diff --git a/.travis.yml b/.travis.yml
index a63c101..6b3594a 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,7 +4,7 @@ os:
   - osx
 julia:
   - 1.0
-  - 1.1
+  - 1.3
   - nightly
 notifications:
   email: false
@@ -17,8 +17,7 @@ before_install:
   - if [ $TRAVIS_OS_NAME = linux ]; then
       sudo apt-get install gfortran -y;
     else
-      brew cask uninstall oclint;
-      brew install gcc;
+      brew update && brew install gcc;
     fi
 
 after_success:
@@ -27,7 +26,7 @@ after_success:
 jobs:
   include:
     - stage: "Documentation"
-      julia: 1.1
+      julia: 1.3
       os: linux
       script:
         - julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
diff --git a/Project.toml b/Project.toml
index 7750b76..f4a3bfd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Lasso"
 uuid = "b4fcebef-c861-5a0f-a7e2-ba9dc32b180a"
-version = "0.5.0"
+version = "0.5.1"
 
 [deps]
 DSP = "717857b8-e6f2-59f4-9121-6e50c889abd2"
@@ -15,7 +15,12 @@ StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
 
 [compat]
+DSP = "0.6"
+Distributions = "0.21"
 GLM = "1.3"
+MLBase = "0.8"
+Reexport = "0.2"
+StatsBase = "0.32"
 StatsModels = "0.6"
 julia = "0.7, 1"
 
diff --git a/docs/src/index.md b/docs/src/index.md
index 237ec08..15f8e55 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -41,30 +41,28 @@ julia> data = DataFrame(X=[1,2,3], Y=[2,4,7])
 │ 3   │ 3     │ 7     │
 
 julia> m = fit(LassoModel, @formula(Y ~ X), data)
-StatsModels.TableRegressionModel{LassoModel{LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredQR{Float64}}},Array{Float64,2}}
-
-Y ~ X
+LassoModel using MinAICc(2) segment of the regulatization path.
 
 Coefficients:
-──────────────────────────────────────────────────────────────────
-    Estimate  Std. Error   t value  Pr(>|t|)  Lower 95%  Upper 95%
-──────────────────────────────────────────────────────────────────
-x1  3.88915      4.86043  0.800166    0.5704   -57.8684    65.6467
-x2  0.222093     1.83707  0.120895    0.9234   -23.1201    23.5643
-──────────────────────────────────────────────────────────────────
-
-julia> stderror(m)
-2-element Array{Float64,1}:
- 4.860427341926979
- 1.8370688588910695
+────────────
+    Estimate
+────────────
+x1  3.88915 
+x2  0.222093
+────────────
 
 julia> predict(m)
 3-element Array{Float64,1}:
- 4.161154511001072
- 4.433161908091373
- 4.705169305181673
-
+ 4.111240223622052
+ 4.333333333333333
+ 4.555426443044614
+
+julia> predict(m, data[2:end,:])
+2-element Array{Union{Missing, Float64},1}:
+ 4.333333333333333
+ 4.555426443044614
 ```
+
 To get an entire Lasso regularization path with default parameters:
 
 ```julia
diff --git a/docs/src/lasso.md b/docs/src/lasso.md
index ddab76e..74e20de 100644
--- a/docs/src/lasso.md
+++ b/docs/src/lasso.md
@@ -73,17 +73,15 @@ julia> data = DataFrame(X=[1,2,3], Y=[2,4,7])
 │ 3   │ 3     │ 7     │
 
 julia> m = fit(LassoModel, @formula(Y ~ X), data; select=MinCVmse(Kfold(3,2)))
-StatsModels.TableRegressionModel{LassoModel{LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredQR{Float64}}},Array{Float64,2}}
-
-Y ~ X
+LassoModel using MinCVmse(Kfold([3, 1, 2], 2, 1.5)) segment of the regulatization path.
 
 Coefficients:
-──────────────────────────────────────────────────────────────────
-    Estimate  Std. Error   t value  Pr(>|t|)  Lower 95%  Upper 95%
-──────────────────────────────────────────────────────────────────
-x1   4.33333      5.4365  0.797081    0.5716   -64.744     73.4106
-x2   0.0          2.0548  0.0         1.0000   -26.1088    26.1088
-──────────────────────────────────────────────────────────────────
+────────────
+    Estimate
+────────────
+x1   4.33333
+x2   0.0    
+────────────
 
 julia> coef(m)
 2-element Array{Float64,1}:
diff --git a/src/Lasso.jl b/src/Lasso.jl
index 1157bf6..be554e9 100644
--- a/src/Lasso.jl
+++ b/src/Lasso.jl
@@ -14,7 +14,7 @@ include("TrendFiltering.jl")
 using Reexport, LinearAlgebra, SparseArrays, Random, .Util, MLBase
 import Random: Sampler
 @reexport using GLM, Distributions, .FusedLassoMod, .TrendFiltering
-using GLM: FPVector, LinPred, Link, LmResp, GlmResp, DensePredQR, updateμ!,
+using GLM: FPVector, LinPred, Link, LmResp, GlmResp, cholpred, updateμ!,
     linkfun, linkinv, LinPredModel
 export RegularizationPath, LassoPath, GammaLassoPath, NaiveCoordinateDescent,
        CovarianceCoordinateDescent, fit, fit!, coef, predict,
@@ -597,6 +597,20 @@ function StatsBase.predict(path::RegularizationPath, newX::AbstractMatrix{T}; of
     end
 end
 
+"predicted values for data used to estimate `path`"
+function StatsBase.predict(path::RegularizationPath; select=AllSeg())
+    X = path.m.pp.X 
+    offset = path.m.rr.offset
+
+    # destandardize X if needed
+    if !isempty(path.Xnorm)
+        X = X ./ transpose(path.Xnorm)
+    end
+
+    predict(path, X; offset=offset, select=select)
+end
+
+
 "distribution of underlying GLM"
 distfun(path::RegularizationPath{M}) where {M<:LinearModel} = Normal()
 distfun(path::RegularizationPath) = path.m.rr.d
diff --git a/src/segselect.jl b/src/segselect.jl
index 1f63a8a..2d13534 100644
--- a/src/segselect.jl
+++ b/src/segselect.jl
@@ -119,15 +119,17 @@ segselect(path::RegularizationPath,
 abstract type RegularizedModel <: RegressionModel end
 
 "LassoModel represents a selected segment from a LassoPath"
-struct LassoModel{M<:LinPredModel} <: RegularizedModel
+struct LassoModel{M<:LinPredModel, S<:SegSelect} <: RegularizedModel
     lpm::M          # underlying GLM
     intercept::Bool # whether path added an intercept
+    select::S       # segment selector
 end
 
 "GammaLassoModel represents a selected segment from a GammaLassoPath"
-struct GammaLassoModel{M<:LinPredModel} <: RegularizedModel
+struct GammaLassoModel{M<:LinPredModel, S<:SegSelect} <: RegularizedModel
     lpm::M          # underlying GLM
     intercept::Bool # whether path added an intercept
+    select::S       # segment selector
 end
 
 """
@@ -140,7 +142,7 @@ Predicted values using a selected segment of a regularization path.
 m = fit(LassoModel, X, y; select=MinBIC())
 predict(m, newX)     # predict using BIC minimizing segment
 """
-function StatsBase.predict(m::RegularizedModel, newX::AbstractMatrix{T}; kwargs...) where {T<:AbstractFloat}
+function StatsBase.predict(m::RegularizedModel, newX::AbstractMatrix{T}; kwargs...) where T
     # add an interecept to newX if the model has one
     if m.intercept
         newX = [ones(T,size(newX,1),1) newX]
@@ -169,8 +171,14 @@ selectmodel(path, MinCVmse(path, 5))   # 5-fold CV mse minimizing model
 function selectmodel(path::R, select::SegSelect) where R<:RegularizationPath
     # extract reusable path parts
     m = path.m
+    rr = deepcopy(m.rr)
     pp = m.pp
-    X = pp.X
+    X = pp.X 
+    
+    # destandardize X if needed
+    if !isempty(path.Xnorm)
+        X = X ./ transpose(path.Xnorm)
+    end
 
     # add an interecept to X if the model has one
     if hasintercept(path)
@@ -183,17 +191,21 @@ function selectmodel(path::R, select::SegSelect) where R<:RegularizationPath
     beta0 = Vector{Float64}(coef(path, select))
 
     # create new linear predictor
-    segpp = DensePredQR(segX, beta0)
+    pivot = true
+    p = cholpred(segX, pivot)
 
     # rescale weights, which in GLM sum to nobs
-    m.rr.wts .*= nobs(path)
+    rr.wts .*= nobs(path)
 
     # same things GLM does to init just before fit!
-    GLM.installbeta!(segpp)
-    updateμ!(m.rr, linpred(segpp, zero(eltype(m.rr.y))))
+    lp = rr.mu
+    copyto!(p.beta0, beta0)
+    fill!(p.delbeta, 0)
+    GLM.linpred!(lp, p, 0)
+    updateμ!(rr, lp)
 
     # create a LinearModel or GeneralizedLinearModel with the new linear predictor
-    newglm(m, segpp)
+    newglm(m, rr, p)
 end
 
 """
@@ -275,11 +287,11 @@ function StatsBase.fit(::Type{R}, X::AbstractMatrix{T}, y::V,
     M = pathtype(R)
     path = fit(M, X, y, d, l; intercept=intercept, kwargs...)
 
-    R(selectmodel(path, select), intercept)
+    R(selectmodel(path, select), intercept, select)
 end
 
-newglm(m::LinearModel, pp) = LinearModel(m.rr, pp)
-newglm(m::GeneralizedLinearModel, pp) = GeneralizedLinearModel(m.rr, pp, true)
+newglm(m::LinearModel, rr, pp) = LinearModel(rr, pp)
+newglm(m::GeneralizedLinearModel, rr, pp) = GeneralizedLinearModel(rr, pp, true)
 
 # don't add an intercept when using a @formula because we use the intercept keyword arg to add an intercept
 StatsModels.drop_intercept(::Type{R}) where R<:RegularizedModel = true
@@ -291,9 +303,7 @@ for modeltype in (:LassoModel, :GammaLassoModel)
                                      StatsBase.deviance, StatsBase.nulldeviance,
                                      StatsBase.loglikelihood, StatsBase.nullloglikelihood,
                                      StatsBase.dof, StatsBase.dof_residual, StatsBase.nobs,
-                                     StatsBase.stderror, StatsBase.vcov,
-                                     StatsBase.residuals, StatsBase.response,
-                                     StatsBase.coeftable
+                                     StatsBase.residuals, StatsBase.response
                                      ]
     end
 end
@@ -306,3 +316,19 @@ StatsBase.fit(::Type{M},
     d::UnivariateDistribution=Normal(),
     l::Link=canonicallink(d); kwargs...) where {M<:Union{RegularizationPath, RegularizedModel}} =
     fit(M, float(X), float(y), d, l; kwargs...)
+
+function coeftable(mm::RegularizedModel)
+    cc = coef(mm)
+    CoefTable([cc],
+                ["Estimate"],
+                ["x$i" for i = 1:size(mm.lpm.pp.X, 2)])
+end
+    
+function Base.show(io::IO, obj::RegularizedModel)
+    # prefix = isa(obj.m, GeneralizedLinearModel) ? string(typeof(distfun(path)).name.name, " ") : ""
+    println(io, "$(typeof(obj).name.name) using $(obj.select) segment of the regulatization path.")
+
+    println(io, "\nCoefficients:\n", coeftable(obj))
+end
+
+StatsBase.vcov(obj::RegularizedModel, args...) = error("variance-covariance matrix for a regularized model is not yet implemented")
diff --git a/test/segselect.jl b/test/segselect.jl
index 2177662..1cc4eae 100644
--- a/test/segselect.jl
+++ b/test/segselect.jl
@@ -1,5 +1,18 @@
 # tests for segment selection and StatsModels @formula+df interface
 using Random
+using GLM: predict
+
+"Tests whether the output of `show(expr)` converted to String contains `expected`"
+macro test_show(expr, expected)
+    s = quote
+        local o = IOBuffer()
+        show(o, $expr)
+        String(take!(o))
+    end
+    substr = quote $expected end
+    :(@test occursin($(esc(substr)), $(esc(s))))
+end
+
 @testset "segment/model selection" begin
 
 datapath = joinpath(dirname(@__FILE__), "data")
@@ -25,13 +38,18 @@ datapath = joinpath(dirname(@__FILE__), "data")
 
                 Random.seed!(421)
                 pathpredict = Lasso.predict(path, data; select=select, offset=offset)
+                @test pathpredict ≈ Lasso.predict(path; select=select)
 
                 @test pathcoefs == coef(m)
                 if isa(dist, Normal)
-                    @test pathpredict == GLM.predict(m, data) + offset
+                    @test pathpredict ≈ predict(m, data) + offset
+                    @test pathpredict ≈ predict(m)
                 else
-                    @test pathpredict == GLM.predict(m, data; offset=offset)
+                    @test pathpredict ≈ predict(m, data; offset=offset)
+                    @test pathpredict ≈ predict(m)
                 end
+
+                @test_show m string(L)
             end
         end
     end