -7.105427e-15 0.000000e+00
## X145080.0 0.0718662867 -8.881784e-16 3.330669e-16 4.440892e-16
## X145110.0 0.1209457020 -1.110223e-15 -4.440892e-16 2.220446e-16
## X145111.0 1.8404815307 -3.552714e-15 -3.552714e-15 -3.552714e-15
## X145233.0 0.0297982164 -5.551115e-16 1.110223e-16 5.551115e-17
## X2 -0.0008764181 1.734723e-18 1.734723e-18 1.734723e-18
## 21 22 23 24
## (Intercept) -5.5810306554 0.000000e+00 -1.421085e-14 -2.842171e-14
## X13.26 0.0245397077 1.054712e-15 1.998401e-15 1.665335e-15
## X13.32 -0.2348800590 -1.332268e-15 -1.332268e-15 -1.776357e-15
## X13.42 0.0153373173 6.106227e-16 1.998401e-15 1.332268e-15
## X13.45 0.0061349269 -6.938894e-17 5.551115e-17 1.249001e-16
## X13.58 -0.0008764181 5.898060e-17 -9.194034e-17 -9.714451e-16
## X13.61 -0.4268156296 8.881784e-16 -8.881784e-16 0.000000e+00
## X13.66 -0.1560024272 2.220446e-15 2.664535e-15 1.776357e-15
## X13.78 -0.2664311117 -1.776357e-15 -2.664535e-15 -3.552714e-15
## X13.82 -0.4574902642 0.000000e+00 0.000000e+00 -1.776357e-15
## X13.92 -0.8150688614 0.000000e+00 0.000000e+00 -1.776357e-15
## X13.97 -0.6546843435 1.776357e-15 0.000000e+00 -1.776357e-15
## X14.25 -1.0324205578 -3.552714e-15 0.000000e+00 0.000000e+00
## X14.41 -1.3698415381 -3.552714e-15 -7.105427e-15 -7.105427e-15
## X14.49 -1.5153269477 -3.552714e-15 -3.552714e-15 -1.065814e-14
## X14.58 -2.0587061887 1.000000e+00 -7.105427e-15 -7.105427e-15
## X14.69 -2.2988447565 0.000000e+00 1.000000e+00 -7.105427e-15
## X14.71 -2.4636113650 7.105427e-15 0.000000e+00 1.000000e+00
## X14.78 -2.5854334852 7.105427e-15 0.000000e+00 0.000000e+00
## X145080.0 -0.0718662867 -4.440892e-16 -4.440892e-16 0.000000e+00
## X145110.0 -0.1209457020 -4.440892e-16 -6.661338e-16 -4.440892e-16
## X145111.0 -0.8404815307 -3.552714e-15 -7.105427e-15 -3.552714e-15
## X145233.0 -0.0297982164 0.000000e+00 5.551115e-17 2.220446e-16
## X2 0.0008764181 1.734723e-18 1.734723e-18 1.734723e-18
## 25
## (Intercept) -1.421085e-14
## X13.26 1.332268e-15
## X13.32 -3.108624e-15
## X13.42 -3.330669e-16
## X13.45 -1.276756e-15
## X13.58 -8.690965e-16
## X13.61 -1.776357e-15
## X13.66 8.881784e-16
## X13.78 -4.440892e-15
## X13.82 -8.881784e-16
## X13.92 -3.552714e-15
## X13.97 -1.776357e-15
## X14.25 -7.105427e-15
## X14.41 -1.065814e-14
## X14.49 -1.065814e-14
## X14.58 -7.105427e-15
## X14.69 -7.105427e-15
## X14.71 -7.105427e-15
## X14.78 1.000000e+00
## X145080.0 -8.881784e-16
## X145110.0 -1.110223e-15
## X145111.0 -7.105427e-15
## X145233.0 -5.551115e-17
## X2 3.469447e-18#Matriz P
mat_x%*%mat_A->mat_P
print(mat_P)## 1 2 3 4 5
## 1 1.000000e+00 -3.327200e-15 -1.776357e-15 5.554585e-15 1.266001e-14
## 2 -1.431147e-15 1.000000e+00 0.000000e+00 4.786102e-15 1.189153e-14
## 3 -3.143319e-15 -4.475587e-15 1.000000e+00 3.518019e-15 1.017936e-14
## 4 -2.480655e-15 -3.812922e-15 -2.220446e-16 1.000000e+00 1.128611e-14
## 5 -2.688821e-15 -3.577000e-15 -5.551115e-16 3.861494e-15 1.000000e+00
## 6 -2.605555e-15 -3.715778e-15 -4.440892e-16 3.833739e-15 1.116121e-14
## 7 -3.164136e-15 -3.164136e-15 0.000000e+00 3.941292e-15 1.104672e-14
## 8 -1.214306e-15 -2.324529e-15 1.332268e-15 5.224987e-15 1.249695e-14
## 9 -1.170938e-15 -2.281161e-15 1.221245e-15 5.129577e-15 1.254032e-14
## 10 -1.165734e-15 -2.275957e-15 1.221245e-15 5.134781e-15 1.254552e-14
## 11 -2.399123e-15 -3.662001e-15 -1.110223e-16 3.943026e-15 1.127050e-14
## 12 -3.136380e-15 -4.340278e-15 -9.159340e-16 3.009745e-15 1.019324e-14
## 13 3.122502e-17 -1.301043e-15 1.998401e-15 6.026429e-15 1.335390e-14
## 14 -5.301315e-15 -6.633583e-15 -3.552714e-15 1.360023e-15 8.465451e-15
## 15 -2.258610e-15 -3.146788e-15 0.000000e+00 4.846817e-15 1.195224e-14
## 16 -1.868297e-15 -2.756476e-15 8.881784e-16 5.237130e-15 1.234256e-14
## 17 -1.500536e-15 -8.605963e-15 -1.776357e-15 3.828535e-15 9.157605e-15
## 18 -2.896988e-15 -4.673345e-15 -3.552714e-15 4.208439e-15 1.131387e-14
## 19 -4.005477e-15 -4.005477e-15 -3.552714e-15 3.099951e-15 1.020538e-14
## 20 -3.717512e-15 -7.270226e-15 -3.552714e-15 -1.647987e-16 1.049334e-14
## 21 4.787837e-16 -6.626644e-15 -1.776357e-15 5.807854e-15 1.113692e-14
## 22 -2.641984e-15 -6.194698e-15 0.000000e+00 4.463444e-15 1.156887e-14
## 23 -2.166670e-15 -5.719383e-15 -3.552714e-15 4.938758e-15 1.204419e-14
## 24 5.264886e-15 1.712172e-15 3.552714e-15 8.817599e-15 1.947574e-14
## 25 1.953299e-15 -1.599415e-15 -3.552714e-15 9.058726e-15 1.616415e-14
## 6 7 8 9 10
## 1 9.332812e-15 6.654399e-15 3.778228e-15 5.238865e-16 -2.300243e-15
## 2 8.684026e-15 5.970918e-15 3.897924e-15 2.275957e-15 -1.387779e-15
## 3 7.480128e-15 4.954370e-15 2.629841e-15 9.783840e-16 -2.754741e-15
## 4 8.139323e-15 5.405398e-15 3.514550e-15 1.786765e-15 -2.008810e-15
## 5 7.945034e-15 5.599687e-15 3.639450e-15 1.772887e-15 -1.883910e-15
## 6 1.000000e+00 5.322132e-15 3.556183e-15 1.634110e-15 -2.022688e-15
## 7 7.882583e-15 1.000000e+00 3.941292e-15 1.831868e-15 -1.831868e-15
## 8 9.339751e-15 7.091550e-15 1.000000e+00 2.879641e-15 -7.147061e-16
## 9 9.010154e-15 6.949302e-15 5.046311e-15 5.000035e-01 4.999965e-01
## 10 9.020562e-15 6.938894e-15 5.051515e-15 4.999965e-01 5.000035e-01
## 11 7.899931e-15 5.908468e-15 3.832004e-15 1.955033e-15 -1.691355e-15
## 12 6.938894e-15 4.548445e-15 2.869233e-15 8.847090e-16 -2.756476e-15
## 13 1.005446e-14 7.709111e-15 5.582340e-15 3.826800e-15 1.700029e-16
## 14 5.384582e-15 2.831069e-15 9.159340e-16 -1.137979e-15 -4.635181e-15
## 15 9.693635e-15 6.293577e-15 3.958639e-15 2.008810e-15 -1.120631e-15
## 16 9.586082e-15 6.401130e-15 4.348952e-15 2.435552e-15 -6.591949e-16
## 17 5.880713e-15 6.553785e-15 2.052178e-15 1.314627e-03 -1.314627e-03
## 18 8.416878e-15 5.793976e-15 2.432082e-15 6.487866e-16 -2.425143e-15
## 19 7.976259e-15 4.458239e-15 1.323594e-15 -5.342948e-16 -4.794776e-15
## 20 6.775830e-15 3.882311e-15 -1.647987e-16 -2.567391e-15 -4.538037e-15
## 21 9.839352e-15 2.595146e-15 4.031497e-15 -1.314627e-03 1.314627e-03
## 22 1.247960e-14 5.283968e-15 9.107298e-16 1.297573e-15 -1.297573e-15
## 23 9.877515e-15 7.886053e-15 4.938758e-15 -1.318390e-15 -5.787038e-15
## 24 1.763520e-14 1.078651e-14 8.817599e-15 4.850287e-15 2.255141e-15
## 25 1.456474e-14 1.030426e-14 5.506012e-15 2.515349e-15 -2.515349e-15
## 11 12 13 14 15
## 1 3.778228e-15 1.643824e-14 -3.327200e-15 1.266001e-14 0.000000e+00
## 2 3.897924e-15 1.667763e-14 -3.207504e-15 1.189153e-14 0.000000e+00
## 3 3.073930e-15 1.414147e-14 -4.475587e-15 1.017936e-14 -8.881784e-16
## 4 3.292505e-15 1.502271e-14 -3.590878e-15 1.106407e-14 -2.220446e-16
## 5 3.417405e-15 1.505046e-14 -3.465978e-15 1.085590e-14 -1.110223e-16
## 6 3.389650e-15 1.477291e-14 -3.216177e-15 1.082814e-14 0.000000e+00
## 7 3.941292e-15 1.498801e-14 -3.164136e-15 1.104672e-14 0.000000e+00
## 8 4.780898e-15 1.622313e-14 -1.880440e-15 1.221939e-14 1.776357e-15
## 9 4.657733e-15 1.600456e-14 -2.059117e-15 1.220725e-14 1.443290e-15
## 10 4.662937e-15 1.601497e-14 -2.053913e-15 1.221245e-14 1.443290e-15
## 11 1.000000e+00 1.490821e-14 -3.426079e-15 1.092355e-14 2.636780e-16
## 12 2.478920e-15 1.000000e+00 -4.277828e-15 1.025742e-14 -8.656270e-16
## 13 5.582340e-15 1.715988e-14 1.000000e+00 1.313186e-14 1.998401e-15
## 14 9.159340e-16 1.204592e-14 -6.189493e-15 1.000000e+00 -3.108624e-15
## 15 3.958639e-15 1.591088e-14 -3.146788e-15 1.106407e-14 1.000000e+00
## 16 5.237130e-15 1.757969e-14 -2.756476e-15 1.145438e-14 0.000000e+00
## 17 2.052178e-15 1.476250e-14 -6.829606e-15 9.157605e-15 0.000000e+00
## 18 4.208439e-15 1.552231e-14 -4.673345e-15 9.537510e-15 -1.776357e-15
## 19 1.323594e-15 1.508169e-14 -5.781833e-15 6.652665e-15 -3.552714e-15
## 20 -1.647987e-16 1.388126e-14 -3.717512e-15 6.940629e-15 -3.552714e-15
## 21 4.031497e-15 1.872114e-14 -4.850287e-15 1.113692e-14 0.000000e+00
## 22 4.463444e-15 1.603231e-14 -6.194698e-15 1.156887e-14 0.000000e+00
## 23 4.938758e-15 2.053566e-14 -2.166670e-15 1.204419e-14 0.000000e+00
## 24 1.237031e-14 2.118791e-14 -1.840542e-15 1.592303e-14 3.552714e-15
## 25 9.058726e-15 2.167017e-14 -1.599415e-15 1.616415e-14 0.000000e+00
## 16 17 18 19 20
## 1 1.266001e-14 7.105427e-15 1.266001e-14 -1.550843e-15 -3.327200e-15
## 2 1.100335e-14 5.329071e-15 1.011517e-14 -2.319325e-15 -5.429684e-16
## 3 1.017936e-14 3.552714e-15 9.735268e-15 -3.143319e-15 -3.587408e-15
## 4 1.084202e-14 4.440892e-15 1.017589e-14 -3.368833e-15 -2.702699e-15
## 5 1.107794e-14 4.440892e-15 1.030079e-14 -2.688821e-15 -2.577799e-15
## 6 1.082814e-14 4.440892e-15 1.055059e-14 -2.994133e-15 -3.049644e-15
## 7 1.104672e-14 8.881784e-15 1.104672e-14 -3.164136e-15 -3.164136e-15
## 8 1.210837e-14 6.217249e-15 1.144224e-14 -1.214306e-15 -6.036838e-16
## 9 1.195745e-14 1.314627e-03 1.143009e-14 -1.004405e-15 -1.059916e-15
## 10 1.196265e-14 -1.314627e-03 1.143530e-14 -9.992007e-16 -1.054712e-15
## 11 1.107621e-14 5.329071e-15 1.004925e-14 -1.982789e-15 -2.870967e-15
## 12 9.905271e-15 4.440892e-15 9.587817e-15 -2.746067e-15 -2.825865e-15
## 13 1.335390e-14 6.217249e-15 1.224368e-14 -1.908196e-16 2.532696e-16
## 14 8.021361e-15 1.776357e-15 7.577272e-15 -5.301315e-15 -5.301315e-15
## 15 1.195224e-14 5.329071e-15 1.106407e-14 -2.258610e-15 -2.258610e-15
## 16 1.000000e+00 6.217249e-15 1.056620e-14 -9.194034e-17 -9.194034e-17
## 17 9.157605e-15 9.999965e-01 9.157605e-15 -5.053249e-15 -5.053249e-15
## 18 1.131387e-14 6.217249e-15 1.000000e+00 -2.896988e-15 -2.896988e-15
## 19 1.020538e-14 1.776357e-15 6.652665e-15 1.000000e+00 -4.005477e-15
## 20 6.940629e-15 2.664535e-15 6.940629e-15 -7.270226e-15 1.000000e+00
## 21 1.113692e-14 3.456513e-06 1.113692e-14 -3.073930e-15 -3.073930e-15
## 22 1.156887e-14 7.105427e-15 1.156887e-14 9.107298e-16 -2.641984e-15
## 23 8.491471e-15 7.993606e-15 1.204419e-14 -2.166670e-15 1.386044e-15
## 24 1.592303e-14 1.598721e-14 1.592303e-14 1.712172e-15 1.712172e-15
## 25 1.616415e-14 5.329071e-15 1.616415e-14 -5.152129e-15 1.953299e-15
## 21 22 23 24 25
## 1 4.440892e-15 1.266001e-14 -1.550843e-15 -1.753805e-14 7.556455e-15
## 2 3.552714e-15 1.277971e-14 -3.207504e-15 -1.653018e-14 7.795847e-15
## 3 2.664535e-15 1.017936e-14 -4.031497e-15 -1.868644e-14 5.703771e-15
## 4 2.664535e-15 1.084202e-14 -3.590878e-15 -1.757969e-14 7.251144e-15
## 5 2.664535e-15 1.074488e-14 -3.465978e-15 -1.723274e-14 7.278900e-15
## 6 3.552714e-15 1.110570e-14 -3.049644e-15 -1.709397e-14 7.945034e-15
## 7 -8.881784e-16 1.104672e-14 -3.164136e-15 -1.737499e-14 7.882583e-15
## 8 5.329071e-15 1.205286e-14 -1.214306e-15 -1.575823e-14 9.117707e-15
## 9 -1.314627e-03 1.162438e-14 -1.198694e-15 -1.607568e-14 7.483597e-15
## 10 1.314627e-03 1.162959e-14 -1.193490e-15 -1.607048e-14 7.494005e-15
## 11 4.440892e-15 1.096519e-14 -3.120768e-15 -1.726223e-14 6.581541e-15
## 12 2.664535e-15 1.110743e-14 -3.254341e-15 -1.834470e-14 7.016956e-15
## 13 5.329071e-15 1.357595e-14 -1.908196e-16 -1.528985e-14 9.388323e-15
## 14 1.776357e-15 9.797718e-15 -5.301315e-15 -2.040035e-14 4.496403e-15
## 15 4.440892e-15 1.195224e-14 -2.258610e-15 -1.824582e-14 8.805456e-15
## 16 6.217249e-15 1.411891e-14 -1.868297e-15 -1.785551e-14 8.697904e-15
## 17 3.456513e-06 9.157605e-15 -8.605963e-15 -1.926410e-14 4.104356e-15
## 18 4.440892e-15 9.537510e-15 -1.120631e-15 -1.533149e-14 4.864165e-15
## 19 8.881784e-16 1.020538e-14 -7.558190e-15 -2.176904e-14 2.647188e-15
## 20 8.881784e-16 1.049334e-14 -3.717512e-15 -2.503379e-14 3.223116e-15
## 21 9.999965e-01 1.113692e-14 -6.626644e-15 -1.728478e-14 8.062995e-15
## 22 5.329071e-15 1.000000e+00 -6.194698e-15 -2.040555e-14 8.926887e-15
## 23 8.881784e-15 1.559690e-14 1.000000e+00 -1.993024e-14 9.877515e-15
## 24 1.243450e-14 2.302845e-14 1.712172e-15 1.000000e+00 1.052977e-14
## 25 5.329071e-15 2.326958e-14 1.953299e-15 -1.225756e-14 1.000000e+00#Matriz M
diag(25)-mat_P->mat_M
print(mat_M)## 1 2 3 4 5
## 1 1.554312e-15 3.327200e-15 1.776357e-15 -5.554585e-15 -1.266001e-14
## 2 1.431147e-15 2.331468e-15 0.000000e+00 -4.786102e-15 -1.189153e-14
## 3 3.143319e-15 4.475587e-15 8.881784e-16 -3.518019e-15 -1.017936e-14
## 4 2.480655e-15 3.812922e-15 2.220446e-16 -3.996803e-15 -1.128611e-14
## 5 2.688821e-15 3.577000e-15 5.551115e-16 -3.861494e-15 -1.110223e-14
## 6 2.605555e-15 3.715778e-15 4.440892e-16 -3.833739e-15 -1.116121e-14
## 7 3.164136e-15 3.164136e-15 0.000000e+00 -3.941292e-15 -1.104672e-14
## 8 1.214306e-15 2.324529e-15 -1.332268e-15 -5.224987e-15 -1.249695e-14
## 9 1.170938e-15 2.281161e-15 -1.221245e-15 -5.129577e-15 -1.254032e-14
## 10 1.165734e-15 2.275957e-15 -1.221245e-15 -5.134781e-15 -1.254552e-14
## 11 2.399123e-15 3.662001e-15 1.110223e-16 -3.943026e-15 -1.127050e-14
## 12 3.136380e-15 4.340278e-15 9.159340e-16 -3.009745e-15 -1.019324e-14
## 13 -3.122502e-17 1.301043e-15 -1.998401e-15 -6.026429e-15 -1.335390e-14
## 14 5.301315e-15 6.633583e-15 3.552714e-15 -1.360023e-15 -8.465451e-15
## 15 2.258610e-15 3.146788e-15 0.000000e+00 -4.846817e-15 -1.195224e-14
## 16 1.868297e-15 2.756476e-15 -8.881784e-16 -5.237130e-15 -1.234256e-14
## 17 1.500536e-15 8.605963e-15 1.776357e-15 -3.828535e-15 -9.157605e-15
## 18 2.896988e-15 4.673345e-15 3.552714e-15 -4.208439e-15 -1.131387e-14
## 19 4.005477e-15 4.005477e-15 3.552714e-15 -3.099951e-15 -1.020538e-14
## 20 3.717512e-15 7.270226e-15 3.552714e-15 1.647987e-16 -1.049334e-14
## 21 -4.787837e-16 6.626644e-15 1.776357e-15 -5.807854e-15 -1.113692e-14
## 22 2.641984e-15 6.194698e-15 0.000000e+00 -4.463444e-15 -1.156887e-14
## 23 2.166670e-15 5.719383e-15 3.552714e-15 -4.938758e-15 -1.204419e-14
## 24 -5.264886e-15 -1.712172e-15 -3.552714e-15 -8.817599e-15 -1.947574e-14
## 25 -1.953299e-15 1.599415e-15 3.552714e-15 -9.058726e-15 -1.616415e-14
## 6 7 8 9 10
## 1 -9.332812e-15 -6.654399e-15 -3.778228e-15 -5.238865e-16 2.300243e-15
## 2 -8.684026e-15 -5.970918e-15 -3.897924e-15 -2.275957e-15 1.387779e-15
## 3 -7.480128e-15 -4.954370e-15 -2.629841e-15 -9.783840e-16 2.754741e-15
## 4 -8.139323e-15 -5.405398e-15 -3.514550e-15 -1.786765e-15 2.008810e-15
## 5 -7.945034e-15 -5.599687e-15 -3.639450e-15 -1.772887e-15 1.883910e-15
## 6 -7.993606e-15 -5.322132e-15 -3.556183e-15 -1.634110e-15 2.022688e-15
## 7 -7.882583e-15 -6.217249e-15 -3.941292e-15 -1.831868e-15 1.831868e-15
## 8 -9.339751e-15 -7.091550e-15 -5.329071e-15 -2.879641e-15 7.147061e-16
## 9 -9.010154e-15 -6.949302e-15 -5.046311e-15 4.999965e-01 -4.999965e-01
## 10 -9.020562e-15 -6.938894e-15 -5.051515e-15 -4.999965e-01 4.999965e-01
## 11 -7.899931e-15 -5.908468e-15 -3.832004e-15 -1.955033e-15 1.691355e-15
## 12 -6.938894e-15 -4.548445e-15 -2.869233e-15 -8.847090e-16 2.756476e-15
## 13 -1.005446e-14 -7.709111e-15 -5.582340e-15 -3.826800e-15 -1.700029e-16
## 14 -5.384582e-15 -2.831069e-15 -9.159340e-16 1.137979e-15 4.635181e-15
## 15 -9.693635e-15 -6.293577e-15 -3.958639e-15 -2.008810e-15 1.120631e-15
## 16 -9.586082e-15 -6.401130e-15 -4.348952e-15 -2.435552e-15 6.591949e-16
## 17 -5.880713e-15 -6.553785e-15 -2.052178e-15 -1.314627e-03 1.314627e-03
## 18 -8.416878e-15 -5.793976e-15 -2.432082e-15 -6.487866e-16 2.425143e-15
## 19 -7.976259e-15 -4.458239e-15 -1.323594e-15 5.342948e-16 4.794776e-15
## 20 -6.775830e-15 -3.882311e-15 1.647987e-16 2.567391e-15 4.538037e-15
## 21 -9.839352e-15 -2.595146e-15 -4.031497e-15 1.314627e-03 -1.314627e-03
## 22 -1.247960e-14 -5.283968e-15 -9.107298e-16 -1.297573e-15 1.297573e-15
## 23 -9.877515e-15 -7.886053e-15 -4.938758e-15 1.318390e-15 5.787038e-15
## 24 -1.763520e-14 -1.078651e-14 -8.817599e-15 -4.850287e-15 -2.255141e-15
## 25 -1.456474e-14 -1.030426e-14 -5.506012e-15 -2.515349e-15 2.515349e-15
## 11 12 13 14 15
## 1 -3.778228e-15 -1.643824e-14 3.327200e-15 -1.266001e-14 0.000000e+00
## 2 -3.897924e-15 -1.667763e-14 3.207504e-15 -1.189153e-14 0.000000e+00
## 3 -3.073930e-15 -1.414147e-14 4.475587e-15 -1.017936e-14 8.881784e-16
## 4 -3.292505e-15 -1.502271e-14 3.590878e-15 -1.106407e-14 2.220446e-16
## 5 -3.417405e-15 -1.505046e-14 3.465978e-15 -1.085590e-14 1.110223e-16
## 6 -3.389650e-15 -1.477291e-14 3.216177e-15 -1.082814e-14 0.000000e+00
## 7 -3.941292e-15 -1.498801e-14 3.164136e-15 -1.104672e-14 0.000000e+00
## 8 -4.780898e-15 -1.622313e-14 1.880440e-15 -1.221939e-14 -1.776357e-15
## 9 -4.657733e-15 -1.600456e-14 2.059117e-15 -1.220725e-14 -1.443290e-15
## 10 -4.662937e-15 -1.601497e-14 2.053913e-15 -1.221245e-14 -1.443290e-15
## 11 -3.108624e-15 -1.490821e-14 3.426079e-15 -1.092355e-14 -2.636780e-16
## 12 -2.478920e-15 -1.398881e-14 4.277828e-15 -1.025742e-14 8.656270e-16
## 13 -5.582340e-15 -1.715988e-14 1.332268e-15 -1.313186e-14 -1.998401e-15
## 14 -9.159340e-16 -1.204592e-14 6.189493e-15 -8.437695e-15 3.108624e-15
## 15 -3.958639e-15 -1.591088e-14 3.146788e-15 -1.106407e-14 8.881784e-16
## 16 -5.237130e-15 -1.757969e-14 2.756476e-15 -1.145438e-14 0.000000e+00
## 17 -2.052178e-15 -1.476250e-14 6.829606e-15 -9.157605e-15 0.000000e+00
## 18 -4.208439e-15 -1.552231e-14 4.673345e-15 -9.537510e-15 1.776357e-15
## 19 -1.323594e-15 -1.508169e-14 5.781833e-15 -6.652665e-15 3.552714e-15
## 20 1.647987e-16 -1.388126e-14 3.717512e-15 -6.940629e-15 3.552714e-15
## 21 -4.031497e-15 -1.872114e-14 4.850287e-15 -1.113692e-14 0.000000e+00
## 22 -4.463444e-15 -1.603231e-14 6.194698e-15 -1.156887e-14 0.000000e+00
## 23 -4.938758e-15 -2.053566e-14 2.166670e-15 -1.204419e-14 0.000000e+00
## 24 -1.237031e-14 -2.118791e-14 1.840542e-15 -1.592303e-14 -3.552714e-15
## 25 -9.058726e-15 -2.167017e-14 1.599415e-15 -1.616415e-14 0.000000e+00
## 16 17 18 19 20
## 1 -1.266001e-14 -7.105427e-15 -1.266001e-14 1.550843e-15 3.327200e-15
## 2 -1.100335e-14 -5.329071e-15 -1.011517e-14 2.319325e-15 5.429684e-16
## 3 -1.017936e-14 -3.552714e-15 -9.735268e-15 3.143319e-15 3.587408e-15
## 4 -1.084202e-14 -4.440892e-15 -1.017589e-14 3.368833e-15 2.702699e-15
## 5 -1.107794e-14 -4.440892e-15 -1.030079e-14 2.688821e-15 2.577799e-15
## 6 -1.082814e-14 -4.440892e-15 -1.055059e-14 2.994133e-15 3.049644e-15
## 7 -1.104672e-14 -8.881784e-15 -1.104672e-14 3.164136e-15 3.164136e-15
## 8 -1.210837e-14 -6.217249e-15 -1.144224e-14 1.214306e-15 6.036838e-16
## 9 -1.195745e-14 -1.314627e-03 -1.143009e-14 1.004405e-15 1.059916e-15
## 10 -1.196265e-14 1.314627e-03 -1.143530e-14 9.992007e-16 1.054712e-15
## 11 -1.107621e-14 -5.329071e-15 -1.004925e-14 1.982789e-15 2.870967e-15
## 12 -9.905271e-15 -4.440892e-15 -9.587817e-15 2.746067e-15 2.825865e-15
## 13 -1.335390e-14 -6.217249e-15 -1.224368e-14 1.908196e-16 -2.532696e-16
## 14 -8.021361e-15 -1.776357e-15 -7.577272e-15 5.301315e-15 5.301315e-15
## 15 -1.195224e-14 -5.329071e-15 -1.106407e-14 2.258610e-15 2.258610e-15
## 16 -1.243450e-14 -6.217249e-15 -1.056620e-14 9.194034e-17 9.194034e-17
## 17 -9.157605e-15 3.456513e-06 -9.157605e-15 5.053249e-15 5.053249e-15
## 18 -1.131387e-14 -6.217249e-15 -1.132427e-14 2.896988e-15 2.896988e-15
## 19 -1.020538e-14 -1.776357e-15 -6.652665e-15 3.996803e-15 4.005477e-15
## 20 -6.940629e-15 -2.664535e-15 -6.940629e-15 7.270226e-15 7.216450e-15
## 21 -1.113692e-14 -3.456513e-06 -1.113692e-14 3.073930e-15 3.073930e-15
## 22 -1.156887e-14 -7.105427e-15 -1.156887e-14 -9.107298e-16 2.641984e-15
## 23 -8.491471e-15 -7.993606e-15 -1.204419e-14 2.166670e-15 -1.386044e-15
## 24 -1.592303e-14 -1.598721e-14 -1.592303e-14 -1.712172e-15 -1.712172e-15
## 25 -1.616415e-14 -5.329071e-15 -1.616415e-14 5.152129e-15 -1.953299e-15
## 21 22 23 24 25
## 1 -4.440892e-15 -1.266001e-14 1.550843e-15 1.753805e-14 -7.556455e-15
## 2 -3.552714e-15 -1.277971e-14 3.207504e-15 1.653018e-14 -7.795847e-15
## 3 -2.664535e-15 -1.017936e-14 4.031497e-15 1.868644e-14 -5.703771e-15
## 4 -2.664535e-15 -1.084202e-14 3.590878e-15 1.757969e-14 -7.251144e-15
## 5 -2.664535e-15 -1.074488e-14 3.465978e-15 1.723274e-14 -7.278900e-15
## 6 -3.552714e-15 -1.110570e-14 3.049644e-15 1.709397e-14 -7.945034e-15
## 7 8.881784e-16 -1.104672e-14 3.164136e-15 1.737499e-14 -7.882583e-15
## 8 -5.329071e-15 -1.205286e-14 1.214306e-15 1.575823e-14 -9.117707e-15
## 9 1.314627e-03 -1.162438e-14 1.198694e-15 1.607568e-14 -7.483597e-15
## 10 -1.314627e-03 -1.162959e-14 1.193490e-15 1.607048e-14 -7.494005e-15
## 11 -4.440892e-15 -1.096519e-14 3.120768e-15 1.726223e-14 -6.581541e-15
## 12 -2.664535e-15 -1.110743e-14 3.254341e-15 1.834470e-14 -7.016956e-15
## 13 -5.329071e-15 -1.357595e-14 1.908196e-16 1.528985e-14 -9.388323e-15
## 14 -1.776357e-15 -9.797718e-15 5.301315e-15 2.040035e-14 -4.496403e-15
## 15 -4.440892e-15 -1.195224e-14 2.258610e-15 1.824582e-14 -8.805456e-15
## 16 -6.217249e-15 -1.411891e-14 1.868297e-15 1.785551e-14 -8.697904e-15
## 17 -3.456513e-06 -9.157605e-15 8.605963e-15 1.926410e-14 -4.104356e-15
## 18 -4.440892e-15 -9.537510e-15 1.120631e-15 1.533149e-14 -4.864165e-15
## 19 -8.881784e-16 -1.020538e-14 7.558190e-15 2.176904e-14 -2.647188e-15
## 20 -8.881784e-16 -1.049334e-14 3.717512e-15 2.503379e-14 -3.223116e-15
## 21 3.456513e-06 -1.113692e-14 6.626644e-15 1.728478e-14 -8.062995e-15
## 22 -5.329071e-15 -1.509903e-14 6.194698e-15 2.040555e-14 -8.926887e-15
## 23 -8.881784e-15 -1.559690e-14 -1.332268e-15 1.993024e-14 -9.877515e-15
## 24 -1.243450e-14 -2.302845e-14 -1.712172e-15 1.254552e-14 -1.052977e-14
## 25 -5.329071e-15 -2.326958e-14 -1.953299e-15 1.225756e-14 -1.110223e-14