LinearAlgebra[LeastSquares](X,Y)^+;
# [4.33701132468683, -2.78654498997457, -1.41840666085642, 2.92065133466547, 1.76076442997642]

Statistics[LinearFit]([x1,x2,x3,x4,c],X,Y,[x1,x2,x3,x4,c],summarize=true)
# Summary:
# ----------------
# Model: 4.3370113*x1-2.7865450*x2-1.4184067*x3+2.9206513*x4+1.7607644*c
# ----------------
# Coefficients:
#               Estimate  Std. Error  t-value  P(>|t|)
# Parameter 1    4.3370    0.0691      62.7409   0.0000
# Parameter 2   -2.7865    0.0661     -42.1637   0.0000
# Parameter 3   -1.4184    0.0699     -20.2937   0.0000
# Parameter 4    2.9207    0.0687      42.5380   0.0000
# Parameter 5    1.7608    0.0701      25.1210   0.0000
# ----------------
# R-squared: 0.9767, Adjusted R-squared: 0.9761
# 4.33701132468683 x1 - 2.78654498997457 x2 - 1.41840666085642 x3
#    + 2.92065133466547 x4 + 1.76076442997642 c