Show R^2 and F-statistic for regression models

[OndrejSlamecka]

Adds R² and F-statistic for regression models, bringing the output closer to what users might expect when coming from R.

An example implementation of fstatistic is in JuliaStats/GLM.jl#424 -- I am unsure about import/export/using/... and welcome advice, thanks!

Example output:

julia> ols_lin = 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)  -442.0     54.5539  -8.10    <1e-09  -551.688   -332.312
x              51.0      1.8619  27.39    <1e-30    47.2564    54.7436
──────────────────────────────────────────────────────────────────────

R²: 0.9399	Adjusted R²: 0.9386
F-statistic: 750.3 on 50.0 and 1.0 degrees of freedom, p-value: 0.0290

[OndrejSlamecka]

Thanks @palday for the good suggestions, I implemented them.

[nalimilan]

How about printing also the number of observations and degrees of freedom?

Can you also add tests?

[nalimilan]

This should ensure that 4 digits are always used, and that "Ajusted" is aligned with the value of the F-statistic on the next line.

Suggested change

	println("R²: ", round(r2(model), sigdigits=4),
	"\t Adjusted R²: ", round(adjr2(model), sigdigits=4))
	@printf(io, "R²: %.4f Adjusted R²: %.4f", r2(model), adjr2(model))

[nalimilan]

fstatistic doesn't exist anywhere currently, and only GLM provides the needed functionality via ftest (JuliaStats/GLM.jl#424). An empty ftest definition should be added to StatsAPI first. Probably the API can just require that the returned object has the dof, fstat and pval properties so that you can extract them and print them.

Suggested change

	fstat = fstatistic(model)
	println(io, fstat)
	ftr = ftest(model)
	@printf(io, "F-statistic: %.4f on %s degrees of freedom, p-value %s",
	ftr.fstat, ftr.dof, PValue(ftr.pvalue))

[xgdgsc]

@nalimilan what if adding a print API to StatsAPI so packages can implement their own printing?

[palday]

@xgdgsc every package is free to implement Base.show methods for their own types