How to export R results to Excel

This works for my with your data on rstudio server linux version, but If you are on windows you might be having problems with xlsx package and your Java installation, if you don't mind the .csv extension you can use readr::write_excel_csv() instead.

library(Hmisc)
library(xlsx)

my_data <- data.frame(
    Annelida. = c(-0.131778305, -0.030880161, 3.995076341, 0.045341,
                  -0.161345401, -0.045219353, 3.977922041, -0.262785757,
                  -0.206141008, -0.160736468, 3.711160423, -0.223712782,
                  -0.189363136, 1.002411927, 1.979772939, 1.684596561),
    Arthropoda = c(-0.094260992, 0.769075751, -0.130124631, 0.255073383,
                   -0.204691037, -0.12415447, -0.174578416, -0.083796551,
                   -0.223197192, -0.210846358, -0.247095059, -0.123972223,
                   -0.259272506, -0.344794918, 0.211751103, -0.427072885),
    Cnidaria = c(-0.259337169, -0.31086473, -0.264059728, -0.282365849,
                 -0.248036673, -0.262290926, -0.281878169, -0.262785757,
                 -0.23684214, -0.24553782, -0.318802586, -0.243660894,
                 -0.259272506, -0.344794918, -0.426701227, -0.427072885),
    Echinodermata = c(-0.259337169, -0.31086473, -0.264059728, -0.282365849,
                      -0.248036673, -0.208023032, -0.271148194, -0.262785757,
                      -0.233430903, -0.24553782, -0.333144092, -0.248647922,
                      -0.259272506, 0.318116387, -0.181142639, 1.409161416),
    Mollusca = c(4.002629584, 3.871761896, 0.046669696, 3.964714909,
                 4.006027853, 4.000205413, 0.233160647, 4.00312365,
                 4.006736539, 4.006093603, 1.287446015, 4.005286922, 4.005199083,
                 3.760978323, 3.305789316, 3.092376191),
    Nemertea. = c(-0.214316393, -0.299436788, -0.264059728, -0.269257575,
                  -0.229459972, -0.257357481, -0.206768342, -0.262785757,
                  -0.219785955, -0.230119392, -0.304461081, -0.233686838,
                  -0.212666259, -0.195105268, -0.37758951, -0.21284555),
    Nemotoda = c(-0.259337169, -0.31086473, -0.264059728, -0.295474123,
                 -0.248036673, -0.257455656, -0.281878169, -0.262785757,
                 -0.243664613, -0.24553782, -0.289413973, -0.248647922,
                 -0.259272506, -0.366179153, -0.426701227, -0.45767679),
    H = c(-0.258516586, -0.310350875, -0.263423863, -0.29396544,
          -0.247400525, -0.261868287, -0.280743747, -0.260208491,
          -0.243258602, -0.245235106, -0.331887246, -0.24807019,
          -0.257924494, -0.364629858, -0.423752036, -0.453681971),
    Dep = c(-0.249243246, -0.305147795, -0.255658461, -0.27724616,
            -0.233637653, -0.253873975, -0.257683464, -0.19672979,
            -0.232120043, -0.235579408, -0.282339984, -0.232898389,
            -0.150736596, -0.288020707, -0.180680989, -0.308416517),
    Temp = c(-0.247196727, -0.298691082, -0.256405238, -0.281995094,
             -0.239577871, -0.252169008, -0.266459571, -0.231883693,
             -0.240116893, -0.239676451, -0.312819187, -0.243582205,
             -0.228055451, -0.345390349, -0.362254684, -0.427232027),
    Salinity = c(-0.244958746, -0.302530531, -0.253542958, -0.269790375,
                 -0.236221853, -0.25506751, -0.260803529, -0.204114523,
                 -0.236931466, -0.239851823, -0.304918276, -0.238847442,
                 -0.214986029, -0.33439863, -0.329341801, -0.397285512),
    DO = c(-0.250882094, -0.307038446, -0.258031226, -0.279260683,
           -0.24076242, -0.258905194, -0.269893382, -0.225880927,
           -0.23958563, -0.242759749, -0.317169419, -0.242460379,
           -0.232914871, -0.348470706, -0.374009308, -0.419875019),
    Chl_a = c(-0.25732373, -0.310325051, -0.26261275, -0.292426781,
              -0.246143724, -0.261578666, -0.279225632, -0.255764008,
              -0.242803163, -0.24457332, -0.33029591, -0.247627663,
              -0.252735595, -0.362899326, -0.418711673, -0.451419975)
)

result <- rcorr(as.matrix(my_data), type="pearson")
write.xlsx(as.data.frame(result$r), file = "results.xlsx")

Created on 2019-01-06 by the reprex package (v0.2.1)

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