Return basic statistics to Base

Revert "move cor, cov, std, stdm, var, varm and linreg to StatsBase (#27152)"
This reverts commit 746d08f.
Fixes #27374

base/deprecated.jl

@@ -293,6 +293,12 @@ deprecate(Base, :DSP, 2)
 using .DSP
 export conv, conv2, deconv, filt, filt!, xcorr
 
+# PR #21709
+@deprecate cov(x::AbstractVector, corrected::Bool) cov(x, corrected=corrected)
+@deprecate cov(x::AbstractMatrix, vardim::Int, corrected::Bool) cov(x, dims=vardim, corrected=corrected)
+@deprecate cov(X::AbstractVector, Y::AbstractVector, corrected::Bool) cov(X, Y, corrected=corrected)
+@deprecate cov(X::AbstractVecOrMat, Y::AbstractVecOrMat, vardim::Int, corrected::Bool) cov(X, Y, dims=vardim, corrected=corrected)
+
 # PR #22325
 # TODO: when this replace is removed from deprecated.jl:
 # 1) rename the function replace_new from strings/util.jl to replace
@@ -1367,6 +1373,13 @@ export readandwrite
 @deprecate findmin(A::AbstractArray, dims)    findmin(A, dims=dims)
 
 @deprecate mean(A::AbstractArray, dims)                              mean(A, dims=dims)
+@deprecate varm(A::AbstractArray, m::AbstractArray, dims; kwargs...) varm(A, m; kwargs..., dims=dims)
+@deprecate var(A::AbstractArray, dims; kwargs...)                    var(A; kwargs..., dims=dims)
+@deprecate std(A::AbstractArray, dims; kwargs...)                    std(A; kwargs..., dims=dims)
+@deprecate cov(X::AbstractMatrix, dim::Int; kwargs...)               cov(X; kwargs..., dims=dim)
+@deprecate cov(x::AbstractVecOrMat, y::AbstractVecOrMat, dim::Int; kwargs...) cov(x, y; kwargs..., dims=dim)
+@deprecate cor(X::AbstractMatrix, dim::Int)                          cor(X, dims=dim)
+@deprecate cor(x::AbstractVecOrMat, y::AbstractVecOrMat, dim::Int)   cor(x, y, dims=dim)
 @deprecate median(A::AbstractArray, dims; kwargs...)                 median(A; kwargs..., dims=dims)
 
 @deprecate mapreducedim(f, op, A::AbstractArray, dims)     mapreduce(f, op, A, dims=dims)
@@ -1687,15 +1700,6 @@ function Rounding.setrounding(::Type{T}, r::RoundingMode) where {T<:Union{Float3
     Rounding.setrounding_raw(T, Rounding.to_fenv(r))
 end
 
-# #27140, #27152
-@deprecate_moved cor "StatsBase"
-@deprecate_moved cov "StatsBase"
-@deprecate_moved std "StatsBase"
-@deprecate_moved stdm "StatsBase"
-@deprecate_moved var "StatsBase"
-@deprecate_moved varm "StatsBase"
-@deprecate_moved linreg "StatsBase"
-
 # issue #27093
 # in src/jlfrontend.scm a call to `@deprecate` is generated for per-module `eval(m, x)`
 @eval Core Main.Base.@deprecate(eval(e), Core.eval(Main, e))

base/exports.jl

@@ -633,13 +633,19 @@ export
     set_zero_subnormals,
 
 # statistics
+    cor,
+    cov,
     mean!,
     mean,
     median!,
     median,
     middle,
     quantile!,
     quantile,
+    std,
+    stdm,
+    var,
+    varm,
 
 # iteration
     done,