From 3dd01f4cb62b47d95725ab02b477fa98f579a646 Mon Sep 17 00:00:00 2001
From: KronosTheLate <61620837+KronosTheLate@users.noreply.github.com>
Date: Thu, 11 Nov 2021 15:14:49 +0100
Subject: [PATCH 1/2] Docs for not using a DataFrame

This PR adds documentation on how to do a fit without using a DataFrame, as suggested by @pdeffebach in [this thread](https://discourse.julialang.org/t/the-simplest-linear-fit-with-glm/71316/11).
---
 docs/src/examples.md | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)

diff --git a/docs/src/examples.md b/docs/src/examples.md
index cd5797da..6c74661d 100644
--- a/docs/src/examples.md
+++ b/docs/src/examples.md
@@ -44,6 +44,42 @@ julia> round.(predict(ols), digits=5)
  6.83333
 ```
 
+### Without DataFrame
+Because a named tuple follows common table-interface defined in `Tables.jl` 
+(which is the one followed by a DataFrame), the problem can also be specified 
+with data in a named tuple as opposed to a `DataFrame`:
+```jldoctetst
+julia> using GLM
+
+julia> X=[1,2,3]
+3-element Vector{Int64}:
+ 1
+ 2
+ 3
+
+julia> Y=[2,4,7]
+3-element Vector{Int64}:
+ 2
+ 4
+ 7
+
+julia> data = (;X, Y)  # Equivalent to (X=X, Y=Y)
+(X = [1, 2, 3], Y = [2, 4, 7])
+
+julia> lm(@formula(Y~X), data)
+StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}
+
+Y ~ 1 + X
+
+Coefficients:
+─────────────────────────────────────────────────────────────────────────
+                 Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%
+─────────────────────────────────────────────────────────────────────────
+(Intercept)  -0.666667    0.62361   -1.07    0.4788   -8.59038    7.25704
+X             2.5         0.288675   8.66    0.0732   -1.16797    6.16797
+─────────────────────────────────────────────────────────────────────────
+```
+
 ## Probit regression
 ```jldoctest
 julia> data = DataFrame(X=[1,2,2], Y=[1,0,1])

From 5a5b08f615e0e664f1cd4a3a2305f330d3cf0d4d Mon Sep 17 00:00:00 2001
From: KronosTheLate <61620837+KronosTheLate@users.noreply.github.com>
Date: Thu, 11 Nov 2021 15:45:51 +0100
Subject: [PATCH 2/2] Added example without intercept

This commit adds another very basic example, that I would have appreciated when I first met GLM. It also links to the documentation of `@formula`, which I think is highly relevant.
---
 docs/src/examples.md | 22 +++++++++++++++++++++-
 1 file changed, 21 insertions(+), 1 deletion(-)

diff --git a/docs/src/examples.md b/docs/src/examples.md
index 6c74661d..e8f210bf 100644
--- a/docs/src/examples.md
+++ b/docs/src/examples.md
@@ -44,7 +44,7 @@ julia> round.(predict(ols), digits=5)
  6.83333
 ```
 
-### Without DataFrame
+### Without data as a DataFrame
 Because a named tuple follows common table-interface defined in `Tables.jl` 
 (which is the one followed by a DataFrame), the problem can also be specified 
 with data in a named tuple as opposed to a `DataFrame`:
@@ -80,6 +80,26 @@ X             2.5         0.288675   8.66    0.0732   -1.16797    6.16797
 ─────────────────────────────────────────────────────────────────────────
 ```
 
+### Without intercept
+To make a fit without an intercept (Going through `(0, 0)`), one can specify the fomula as follows:
+```jldoctest
+julia> X=[1,2,3]; Y=[2,4,7]; data = (;X, Y)
+(X = [1, 2, 3], Y = [2, 4, 7])
+
+julia> lm(@formula(Y~0+X), data)
+StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}
+
+Y ~ 0 + X
+
+Coefficients:
+─────────────────────────────────────────────────────────────
+     Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%
+─────────────────────────────────────────────────────────────
+X  2.21429    0.112938  19.61    0.0026    1.72835    2.70022
+─────────────────────────────────────────────────────────────
+```
+To read more about the `@formula` syntax, check out [the documentation for `@formula`](https://juliastats.org/StatsModels.jl/stable/formula/#The-@formula-language)
+
 ## Probit regression
 ```jldoctest
 julia> data = DataFrame(X=[1,2,2], Y=[1,0,1])