This is a function to illustrate the use of sparse linear algebra to solve a linear least squares problem using Cholesky decomposition. The syntax and output attempt to emulate lm() but may fail to do so fully satisfactorily. Ideally, this would eventually become a method for lm. The main obstacle to this step is that it would be necessary to have a model.matrix function that returned an object in sparse csr form. For the present, the objects represented in the formula must be in dense form. If the user wishes to specify fitting with a design matrix that is already in sparse form, then the lower level function slm.fit() should be used.

slm(formula, data, weights, na.action, method = "csr", contrasts = NULL, ...)

Arguments

formula

a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right. As in lm(), the response variable in the formula can be matrix valued.

data

a data.frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases – see below for details.

weights

vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous.

na.action

a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values.

method

there is only one method based on Cholesky factorization

contrasts

a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels.

...

additional arguments for the fitting routines

Value

A list of class slm consisting of:

coefficients

estimated coefficients

chol

cholesky object from fitting

residuals

residuals

fitted

fitted values

terms

terms

call

call

...

References

Koenker, R and Ng, P. (2002). SparseM: A Sparse Matrix Package for R,
http://www.econ.uiuc.edu/~roger/research/home.html

Author

Roger Koenker

See also

slm.methods for methods summary, print, fitted, residuals and coef associated with class slm, and slm.fit for lower level fitting functions. The latter functions are of special interest if you would like to pass a sparse form of the design matrix directly to the fitting process.

Examples

data(lsq)
X <- model.matrix(lsq) #extract the design matrix
y <- model.response(lsq) # extract the rhs
X1 <- as.matrix(X)
slm.time <- system.time(slm(y~X1-1) -> slm.o) # pretty fast
lm.time <- system.time(lm(y~X1-1) -> lm.o) # very slow
cat("slm time =",slm.time,"\n")
#> slm time = 0.137 0.006 0.143 0 0 
cat("slm Results: Reported Coefficients Truncated to 5  ","\n")
#> slm Results: Reported Coefficients Truncated to 5   
sum.slm <- summary(slm.o)
sum.slm$coef <- sum.slm$coef[1:5,]
sum.slm
#> 
#> Call:
#> slm(formula = y ~ X1 - 1)
#> 
#> Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -1.952e-01 -1.400e-02  5.329e-15  1.442e-02  1.783e-01 
#> 
#> Coefficients:
#>      Estimate Std. Error t value Pr(>|t|)    
#> [1,] 823.3613     0.1274  6460.4   <2e-16 ***
#> [2,] 340.1156     0.1711  1987.3   <2e-16 ***
#> [3,] 472.9760     0.1379  3429.6   <2e-16 ***
#> [4,] 349.3175     0.1743  2004.0   <2e-16 ***
#> [5,] 187.5595     0.2100   893.3   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.03789 on 1138 degrees of freedom
#> Multiple R-Squared:     1,	Adjusted R-squared:     1 
#> F-statistic: 4.504e+07 on 712 and 1138 DF,	p-value:     0 
#> 
cat("lm time =",lm.time,"\n")
#> lm time = 0.154 0.009 0.163 0 0 
cat("lm Results: Reported Coefficients Truncated to 5  ","\n")
#> lm Results: Reported Coefficients Truncated to 5   
sum.lm <- summary(lm.o)
sum.lm$coef <- sum.lm$coef[1:5,]
sum.lm
#> 
#> Call:
#> lm(formula = y ~ X1 - 1)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -0.19522 -0.01400  0.00000  0.01442  0.17833 
#> 
#> Coefficients:
#>         Estimate Std. Error    t value Pr(>|t|)    
#> X11    8.234e+02  1.274e-01   6460.386  < 2e-16 ***
#> X12    3.401e+02  1.711e-01   1987.263  < 2e-16 ***
#> X13    4.730e+02  1.379e-01   3429.576  < 2e-16 ***
#> X14    3.493e+02  1.743e-01   2004.020  < 2e-16 ***
#> X15    1.876e+02  2.100e-01    893.267  < 2e-16 ***
#> X16    1.591e+02  2.201e-01    722.478  < 2e-16 ***
#> X17   -5.488e+01  3.198e-01   -171.592  < 2e-16 ***
#> X18    4.977e+02  1.403e-01   3546.771  < 2e-16 ***
#> X19    5.748e+02  1.421e-01   4045.421  < 2e-16 ***
#> X110   5.844e+02  1.943e-01   3007.059  < 2e-16 ***
#> X111   4.434e+02  1.699e-01   2609.047  < 2e-16 ***
#> X112   4.598e+02  1.657e-01   2775.764  < 2e-16 ***
#> X113   4.378e+02  2.098e-01   2086.192  < 2e-16 ***
#> X114   4.719e+02  2.739e-01   1722.694  < 2e-16 ***
#> X115   2.519e+02  1.544e-01   1631.287  < 2e-16 ***
#> X116   3.870e+02  2.107e-01   1837.190  < 2e-16 ***
#> X117   3.069e+02  1.895e-01   1619.806  < 2e-16 ***
#> X118   4.240e+02  2.062e-01   2056.508  < 2e-16 ***
#> X119   2.789e+02  1.923e-01   1450.341  < 2e-16 ***
#> X120   2.793e+02  2.229e-01   1252.998  < 2e-16 ***
#> X121   1.343e+02  2.137e-01    628.730  < 2e-16 ***
#> X122   1.752e+02  1.836e-01    953.829  < 2e-16 ***
#> X123   1.964e+02  2.276e-01    863.032  < 2e-16 ***
#> X124   1.841e+02  1.929e-01    954.249  < 2e-16 ***
#> X125   1.475e+02  2.229e-01    661.807  < 2e-16 ***
#> X126   1.251e+02  1.835e-01    681.786  < 2e-16 ***
#> X127   2.065e+02  1.628e-01   1268.282  < 2e-16 ***
#> X128   2.070e+02  1.491e-01   1388.127  < 2e-16 ***
#> X129   2.293e+02  1.824e-01   1256.784  < 2e-16 ***
#> X130   1.559e+02  1.820e-01    856.952  < 2e-16 ***
#> X131   1.519e+02  1.684e-01    902.168  < 2e-16 ***
#> X132   7.015e+01  1.937e-01    362.217  < 2e-16 ***
#> X133   3.906e+01  2.060e-01    189.602  < 2e-16 ***
#> X134   8.531e+01  2.364e-01    360.904  < 2e-16 ***
#> X135   1.544e+02  2.777e-01    555.831  < 2e-16 ***
#> X136   2.057e+02  1.804e-01   1140.298  < 2e-16 ***
#> X137   2.319e+02  1.793e-01   1293.165  < 2e-16 ***
#> X138   9.777e+02  8.520e-02  11475.452  < 2e-16 ***
#> X139   7.926e+02  7.892e-02  10043.139  < 2e-16 ***
#> X140   8.881e+02  9.262e-02   9588.906  < 2e-16 ***
#> X141   2.354e+02  1.977e-01   1190.706  < 2e-16 ***
#> X142   4.793e+02  1.907e-01   2513.556  < 2e-16 ***
#> X143   3.281e+02  1.495e-01   2194.986  < 2e-16 ***
#> X144   4.430e+02  2.242e-01   1975.946  < 2e-16 ***
#> X145   2.186e+02  2.098e-01   1042.052  < 2e-16 ***
#> X146   1.564e+02  2.314e-01    675.964  < 2e-16 ***
#> X147   2.958e+02  1.734e-01   1705.497  < 2e-16 ***
#> X148   3.844e+02  1.675e-01   2295.125  < 2e-16 ***
#> X149   4.234e+02  1.678e-01   2523.020  < 2e-16 ***
#> X150   5.510e+02  1.528e-01   3606.014  < 2e-16 ***
#> X151   6.759e+02  1.417e-01   4768.629  < 2e-16 ***
#> X152   8.036e+02  1.964e-01   4091.324  < 2e-16 ***
#> X153   6.622e+02  1.545e-01   4284.931  < 2e-16 ***
#> X154   6.011e+02  2.545e-01   2362.287  < 2e-16 ***
#> X155   3.681e+02  2.146e-01   1714.845  < 2e-16 ***
#> X156   5.664e+02  2.542e-01   2227.752  < 2e-16 ***
#> X157   3.950e+02  1.507e-01   2620.673  < 2e-16 ***
#> X158   2.959e+02  2.237e-01   1323.095  < 2e-16 ***
#> X159   4.336e+02  3.498e-01   1239.563  < 2e-16 ***
#> X160   3.105e+02  2.865e-01   1083.648  < 2e-16 ***
#> X161   2.954e+02  3.152e-01    937.051  < 2e-16 ***
#> X162   4.065e+02  4.372e-01    929.880  < 2e-16 ***
#> X163   3.047e+02  4.024e-01    757.320  < 2e-16 ***
#> X164   3.896e+02  5.658e-01    688.553  < 2e-16 ***
#> X165   3.645e+02  4.785e-01    761.672  < 2e-16 ***
#> X166   4.792e+02  5.960e-01    804.073  < 2e-16 ***
#> X167   4.739e+02  6.084e-01    778.969  < 2e-16 ***
#> X168   3.893e+02  4.971e-01    783.194  < 2e-16 ***
#> X169   4.115e+02  2.522e-01   1631.809  < 2e-16 ***
#> X170   3.263e+02  1.784e-01   1828.540  < 2e-16 ***
#> X171   3.522e+02  1.278e-01   2756.070  < 2e-16 ***
#> X172   2.109e+02  2.847e-01    740.936  < 2e-16 ***
#> X173   4.868e+01  1.068e-01    455.766  < 2e-16 ***
#> X174   2.854e+02  3.118e-01    915.273  < 2e-16 ***
#> X175   1.666e+02  2.430e-01    685.463  < 2e-16 ***
#> X176   2.158e+02  1.152e-01   1873.721  < 2e-16 ***
#> X177   2.943e+02  1.981e-01   1485.412  < 2e-16 ***
#> X178   1.275e+03  6.370e-02  20019.793  < 2e-16 ***
#> X179   4.377e+02  7.123e-02   6145.514  < 2e-16 ***
#> X180   1.141e+03  7.149e-02  15967.053  < 2e-16 ***
#> X181   6.744e+02  6.639e-02  10157.186  < 2e-16 ***
#> X182   5.796e+02  9.957e-02   5821.384  < 2e-16 ***
#> X183   8.076e+02  1.078e-01   7491.859  < 2e-16 ***
#> X184   3.486e+02  1.955e-01   1783.574  < 2e-16 ***
#> X185   3.109e+02  1.538e-01   2021.958  < 2e-16 ***
#> X186   3.236e+02  1.620e-01   1997.389  < 2e-16 ***
#> X187   3.141e+02  1.395e-01   2251.087  < 2e-16 ***
#> X188   2.645e+02  2.033e-01   1301.360  < 2e-16 ***
#> X189   2.516e+02  2.290e-01   1098.599  < 2e-16 ***
#> X190   2.668e+01  3.111e-01     85.769  < 2e-16 ***
#> X191   1.040e+02  2.809e-01    370.280  < 2e-16 ***
#> X192   4.310e+02  1.585e-01   2719.302  < 2e-16 ***
#> X193   6.200e+02  1.271e-01   4878.706  < 2e-16 ***
#> X194   6.680e+02  1.432e-01   4665.654  < 2e-16 ***
#> X195   6.721e+02  1.219e-01   5511.232  < 2e-16 ***
#> X196   2.009e+02  1.099e-01   1827.308  < 2e-16 ***
#> X197   1.034e+02  1.202e-01    860.686  < 2e-16 ***
#> X198   1.984e+02  1.065e-01   1862.161  < 2e-16 ***
#> X199   1.734e+02  1.209e-01   1434.641  < 2e-16 ***
#> X1100  1.182e+02  9.987e-02   1183.055  < 2e-16 ***
#> X1101  2.293e+02  1.053e-01   2176.799  < 2e-16 ***
#> X1102  1.520e+02  7.065e-02   2151.755  < 2e-16 ***
#> X1103  1.810e+02  1.219e-01   1484.616  < 2e-16 ***
#> X1104  8.823e+01  8.825e-02    999.766  < 2e-16 ***
#> X1105  7.352e+01  9.662e-02    760.974  < 2e-16 ***
#> X1106  7.937e+02  6.290e-02  12618.209  < 2e-16 ***
#> X1107  9.773e+02  9.477e-02  10311.581  < 2e-16 ***
#> X1108  6.511e+02  8.438e-02   7716.399  < 2e-16 ***
#> X1109  5.467e+02  1.396e-01   3916.731  < 2e-16 ***
#> X1110  4.611e+02  1.346e-01   3425.340  < 2e-16 ***
#> X1111  3.752e+02  1.337e-01   2806.966  < 2e-16 ***
#> X1112  6.065e+02  1.214e-01   4993.764  < 2e-16 ***
#> X1113  1.147e+03  1.132e-01  10128.942  < 2e-16 ***
#> X1114  8.705e+02  1.400e-01   6218.146  < 2e-16 ***
#> X1115  7.477e+02  9.636e-02   7759.706  < 2e-16 ***
#> X1116  1.567e+03  1.214e-01  12906.907  < 2e-16 ***
#> X1117  1.109e+03  1.311e-01   8463.654  < 2e-16 ***
#> X1118  1.234e+03  1.281e-01   9639.834  < 2e-16 ***
#> X1119  3.679e+02  1.150e-01   3198.621  < 2e-16 ***
#> X1120  1.603e+03  2.128e-01   7530.155  < 2e-16 ***
#> X1121  6.098e+02  1.272e-01   4792.892  < 2e-16 ***
#> X1122  1.056e+03  7.865e-02  13432.586  < 2e-16 ***
#> X1123  1.026e+03  8.464e-02  12126.140  < 2e-16 ***
#> X1124  1.153e+03  1.038e-01  11111.348  < 2e-16 ***
#> X1125  9.730e+02  1.446e-01   6730.978  < 2e-16 ***
#> X1126  8.504e+02  1.063e-01   8003.102  < 2e-16 ***
#> X1127  1.178e+03  1.073e-01  10976.791  < 2e-16 ***
#> X1128  1.540e+03  1.226e-01  12558.779  < 2e-16 ***
#> X1129  4.387e+02  1.198e-01   3661.832  < 2e-16 ***
#> X1130  9.095e+02  1.757e-01   5177.348  < 2e-16 ***
#> X1131  5.232e+02  1.616e-01   3237.408  < 2e-16 ***
#> X1132  4.384e+02  1.544e-01   2840.400  < 2e-16 ***
#> X1133  5.248e+02  2.436e-01   2154.298  < 2e-16 ***
#> X1134  3.541e+02  3.496e-01   1012.775  < 2e-16 ***
#> X1135  9.983e+01  1.209e-01    825.465  < 2e-16 ***
#> X1136  1.415e+02  1.646e-01    859.264  < 2e-16 ***
#> X1137  3.041e+02  1.712e-01   1776.904  < 2e-16 ***
#> X1138  4.789e+02  2.187e-01   2189.907  < 2e-16 ***
#> X1139  7.907e+02  2.940e-01   2689.450  < 2e-16 ***
#> X1140  1.281e+03  1.889e-01   6779.784  < 2e-16 ***
#> X1141  7.797e+02  2.281e-01   3417.965  < 2e-16 ***
#> X1142  1.187e+03  2.240e-01   5297.147  < 2e-16 ***
#> X1143  9.128e+02  1.420e-01   6426.088  < 2e-16 ***
#> X1144  5.313e+02  1.603e-01   3314.124  < 2e-16 ***
#> X1145  8.118e+02  1.912e-01   4245.266  < 2e-16 ***
#> X1146  4.575e+02  1.322e-01   3461.520  < 2e-16 ***
#> X1147  5.216e+02  1.238e-01   4214.364  < 2e-16 ***
#> X1148  1.585e+03  1.365e-01  11611.155  < 2e-16 ***
#> X1149  1.317e+03  1.219e-01  10801.832  < 2e-16 ***
#> X1150  9.140e+02  2.189e-01   4174.664  < 2e-16 ***
#> X1151  1.217e+03  1.420e-01   8568.757  < 2e-16 ***
#> X1152  4.148e+02  1.809e-01   2292.191  < 2e-16 ***
#> X1153  1.186e+03  2.170e-01   5467.456  < 2e-16 ***
#> X1154  7.412e+02  1.689e-01   4388.878  < 2e-16 ***
#> X1155  1.027e+03  1.483e-01   6923.778  < 2e-16 ***
#> X1156  1.075e+03  2.188e-01   4916.076  < 2e-16 ***
#> X1157  5.818e+02  1.979e-01   2939.852  < 2e-16 ***
#> X1158  5.458e+02  5.405e-02  10097.381  < 2e-16 ***
#> X1159  1.213e+03  1.052e-01  11528.368  < 2e-16 ***
#> X1160  1.540e+03  7.850e-02  19622.334  < 2e-16 ***
#> X1161  1.236e+03  7.629e-02  16206.498  < 2e-16 ***
#> X1162  1.852e+03  8.476e-02  21845.605  < 2e-16 ***
#> X1163  9.306e+02  9.751e-02   9544.293  < 2e-16 ***
#> X1164  1.372e+03  9.910e-02  13844.984  < 2e-16 ***
#> X1165  1.363e+03  8.391e-02  16239.980  < 2e-16 ***
#> X1166  1.813e+03  1.215e-01  14922.853  < 2e-16 ***
#> X1167  1.286e+03  9.872e-02  13031.072  < 2e-16 ***
#> X1168  1.235e+03  1.674e-01   7377.502  < 2e-16 ***
#> X1169  1.149e+03  1.154e-01   9962.512  < 2e-16 ***
#> X1170  8.808e+02  1.013e-01   8693.858  < 2e-16 ***
#> X1171  5.961e+02  1.435e-01   4153.097  < 2e-16 ***
#> X1172  1.694e+03  2.470e-01   6858.168  < 2e-16 ***
#> X1173  1.596e+03  1.265e-01  12614.228  < 2e-16 ***
#> X1174  1.444e+03  1.071e-01  13489.562  < 2e-16 ***
#> X1175  2.077e+03  1.573e-01  13206.200  < 2e-16 ***
#> X1176  1.325e+03  1.049e-01  12635.881  < 2e-16 ***
#> X1177  1.261e+03  1.033e-01  12204.144  < 2e-16 ***
#> X1178  2.005e+03  1.751e-01  11449.359  < 2e-16 ***
#> X1179  9.713e+02  1.097e-01   8851.314  < 2e-16 ***
#> X1180  8.840e+02  1.405e-01   6292.842  < 2e-16 ***
#> X1181  1.402e+03  1.948e-01   7197.303  < 2e-16 ***
#> X1182  1.215e+03  1.675e-01   7255.140  < 2e-16 ***
#> X1183  1.240e+03  2.028e-01   6114.595  < 2e-16 ***
#> X1184  9.551e+02  1.034e-01   9237.498  < 2e-16 ***
#> X1185  1.063e+03  1.338e-01   7944.332  < 2e-16 ***
#> X1186  1.200e+03  1.700e-01   7058.801  < 2e-16 ***
#> X1187  1.308e+03  1.355e-01   9654.111  < 2e-16 ***
#> X1188  5.451e+02  1.251e-01   4357.843  < 2e-16 ***
#> X1189  1.182e+03  2.327e-01   5078.543  < 2e-16 ***
#> X1190  6.112e+02  1.301e-01   4699.360  < 2e-16 ***
#> X1191  1.265e+03  2.500e-01   5058.889  < 2e-16 ***
#> X1192  1.604e+03  1.382e-01  11604.956  < 2e-16 ***
#> X1193  5.883e+02  1.179e-01   4988.456  < 2e-16 ***
#> X1194  1.501e+03  1.251e-01  11996.706  < 2e-16 ***
#> X1195  1.119e+03  1.994e-01   5614.454  < 2e-16 ***
#> X1196  4.965e+02  9.883e-02   5023.705  < 2e-16 ***
#> X1197  1.198e+03  1.121e-01  10681.700  < 2e-16 ***
#> X1198  1.606e+03  1.277e-01  12580.585  < 2e-16 ***
#> X1199  1.549e+03  1.093e-01  14172.536  < 2e-16 ***
#> X1200  1.698e+03  1.370e-01  12391.530  < 2e-16 ***
#> X1201  1.883e+03  3.267e-01   5762.772  < 2e-16 ***
#> X1202  1.071e+03  1.439e-01   7440.859  < 2e-16 ***
#> X1203  8.124e+02  1.421e-01   5718.640  < 2e-16 ***
#> X1204  1.149e+03  2.005e-01   5730.789  < 2e-16 ***
#> X1205  9.166e+02  1.693e-01   5413.110  < 2e-16 ***
#> X1206  1.337e+03  2.484e-01   5382.088  < 2e-16 ***
#> X1207  1.206e+03  2.084e-01   5787.657  < 2e-16 ***
#> X1208  1.723e+03  2.229e-01   7730.322  < 2e-16 ***
#> X1209  1.364e+03  1.406e-01   9697.856  < 2e-16 ***
#> X1210  1.329e+03  1.295e-01  10256.725  < 2e-16 ***
#> X1211  1.010e+03  1.537e-01   6572.760  < 2e-16 ***
#> X1212  3.485e+02  1.182e-01   2948.867  < 2e-16 ***
#> X1213  9.050e+02  4.674e-02  19363.770  < 2e-16 ***
#> X1214  9.050e+02  4.674e-02  19361.825  < 2e-16 ***
#> X1215  4.532e+02  1.109e-01   4087.539  < 2e-16 ***
#> X1216  1.222e+02  1.140e-01   1071.709  < 2e-16 ***
#> X1217  1.274e+03  1.230e-01  10354.733  < 2e-16 ***
#> X1218  5.744e+02  7.419e-02   7743.055  < 2e-16 ***
#> X1219  6.686e+01  1.015e-01    658.750  < 2e-16 ***
#> X1220  1.650e+02  1.258e-01   1311.849  < 2e-16 ***
#> X1221  2.400e+02  9.453e-02   2538.480  < 2e-16 ***
#> X1222  7.774e+01  7.347e-02   1058.189  < 2e-16 ***
#> X1223  7.419e+02  4.787e-02  15496.456  < 2e-16 ***
#> X1224  6.932e+02  4.876e-02  14215.033  < 2e-16 ***
#> X1225  6.202e+02  4.474e-02  13863.481  < 2e-16 ***
#> X1226  4.110e+02  4.758e-02   8639.744  < 2e-16 ***
#> X1227  4.989e+02  4.605e-02  10834.409  < 2e-16 ***
#> X1228  6.085e+02  4.813e-02  12642.358  < 2e-16 ***
#> X1229  5.217e+02  4.573e-02  11406.058  < 2e-16 ***
#> X1230  7.559e+02  4.832e-02  15642.958  < 2e-16 ***
#> X1231  6.975e+02  4.853e-02  14372.650  < 2e-16 ***
#> X1232  9.131e+02  4.714e-02  19367.700  < 2e-16 ***
#> X1233  8.533e+02  4.716e-02  18093.190  < 2e-16 ***
#> X1234  9.547e+02  4.730e-02  20184.688  < 2e-16 ***
#> X1235  1.004e+03  4.705e-02  21330.548  < 2e-16 ***
#> X1236  3.718e+02  4.858e-02   7653.333  < 2e-16 ***
#> X1237  5.195e+02  4.580e-02  11342.799  < 2e-16 ***
#> X1238  6.616e+02  4.756e-02  13910.194  < 2e-16 ***
#> X1239  5.449e+02  4.553e-02  11968.303  < 2e-16 ***
#> X1240  6.171e+02  4.466e-02  13817.739  < 2e-16 ***
#> X1241  5.679e+02  4.517e-02  12572.227  < 2e-16 ***
#> X1242  6.594e+02  4.322e-02  15256.352  < 2e-16 ***
#> X1243  5.743e+02  4.273e-02  13441.371  < 2e-16 ***
#> X1244  6.086e+02  4.286e-02  14200.494  < 2e-16 ***
#> X1245  6.415e+02  4.499e-02  14258.335  < 2e-16 ***
#> X1246  6.260e+02  5.065e-02  12359.675  < 2e-16 ***
#> X1247  4.611e+02  4.679e-02   9855.173  < 2e-16 ***
#> X1248  4.867e+02  5.006e-02   9722.877  < 2e-16 ***
#> X1249  4.907e+02  4.938e-02   9938.538  < 2e-16 ***
#> X1250  5.547e+02  5.156e-02  10759.058  < 2e-16 ***
#> X1251  4.522e+02  1.446e-01   3127.363  < 2e-16 ***
#> X1252  2.406e+02  7.456e-02   3227.480  < 2e-16 ***
#> X1253  7.264e+02  5.024e-02  14458.804  < 2e-16 ***
#> X1254  1.088e+03  5.170e-02  21036.946  < 2e-16 ***
#> X1255 -5.978e+02  5.959e-02 -10031.977  < 2e-16 ***
#> X1256  3.021e+02  5.299e-02   5701.379  < 2e-16 ***
#> X1257  1.141e+02  5.050e-02   2259.390  < 2e-16 ***
#> X1258 -3.286e+02  1.466e-01  -2241.274  < 2e-16 ***
#> X1259 -2.646e+02  2.597e-01  -1018.794  < 2e-16 ***
#> X1260 -9.350e+01  3.252e-01   -287.524  < 2e-16 ***
#> X1261  8.480e+01  3.216e-01    263.680  < 2e-16 ***
#> X1262 -4.076e+02  2.234e-01  -1824.687  < 2e-16 ***
#> X1263 -4.906e+02  2.812e-01  -1744.847  < 2e-16 ***
#> X1264 -2.346e+02  1.992e-01  -1177.763  < 2e-16 ***
#> X1265 -3.517e+02  3.062e-01  -1148.421  < 2e-16 ***
#> X1266 -2.621e+02  2.679e-01   -978.494  < 2e-16 ***
#> X1267 -2.184e+02  2.728e-01   -800.480  < 2e-16 ***
#> X1268 -2.932e+02  3.228e-01   -908.190  < 2e-16 ***
#> X1269 -1.013e+02  2.362e-01   -428.692  < 2e-16 ***
#> X1270 -1.418e+02  2.561e-01   -553.611  < 2e-16 ***
#> X1271 -6.184e+01  3.432e-01   -180.213  < 2e-16 ***
#> X1272  5.222e+01  3.863e-01    135.185  < 2e-16 ***
#> X1273 -6.412e+00  2.368e-01    -27.077  < 2e-16 ***
#> X1274 -9.959e+01  3.220e-01   -309.241  < 2e-16 ***
#> X1275 -8.468e+01  2.405e-01   -352.152  < 2e-16 ***
#> X1276 -2.986e+01  2.778e-01   -107.470  < 2e-16 ***
#> X1277  2.176e+00  3.125e-01      6.962 5.65e-12 ***
#> X1278  2.432e+00  3.685e-01      6.601 6.27e-11 ***
#> X1279  5.447e+01  2.751e-01    198.045  < 2e-16 ***
#> X1280 -6.729e+02  1.207e-01  -5576.025  < 2e-16 ***
#> X1281 -3.931e+02  1.278e-01  -3075.689  < 2e-16 ***
#> X1282 -2.133e+02  2.689e-01   -793.244  < 2e-16 ***
#> X1283 -2.612e+02  3.306e-01   -790.080  < 2e-16 ***
#> X1284 -1.294e+02  3.064e-01   -422.492  < 2e-16 ***
#> X1285 -1.452e+02  2.005e-01   -724.200  < 2e-16 ***
#> X1286 -1.729e+02  2.039e-01   -847.833  < 2e-16 ***
#> X1287 -3.642e+02  2.767e-01  -1316.159  < 2e-16 ***
#> X1288 -3.458e+02  2.009e-01  -1721.365  < 2e-16 ***
#> X1289 -3.454e+02  2.035e-01  -1697.560  < 2e-16 ***
#> X1290 -5.181e+02  3.222e-01  -1607.727  < 2e-16 ***
#> X1291 -3.862e+02  2.719e-01  -1420.575  < 2e-16 ***
#> X1292 -3.862e+02  3.193e-01  -1209.376  < 2e-16 ***
#> X1293 -4.575e+02  6.386e-01   -716.348  < 2e-16 ***
#> X1294 -5.558e+02  9.159e-01   -606.903  < 2e-16 ***
#> X1295 -4.696e+02  7.453e-01   -630.071  < 2e-16 ***
#> X1296 -5.181e+02  5.513e-01   -939.699  < 2e-16 ***
#> X1297 -4.881e+02  3.504e-01  -1393.079  < 2e-16 ***
#> X1298 -1.069e+02  2.385e-01   -448.064  < 2e-16 ***
#> X1299 -1.921e+01  2.404e-01    -79.941  < 2e-16 ***
#> X1300 -6.811e+01  4.759e-01   -143.114  < 2e-16 ***
#> X1301 -1.375e+02  3.201e-01   -429.403  < 2e-16 ***
#> X1302 -2.399e+02  2.810e-01   -853.860  < 2e-16 ***
#> X1303 -7.670e+02  9.237e-02  -8303.720  < 2e-16 ***
#> X1304 -7.797e+02  1.031e-01  -7558.933  < 2e-16 ***
#> X1305 -3.011e+02  1.669e-01  -1804.620  < 2e-16 ***
#> X1306 -3.115e+02  1.698e-01  -1834.420  < 2e-16 ***
#> X1307 -1.895e+02  2.721e-01   -696.415  < 2e-16 ***
#> X1308 -1.159e+02  3.140e-01   -369.194  < 2e-16 ***
#> X1309  1.282e+01  2.765e-01     46.348  < 2e-16 ***
#> X1310  1.096e+01  2.486e-01     44.115  < 2e-16 ***
#> X1311  7.316e+01  3.109e-01    235.322  < 2e-16 ***
#> X1312 -1.727e+01  2.740e-01    -63.015  < 2e-16 ***
#> X1313 -1.036e+02  2.436e-01   -425.122  < 2e-16 ***
#> X1314 -2.639e+02  2.942e-01   -896.852  < 2e-16 ***
#> X1315 -2.643e+02  2.912e-01   -907.719  < 2e-16 ***
#> X1316 -4.597e+01  2.690e-01   -170.850  < 2e-16 ***
#> X1317 -3.480e+01  1.536e-01   -226.584  < 2e-16 ***
#> X1318 -2.596e+01  1.044e-01   -248.742  < 2e-16 ***
#> X1319 -1.480e+02  1.823e-01   -811.620  < 2e-16 ***
#> X1320 -6.501e+02  8.256e-02  -7873.410  < 2e-16 ***
#> X1321 -4.910e+02  9.023e-02  -5441.986  < 2e-16 ***
#> X1322 -4.220e+02  9.804e-02  -4304.608  < 2e-16 ***
#> X1323 -4.129e+02  1.240e-01  -3330.518  < 2e-16 ***
#> X1324 -3.376e+02  1.509e-01  -2238.029  < 2e-16 ***
#> X1325 -1.413e+02  1.662e-01   -850.622  < 2e-16 ***
#> X1326 -4.620e+02  1.735e-01  -2663.615  < 2e-16 ***
#> X1327 -3.773e+02  1.486e-01  -2539.451  < 2e-16 ***
#> X1328 -5.899e+02  1.332e-01  -4428.250  < 2e-16 ***
#> X1329 -7.455e+02  1.374e-01  -5427.016  < 2e-16 ***
#> X1330 -4.561e+02  8.432e-02  -5409.146  < 2e-16 ***
#> X1331 -5.890e+02  1.245e-01  -4732.464  < 2e-16 ***
#> X1332 -5.894e+02  1.511e-01  -3901.201  < 2e-16 ***
#> X1333 -3.981e+02  1.286e-01  -3095.966  < 2e-16 ***
#> X1334 -5.142e+02  1.615e-01  -3183.897  < 2e-16 ***
#> X1335 -5.994e+02  1.394e-01  -4298.138  < 2e-16 ***
#> X1336 -1.029e+03  1.882e-01  -5467.410  < 2e-16 ***
#> X1337 -1.140e+03  2.032e-01  -5609.246  < 2e-16 ***
#> X1338 -6.884e+02  1.830e-01  -3762.894  < 2e-16 ***
#> X1339 -3.897e+02  1.613e-01  -2415.081  < 2e-16 ***
#> X1340 -5.064e+02  1.484e-01  -3411.980  < 2e-16 ***
#> X1341 -3.034e+02  2.323e-01  -1306.129  < 2e-16 ***
#> X1342 -2.818e+02  2.353e-01  -1197.584  < 2e-16 ***
#> X1343 -9.205e+01  2.533e-01   -363.379  < 2e-16 ***
#> X1344 -2.283e+02  2.053e-01  -1111.863  < 2e-16 ***
#> X1345 -8.896e+01  2.592e-01   -343.202  < 2e-16 ***
#> X1346 -1.620e+02  2.492e-01   -650.030  < 2e-16 ***
#> X1347 -2.308e+02  1.985e-01  -1162.318  < 2e-16 ***
#> X1348 -3.658e+02  1.472e-01  -2485.884  < 2e-16 ***
#> X1349 -2.333e+02  1.965e-01  -1187.355  < 2e-16 ***
#> X1350 -3.597e+02  1.802e-01  -1996.328  < 2e-16 ***
#> X1351 -2.922e+02  1.999e-01  -1461.909  < 2e-16 ***
#> X1352 -3.922e+02  1.744e-01  -2248.539  < 2e-16 ***
#> X1353 -6.113e+02  1.713e-01  -3567.951  < 2e-16 ***
#> X1354 -8.086e+02  2.450e-01  -3299.838  < 2e-16 ***
#> X1355 -5.712e+02  1.800e-01  -3173.672  < 2e-16 ***
#> X1356 -6.494e+02  1.756e-01  -3698.300  < 2e-16 ***
#> X1357 -9.424e+02  3.286e-01  -2867.400  < 2e-16 ***
#> X1358 -5.153e+02  2.203e-01  -2339.123  < 2e-16 ***
#> X1359 -8.230e+02  3.205e-01  -2568.325  < 2e-16 ***
#> X1360 -6.840e+02  2.186e-01  -3129.218  < 2e-16 ***
#> X1361 -7.122e+02  2.718e-01  -2619.770  < 2e-16 ***
#> X1362 -1.325e+03  1.234e-01 -10738.008  < 2e-16 ***
#> X1363 -7.963e+02  8.047e-02  -9896.364  < 2e-16 ***
#> X1364 -1.125e+03  1.467e-01  -7673.811  < 2e-16 ***
#> X1365 -1.101e+03  1.718e-01  -6410.384  < 2e-16 ***
#> X1366 -1.767e+03  2.066e-01  -8551.651  < 2e-16 ***
#> X1367 -8.479e+02  1.517e-01  -5589.468  < 2e-16 ***
#> X1368 -1.126e+03  2.271e-01  -4957.110  < 2e-16 ***
#> X1369 -5.946e+02  1.704e-01  -3489.348  < 2e-16 ***
#> X1370 -1.109e+03  1.638e-01  -6766.316  < 2e-16 ***
#> X1371 -1.108e+03  1.882e-01  -5887.378  < 2e-16 ***
#> X1372 -1.360e+03  2.300e-01  -5915.697  < 2e-16 ***
#> X1373 -7.511e+02  1.453e-01  -5168.079  < 2e-16 ***
#> X1374 -1.226e+03  2.326e-01  -5270.160  < 2e-16 ***
#> X1375 -7.567e+02  1.658e-01  -4562.637  < 2e-16 ***
#> X1376 -5.474e+02  1.524e-01  -3591.551  < 2e-16 ***
#> X1377 -5.654e+02  1.828e-01  -3092.401  < 2e-16 ***
#> X1378 -7.081e+02  3.125e-01  -2266.099  < 2e-16 ***
#> X1379 -5.923e+02  2.523e-01  -2347.476  < 2e-16 ***
#> X1380 -7.931e+02  1.715e-01  -4624.906  < 2e-16 ***
#> X1381 -1.012e+03  2.352e-01  -4302.116  < 2e-16 ***
#> X1382 -7.623e+02  2.036e-01  -3743.684  < 2e-16 ***
#> X1383 -9.025e+02  2.587e-01  -3488.197  < 2e-16 ***
#> X1384 -7.947e+02  1.870e-01  -4250.705  < 2e-16 ***
#> X1385 -1.210e+03  2.702e-01  -4480.245  < 2e-16 ***
#> X1386 -1.055e+03  2.268e-01  -4649.297  < 2e-16 ***
#> X1387 -1.764e+03  3.691e-01  -4778.763  < 2e-16 ***
#> X1388 -1.050e+03  2.233e-01  -4701.595  < 2e-16 ***
#> X1389 -8.759e+02  1.898e-01  -4615.746  < 2e-16 ***
#> X1390 -1.175e+03  2.358e-01  -4983.001  < 2e-16 ***
#> X1391 -9.273e+02  1.757e-01  -5278.472  < 2e-16 ***
#> X1392 -1.385e+03  2.550e-01  -5433.220  < 2e-16 ***
#> X1393 -1.093e+03  2.034e-01  -5374.731  < 2e-16 ***
#> X1394 -1.112e+03  2.265e-01  -4909.467  < 2e-16 ***
#> X1395 -1.151e+03  2.172e-01  -5296.823  < 2e-16 ***
#> X1396 -8.561e+02  1.655e-01  -5171.622  < 2e-16 ***
#> X1397 -9.969e+02  1.919e-01  -5193.965  < 2e-16 ***
#> X1398 -1.124e+03  2.328e-01  -4826.232  < 2e-16 ***
#> X1399 -1.181e+03  2.263e-01  -5218.913  < 2e-16 ***
#> X1400 -1.298e+03  2.397e-01  -5415.992  < 2e-16 ***
#> X1401 -1.742e+03  3.199e-01  -5443.806  < 2e-16 ***
#> X1402 -1.005e+03  1.784e-01  -5636.698  < 2e-16 ***
#> X1403 -1.231e+03  1.985e-01  -6198.697  < 2e-16 ***
#> X1404 -9.532e+02  1.545e-01  -6171.309  < 2e-16 ***
#> X1405 -4.946e+02  2.010e-01  -2461.020  < 2e-16 ***
#> X1406 -2.747e+02  9.066e-02  -3030.091  < 2e-16 ***
#> X1407 -6.867e+02  1.037e-01  -6623.807  < 2e-16 ***
#> X1408 -1.412e+03  2.068e-01  -6827.410  < 2e-16 ***
#> X1409 -5.811e+02  2.969e-01  -1957.492  < 2e-16 ***
#> X1410 -9.800e+02  2.004e-01  -4890.944  < 2e-16 ***
#> X1411 -4.884e+02  6.403e-02  -7627.350  < 2e-16 ***
#> X1412 -9.263e+02  1.196e-01  -7745.618  < 2e-16 ***
#> X1413 -7.240e+02  7.563e-02  -9573.390  < 2e-16 ***
#> X1414 -7.241e+02  7.603e-02  -9524.942  < 2e-16 ***
#> X1415 -8.508e+02  8.757e-02  -9715.509  < 2e-16 ***
#> X1416 -8.219e+02  8.844e-02  -9292.725  < 2e-16 ***
#> X1417 -1.447e+03  2.698e-01  -5360.865  < 2e-16 ***
#> X1418 -5.960e+02  1.624e-01  -3669.541  < 2e-16 ***
#> X1419 -1.023e+03  2.748e-01  -3724.477  < 2e-16 ***
#> X1420 -1.071e+03  1.759e-01  -6090.807  < 2e-16 ***
#> X1421 -7.290e+02  1.225e-01  -5952.801  < 2e-16 ***
#> X1422 -8.630e+02  1.394e-01  -6190.662  < 2e-16 ***
#> X1423 -1.169e+03  1.906e-01  -6135.066  < 2e-16 ***
#> X1424 -7.314e+02  1.240e-01  -5899.393  < 2e-16 ***
#> X1425 -6.988e+02  1.245e-01  -5612.268  < 2e-16 ***
#> X1426 -1.573e+03  9.793e-02 -16061.504  < 2e-16 ***
#> X1427 -1.471e+03  2.274e-01  -6469.047  < 2e-16 ***
#> X1428  4.810e-02  4.453e-02      1.080 0.280298    
#> X1429  9.282e-02  5.758e-02      1.612 0.107225    
#> X1430  2.396e-02  5.532e-02      0.433 0.664950    
#> X1431 -1.576e-01  3.789e-02     -4.159 3.44e-05 ***
#> X1432 -7.802e-02  5.813e-02     -1.342 0.179759    
#> X1433  9.321e-02  4.682e-02      1.991 0.046733 *  
#> X1434 -3.559e-02  4.324e-02     -0.823 0.410689    
#> X1435  2.103e-02  5.012e-02      0.420 0.674815    
#> X1436 -6.825e-03  1.750e-01     -0.039 0.968901    
#> X1437 -2.042e-02  5.104e-02     -0.400 0.689127    
#> X1438 -1.770e-02  4.055e-02     -0.437 0.662550    
#> X1439 -9.955e-03  3.790e-02     -0.263 0.792851    
#> X1440  5.246e-02  5.159e-02      1.017 0.309421    
#> X1441 -5.148e-02  5.038e-02     -1.022 0.307075    
#> X1442  8.216e-03  4.282e-02      0.192 0.847863    
#> X1443 -4.135e-02  7.928e-02     -0.522 0.602099    
#> X1444  3.611e-02  6.075e-02      0.594 0.552383    
#> X1445  8.504e-02  5.807e-02      1.464 0.143370    
#> X1446  2.164e-02  5.789e-02      0.374 0.708650    
#> X1447 -1.059e-01  4.614e-02     -2.295 0.021942 *  
#> X1448  4.351e-03  4.234e-02      0.103 0.918168    
#> X1449  2.226e-01  5.834e-02      3.816 0.000143 ***
#> X1450 -2.523e-03  4.252e-02     -0.059 0.952705    
#> X1451 -4.096e-02  5.801e-02     -0.706 0.480272    
#> X1452  3.475e-02  6.689e-02      0.520 0.603487    
#> X1453  1.006e-01  5.569e-02      1.805 0.071262 .  
#> X1454  3.660e-03  4.279e-02      0.086 0.931850    
#> X1455 -1.712e-02  4.177e-02     -0.410 0.681924    
#> X1456  1.766e-02  5.854e-02      0.302 0.762902    
#> X1457 -6.476e-03  4.188e-02     -0.155 0.877144    
#> X1458  1.521e-02  4.270e-02      0.356 0.721784    
#> X1459 -9.333e-02  6.657e-02     -1.402 0.161201    
#> X1460 -1.184e-02  3.789e-02     -0.312 0.754783    
#> X1461 -7.011e-02  1.039e-01     -0.675 0.500066    
#> X1462 -2.388e-01  1.648e-01     -1.449 0.147564    
#> X1463 -1.048e-01  6.521e-02     -1.607 0.108282    
#> X1464  1.657e-01  1.206e-01      1.374 0.169610    
#> X1465  2.588e-01  2.309e-01      1.121 0.262680    
#> X1466  1.542e-03  6.044e-02      0.026 0.979649    
#> X1467  2.387e-02  1.376e-01      0.173 0.862299    
#> X1468  1.587e-01  3.802e-02      4.173 3.23e-05 ***
#> X1469 -1.071e-01  1.785e-01     -0.600 0.548401    
#> X1470 -5.617e-02  5.559e-02     -1.010 0.312535    
#> X1471 -2.899e-03  5.297e-02     -0.055 0.956362    
#> X1472  1.104e-01  6.930e-02      1.592 0.111572    
#> X1473  5.841e-04  1.447e-01      0.004 0.996781    
#> X1474 -1.269e-01  9.029e-02     -1.406 0.160009    
#> X1475 -1.359e-02  6.778e-02     -0.201 0.841099    
#> X1476 -2.052e-01  1.248e-01     -1.644 0.100441    
#> X1477 -4.728e-02  5.797e-02     -0.816 0.414939    
#> X1478 -1.940e-02  6.772e-02     -0.287 0.774525    
#> X1479  1.071e-01  9.281e-02      1.154 0.248785    
#> X1480  9.360e-02  5.993e-02      1.562 0.118610    
#> X1481  2.722e-01  6.402e-02      4.251 2.30e-05 ***
#> X1482  2.080e-01  8.557e-02      2.430 0.015237 *  
#> X1483  1.261e-01  4.148e-02      3.040 0.002423 ** 
#> X1484  1.264e-01  6.154e-02      2.054 0.040248 *  
#> X1485  3.788e-02  4.976e-02      0.761 0.446674    
#> X1486 -4.923e-02  8.437e-02     -0.584 0.559644    
#> X1487 -2.419e-03  5.226e-02     -0.046 0.963098    
#> X1488  2.467e-01  3.885e-02      6.349 3.12e-10 ***
#> X1489 -8.668e-02  5.029e-02     -1.723 0.085088 .  
#> X1490 -1.350e-01  6.722e-02     -2.008 0.044920 *  
#> X1491  3.507e-02  7.514e-02      0.467 0.640773    
#> X1492  1.838e-01  7.238e-02      2.540 0.011230 *  
#> X1493  2.741e-02  6.640e-02      0.413 0.679825    
#> X1494  7.079e-01  1.249e-01      5.668 1.83e-08 ***
#> X1495  1.174e-01  1.003e-01      1.170 0.242100    
#> X1496 -1.111e-01  1.372e-01     -0.810 0.418149    
#> X1497  8.523e-04  9.759e-02      0.009 0.993033    
#> X1498 -4.450e-02  3.791e-02     -1.174 0.240737    
#> X1499 -1.845e-02  3.874e-02     -0.476 0.634080    
#> X1500  5.875e-02  4.716e-02      1.246 0.213153    
#> X1501  4.520e-01  8.510e-02      5.311 1.31e-07 ***
#> X1502 -2.231e-02  8.552e-02     -0.261 0.794224    
#> X1503  5.158e-01  7.971e-02      6.471 1.44e-10 ***
#> X1504  2.731e-01  1.210e-01      2.257 0.024211 *  
#> X1505  2.584e-03  4.492e-02      0.058 0.954139    
#> X1506  2.545e-01  8.214e-02      3.098 0.001996 ** 
#> X1507  8.097e-02  4.709e-02      1.720 0.085782 .  
#> X1508  1.655e-02  4.056e-02      0.408 0.683213    
#> X1509  1.074e-02  8.397e-02      0.128 0.898217    
#> X1510 -1.200e-01  8.028e-02     -1.495 0.135211    
#> X1511  6.675e-02  3.877e-02      1.722 0.085375 .  
#> X1512  6.689e-02  4.355e-02      1.536 0.124815    
#> X1513  2.933e-01  9.908e-02      2.960 0.003139 ** 
#> X1514  3.664e-02  8.409e-02      0.436 0.663104    
#> X1515  8.501e-02  6.205e-02      1.370 0.170959    
#> X1516  1.073e-01  5.868e-02      1.829 0.067727 .  
#> X1517 -1.067e-01  4.937e-02     -2.160 0.030956 *  
#> X1518  1.241e-02  4.262e-02      0.291 0.770973    
#> X1519  4.323e-01  8.391e-02      5.152 3.03e-07 ***
#> X1520  4.055e-02  3.790e-02      1.070 0.284865    
#> X1521 -5.427e-02  4.584e-02     -1.184 0.236779    
#> X1522 -2.938e-01  4.318e-02     -6.803 1.65e-11 ***
#> X1523  1.220e-02  5.602e-02      0.218 0.827635    
#> X1524  8.334e-02  5.713e-02      1.459 0.144929    
#> X1525 -5.151e-02  1.186e-01     -0.434 0.664100    
#> X1526  6.183e-02  5.217e-02      1.185 0.236217    
#> X1527  1.178e-01  7.603e-02      1.550 0.121518    
#> X1528 -1.604e-03  4.135e-02     -0.039 0.969066    
#> X1529 -1.665e-01  1.472e-01     -1.131 0.258428    
#> X1530 -3.113e-01  3.807e-02     -8.178 7.64e-16 ***
#> X1531  4.760e-02  4.653e-02      1.023 0.306580    
#> X1532 -3.821e-02  4.922e-02     -0.776 0.437683    
#> X1533 -3.080e-02  3.790e-02     -0.813 0.416573    
#> X1534  3.012e-03  3.815e-02      0.079 0.937088    
#> X1535  1.319e-02  3.789e-02      0.348 0.727729    
#> X1536 -6.578e-02  3.790e-02     -1.735 0.082940 .  
#> X1537  4.349e-02  8.228e-02      0.529 0.597213    
#> X1538  8.559e-02  5.251e-02      1.630 0.103422    
#> X1539 -3.577e-01  2.421e-01     -1.477 0.139860    
#> X1540  2.091e-02  4.117e-02      0.508 0.611622    
#> X1541  5.775e-02  4.056e-02      1.424 0.154722    
#> X1542 -1.219e-01  6.428e-02     -1.896 0.058161 .  
#> X1543 -8.115e-02  4.232e-02     -1.918 0.055381 .  
#> X1544 -3.532e-02  6.579e-02     -0.537 0.591405    
#> X1545 -3.110e-01  8.209e-02     -3.789 0.000159 ***
#> X1546 -2.505e-01  4.762e-02     -5.261 1.72e-07 ***
#> X1547  4.720e-01  1.512e-01      3.122 0.001844 ** 
#> X1548 -1.431e-01  6.290e-02     -2.274 0.023137 *  
#> X1549 -4.010e-01  4.637e-02     -8.648  < 2e-16 ***
#> X1550 -1.193e-01  1.248e-01     -0.956 0.339437    
#> X1551 -3.685e-01  1.312e-01     -2.809 0.005058 ** 
#> X1552 -5.531e-01  1.622e-01     -3.410 0.000673 ***
#> X1553 -3.168e+00  1.092e-01    -29.005  < 2e-16 ***
#> X1554 -6.960e-01  1.945e-01     -3.578 0.000360 ***
#> X1555 -1.106e-01  7.607e-02     -1.454 0.146206    
#> X1556 -1.580e-01  1.011e-01     -1.562 0.118545    
#> X1557 -3.145e-02  1.141e-01     -0.276 0.782825    
#> X1558 -1.123e-01  8.969e-02     -1.252 0.210811    
#> X1559 -6.677e-02  1.173e-01     -0.569 0.569210    
#> X1560  1.697e-02  9.848e-02      0.172 0.863187    
#> X1561  9.299e-03  1.337e-01      0.070 0.944581    
#> X1562 -2.776e-01  1.335e-01     -2.080 0.037762 *  
#> X1563 -5.091e-03  1.310e-01     -0.039 0.969018    
#> X1564  6.528e-02  1.353e-01      0.482 0.629617    
#> X1565  1.021e-01  1.411e-01      0.724 0.469358    
#> X1566 -1.185e-02  1.500e-01     -0.079 0.937069    
#> X1567  1.041e-01  1.755e-01      0.593 0.553188    
#> X1568  7.468e-02  1.448e-01      0.516 0.606132    
#> X1569  4.092e-01  1.362e-01      3.004 0.002722 ** 
#> X1570  3.681e-02  1.143e-01      0.322 0.747497    
#> X1571  1.212e-02  1.233e-01      0.098 0.921705    
#> X1572 -3.380e-02  1.061e-01     -0.319 0.750006    
#> X1573  5.753e-02  1.187e-01      0.484 0.628129    
#> X1574 -4.950e-02  1.372e-01     -0.361 0.718259    
#> X1575 -1.077e-01  1.463e-01     -0.736 0.461886    
#> X1576 -1.812e-01  1.288e-01     -1.407 0.159666    
#> X1577 -3.296e-01  1.862e-01     -1.770 0.076960 .  
#> X1578 -1.106e-01  6.371e-02     -1.735 0.082977 .  
#> X1579  1.365e-01  6.936e-02      1.968 0.049358 *  
#> X1580 -6.824e-02  1.014e-01     -0.673 0.501012    
#> X1581 -8.247e-01  1.572e-01     -5.245 1.86e-07 ***
#> X1582 -4.494e-01  1.344e-01     -3.343 0.000854 ***
#> X1583 -5.389e-01  1.895e-01     -2.845 0.004528 ** 
#> X1584 -1.704e-01  1.246e-01     -1.367 0.171748    
#> X1585 -9.067e-02  1.202e-01     -0.754 0.450796    
#> X1586  1.089e-02  1.203e-01      0.091 0.927881    
#> X1587 -3.509e-02  1.438e-01     -0.244 0.807214    
#> X1588  1.014e-01  1.616e-01      0.628 0.530413    
#> X1589  3.140e-02  2.084e-01      0.151 0.880284    
#> X1590 -6.786e-02  1.699e-01     -0.399 0.689663    
#> X1591  1.238e-01  1.491e-01      0.830 0.406659    
#> X1592  1.550e-01  1.624e-01      0.955 0.339828    
#> X1593  4.156e-02  1.483e-01      0.280 0.779331    
#> X1594 -7.720e-02  1.278e-01     -0.604 0.545937    
#> X1595  6.440e-02  1.230e-01      0.524 0.600523    
#> X1596 -1.208e-02  1.386e-01     -0.087 0.930541    
#> X1597  6.569e-02  2.548e-01      0.258 0.796585    
#> X1598  1.102e-01  2.416e-01      0.456 0.648305    
#> X1599  1.190e-02  1.532e-01      0.078 0.938114    
#> X1600  7.778e-02  5.693e-02      1.366 0.172098    
#> X1601 -1.053e-01  7.138e-02     -1.475 0.140425    
#> X1602  3.548e-02  1.202e-01      0.295 0.767906    
#> X1603 -1.577e-01  1.880e-01     -0.839 0.401868    
#> X1604 -1.604e-01  1.882e-01     -0.852 0.394332    
#> X1605 -1.456e-01  1.758e-01     -0.828 0.407954    
#> X1606 -2.466e-01  2.136e-01     -1.155 0.248480    
#> X1607 -3.019e-01  3.112e-01     -0.970 0.332218    
#> X1608  2.045e-01  2.047e-01      0.999 0.317934    
#> X1609  2.629e-01  1.678e-01      1.566 0.117544    
#> X1610  2.424e-01  1.785e-01      1.358 0.174630    
#> X1611  1.856e-01  1.581e-01      1.174 0.240513    
#> X1612  2.132e-02  9.794e-02      0.218 0.827747    
#> X1613 -4.123e-02  9.346e-02     -0.441 0.659177    
#> X1614  6.041e-02  9.446e-02      0.640 0.522582    
#> X1615  8.698e-03  7.378e-02      0.118 0.906181    
#> X1616  5.625e-02  6.895e-02      0.816 0.414803    
#> X1617  1.008e-01  7.240e-02      1.392 0.164262    
#> X1618  1.335e-01  5.626e-02      2.373 0.017811 *  
#> X1619  2.460e-01  6.862e-02      3.586 0.000350 ***
#> X1620  9.080e-02  7.273e-02      1.248 0.212123    
#> X1621  1.647e-03  9.048e-02      0.018 0.985480    
#> X1622 -1.165e-02  1.086e-01     -0.107 0.914583    
#> X1623  7.394e-02  8.744e-02      0.846 0.397911    
#> X1624  5.827e-02  1.050e-01      0.555 0.578843    
#> X1625  1.516e-01  6.234e-02      2.432 0.015154 *  
#> X1626  1.023e-01  7.009e-02      1.460 0.144486    
#> X1627  3.551e-01  9.688e-02      3.665 0.000259 ***
#> X1628  8.369e-02  8.812e-02      0.950 0.342440    
#> X1629  5.245e-02  9.519e-02      0.551 0.581759    
#> X1630  7.180e-02  1.319e-01      0.544 0.586267    
#> X1631  1.122e-01  8.811e-02      1.274 0.203018    
#> X1632  2.622e-01  8.927e-02      2.937 0.003382 ** 
#> X1633  5.722e-02  1.003e-01      0.571 0.568390    
#> X1634  7.066e-03  6.853e-02      0.103 0.917894    
#> X1635 -3.263e-01  1.085e-01     -3.007 0.002700 ** 
#> X1636  2.544e-02  1.195e-01      0.213 0.831429    
#> X1637  6.530e-02  1.711e-01      0.382 0.702829    
#> X1638 -5.156e-02  1.260e-01     -0.409 0.682493    
#> X1639  3.977e-01  1.523e-01      2.612 0.009116 ** 
#> X1640 -2.602e-02  1.188e-01     -0.219 0.826758    
#> X1641  6.309e-02  1.615e-01      0.391 0.696206    
#> X1642  5.363e-02  1.393e-01      0.385 0.700291    
#> X1643 -2.363e+00  1.066e-01    -22.177  < 2e-16 ***
#> X1644  2.553e-01  1.684e-01      1.516 0.129872    
#> X1645  5.613e-02  1.501e-01      0.374 0.708536    
#> X1646  1.634e-01  1.682e-01      0.971 0.331653    
#> X1647  7.537e-02  1.363e-01      0.553 0.580368    
#> X1648  1.280e-01  6.512e-02      1.966 0.049551 *  
#> X1649  4.783e-01  1.664e-01      2.874 0.004124 ** 
#> X1650  6.879e-01  1.511e-01      4.552 5.89e-06 ***
#> X1651 -1.024e+00  1.587e-01     -6.452 1.63e-10 ***
#> X1652 -1.232e+00  1.975e-01     -6.239 6.21e-10 ***
#> X1653 -1.780e+02  1.420e-01  -1253.827  < 2e-16 ***
#> X1654 -1.541e+02  1.363e-01  -1130.817  < 2e-16 ***
#> X1655 -7.056e-01  1.659e-01     -4.254 2.27e-05 ***
#> X1656 -4.393e-01  1.565e-01     -2.807 0.005086 ** 
#> X1657  2.890e-02  7.931e-02      0.364 0.715628    
#> X1658  2.159e-01  7.606e-02      2.839 0.004605 ** 
#> X1659  2.131e-01  1.071e-01      1.989 0.046916 *  
#> X1660  8.271e-03  6.431e-02      0.129 0.897690    
#> X1661  1.587e-02  1.044e-01      0.152 0.879201    
#> X1662  3.280e-02  8.464e-02      0.388 0.698431    
#> X1663  2.726e-03  1.220e-01      0.022 0.982180    
#> X1664  1.176e-01  9.868e-02      1.191 0.233821    
#> X1665  3.683e-03  8.238e-02      0.045 0.964353    
#> X1666  7.486e-02  1.136e-01      0.659 0.510241    
#> X1667 -1.264e-01  9.971e-02     -1.268 0.205043    
#> X1668  1.308e-01  1.265e-01      1.034 0.301312    
#> X1669  8.924e-02  1.202e-01      0.743 0.457815    
#> X1670  5.418e-02  1.739e-01      0.311 0.755488    
#> X1671  2.097e-01  1.160e-01      1.808 0.070831 .  
#> X1672  2.155e-01  1.138e-01      1.894 0.058515 .  
#> X1673  1.299e-01  1.794e-01      0.724 0.469173    
#> X1674  8.877e-02  1.085e-01      0.818 0.413469    
#> X1675  1.066e-01  1.215e-01      0.878 0.380347    
#> X1676  1.554e-01  1.491e-01      1.043 0.297368    
#> X1677 -1.400e-02  1.482e-01     -0.094 0.924754    
#> X1678 -5.358e-02  1.660e-01     -0.323 0.746985    
#> X1679  4.318e-02  1.211e-01      0.356 0.721582    
#> X1680  6.950e-02  1.127e-01      0.616 0.537697    
#> X1681  1.117e-02  1.248e-01      0.089 0.928713    
#> X1682  8.724e-02  1.354e-01      0.644 0.519418    
#> X1683  7.642e-02  1.576e-01      0.485 0.627926    
#> X1684  6.669e-02  1.423e-01      0.469 0.639426    
#> X1685  3.623e-02  1.115e-01      0.325 0.745185    
#> X1686  3.211e-01  1.395e-01      2.302 0.021542 *  
#> X1687  8.340e-02  1.359e-01      0.614 0.539463    
#> X1688  2.308e-01  1.521e-01      1.517 0.129478    
#> X1689  2.883e-01  8.804e-02      3.274 0.001091 ** 
#> X1690  2.940e-01  1.360e-01      2.162 0.030797 *  
#> X1691  2.025e-01  1.199e-01      1.689 0.091455 .  
#> X1692  1.326e-01  1.109e-01      1.195 0.232152    
#> X1693 -2.477e-02  3.901e-02     -0.635 0.525622    
#> X1694 -2.515e-02  3.901e-02     -0.645 0.519213    
#> X1695  4.254e-01  9.995e-02      4.256 2.25e-05 ***
#> X1696  3.295e-01  9.990e-02      3.298 0.001004 ** 
#> X1697  1.440e-01  7.824e-02      1.841 0.065860 .  
#> X1698 -1.307e+00  2.347e-01     -5.566 3.24e-08 ***
#> X1699 -3.210e+00  2.137e-01    -15.023  < 2e-16 ***
#> X1700 -3.036e+00  1.167e-01    -26.013  < 2e-16 ***
#> X1701 -1.679e-01  1.027e-01     -1.634 0.102453    
#> X1702 -6.456e-01  1.718e-01     -3.758 0.000180 ***
#> X1703  1.274e-01  9.815e-02      1.298 0.194522    
#> X1704 -1.604e-02  6.058e-02     -0.265 0.791187    
#> X1705 -2.342e-01  6.086e-02     -3.849 0.000125 ***
#> X1706 -1.510e-01  7.862e-02     -1.921 0.054974 .  
#> X1707 -2.080e+00  1.331e-01    -15.625  < 2e-16 ***
#> X1708 -6.440e+00  1.429e-01    -45.050  < 2e-16 ***
#> X1709 -1.260e-01  5.398e-02     -2.334 0.019763 *  
#> X1710 -1.192e-01  1.027e-01     -1.160 0.246312    
#> X1711 -2.060e+00  5.817e-02    -35.418  < 2e-16 ***
#> X1712 -7.849e+00  1.809e-01    -43.393  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.03789 on 1138 degrees of freedom
#> Multiple R-squared:      1,	Adjusted R-squared:      1 
#> F-statistic: 4.504e+07 on 712 and 1138 DF,  p-value: < 2.2e-16
#>