diff --git a/M2/TP1-distributions-sol.ipynb b/M2/TP1-distributions-sol.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..245aa80417ce365df12dac3163ca6c623e571239 --- /dev/null +++ b/M2/TP1-distributions-sol.ipynb @@ -0,0 +1,2422 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to `julia` for statistic\n", + "\n", + "- To contact me, here is my email : [joseph.gergaud@toulouse-inp.fr](joseph.gergaud@toulouse-inp.fr)\n", + "\n", + "- The files ares here : \n", + "\n", + "[https://gitlab.irit.fr/toc/etu-n7/julia](https://gitlab.irit.fr/toc/etu-n7/julia)\n", + "\n", + "directory M2\n", + "\n", + "- Evaluation : Homework (notebook)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## empirical cumulative distribution function, eCDF\n", + "### Exercise 1\n", + "1. Build the empirical cumulative distribution function" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element BitVector:\n", + " 1\n", + " 0\n", + " 0" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use broadcasting\n", + "a = [1,2,3.5]\n", + "a .< 2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "empirique([1.,2,3],1.5) = 1\n" + ] + }, + { + "data": { + "text/plain": [ + "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using Test # for tests\n", + "\n", + "\"\"\"\n", + " Compute de number of element in the vactor t less than a value x\n", + " input\n", + " t : Vector of Real\n", + " x : Real\n", + " Output\n", + " Integer\n", + "\"\"\"\n", + "function empirique(t::Vector{<:Real}, x::Real)::Int\n", + " # to complete\n", + " return sum(t .< x) # .< vectorial operation\n", + "end\n", + "\n", + "\n", + "println(\"empirique([1.,2,3],1.5) = \", empirique([1.,2,3],1.5))\n", + "\n", + "@test empirique([1.,2,3],1.5) == 1" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "ename": "MethodError", + "evalue": "MethodError: no method matching empirique(::Vector{ComplexF64}, ::Float64)\n\nClosest candidates are:\n empirique(!Matched::Vector{<:Real}, ::Real)\n @ Main ~/git-ENS/Julia-TSE/enseignants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W3sZmlsZQ==.jl:11\n", + "output_type": "error", + "traceback": [ + "MethodError: no method matching empirique(::Vector{ComplexF64}, ::Float64)\n", + "\n", + "Closest candidates are:\n", + " empirique(!Matched::Vector{<:Real}, ::Real)\n", + " @ Main ~/git-ENS/Julia-TSE/enseignants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W3sZmlsZQ==.jl:11\n", + "\n", + "\n", + "Stacktrace:\n", + " [1] top-level scope\n", + " @ ~/git-ENS/Julia-TSE/enseignants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W4sZmlsZQ==.jl:2" + ] + } + ], + "source": [ + "# If the type of the vector elements is not a real then there is an error\n", + "println(\"empirique([1.+2im,2,3],1.5) = \", empirique([1.,2+2im,3],1.5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Generate a sample of N=1000 datas from a uniform distribution on [0,2] and plot the eCDF of this sample" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Add on the plot the Cumulative Distribution Function\n", + "For thie use de Distributions Package" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# add the cumulative distribution function\n", + "using Distributions\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Distributions Package\n", + "\n", + "### Introduction\n", + "\n", + "There is lots of libraries (Packages in `julia`) : [https://julialang.org/packages/](https://julialang.org/packages/)\n", + "\n", + "For the documentation of the Distributions Package see \n", + "\n", + "[https://juliastats.org/Distributions.jl/stable/](https://juliastats.org/Distributions.jl/stable/)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "type de dist = Uniform{Float64}\n", + "mean(dist) = 1.0\n", + "median(dist) = 1.0\n", + "pdf(1.2) = 0.5\n", + "pdf(3) = 0.0\n", + "cdf(1.2) = 0.6\n", + "cdf(3) = 1.0\n", + "inverse of cdf(0.75) = 1.5\n" + ] + } + ], + "source": [ + "using Distributions\n", + "using Plots\n", + "using LaTeXStrings\n", + "a = 0; b = 2;\n", + "dist = Uniform(a,b) # dist is an object : the uniform distribution on [a,b]\n", + "println(\"type de dist = \",typeof(dist))\n", + "# you can acces to the mean or median of the distribution\n", + "println(\"mean(dist) = \", mean(dist))\n", + "println(\"median(dist) = \", median(dist))\n", + "# and the the PDF, CDF and inverse CDF function of the distribution\n", + "println(\"pdf(1.2) = \", pdf(dist,1.2))\n", + "println(\"pdf(3) = \", pdf(dist,3))\n", + "println(\"cdf(1.2) = \", cdf(dist,1.2))\n", + "println(\"cdf(3) = \", cdf(dist,3))\n", + "println(\"inverse of cdf(0.75) = \", quantile(dist,0.75))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise 2\n", + "\n", + "Plot on the same first graph the CFD of the uniform distribution on [0,2]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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2194.02,86.1857 2243.63,86.1857 2293.23,86.1857 \"/>\n", + "</svg>\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cdf_uniform(x) = cdf(dist,x)\n", + "plot!(p_uniform_cdf,x_grid,cdf_uniform,xlabel=\"x\", ylabel=\"F(x)\", legend=false)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Triangular Distribution\n", + "We consider the distribution with the following density distribution\n", + "$$f(x) = \\begin{cases}\n", + "x\\quad\\textrm{pour}\\quad x\\in[0,1]\\\\\n", + "2-x\\quad\\textrm{pour}\\quad x\\in[1,2]\\\\\n", + "0\\quad\\textrm{sinon}\n", + "\\end{cases}$$\n", + "\n", + "Plot the density, cumulative dendity and inverse cumulative function" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "type de dist = TriangularDist{Float64}\n", + "params(dist) = (0.0, 2.0, 1.0)\n" + ] + }, + { + "data": { + 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4662.41,187.768 4674.02,125.984 \"/>\n", + "</svg>\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using Distributions\n", + "using Plots\n", + "using LaTeXStrings\n", + "a = 0; b = 2;\n", + "dist = TriangularDist(a,b,1) # min = a; max = b; mode = 1\n", + "println(\"type de dist = \",typeof(dist))\n", + "println(\"params(dist) = \", params(dist))\n", + "\n", + "\n", + "# Density function\n", + "p1 = plot(x_grid, x->pdf(dist,x), color = :blue, linewidth=2, xlabel=(L\"x\"), ylabel=(L\"f(x)\")) \n", + "# Cumulative density function\n", + "p2 = plot(a-1:0.01:b+1, x->cdf(dist,x), linewidth=2, xlabel=(L\"x\"), ylabel=(L\"F(x)\")) \n", + "# Inverse cumulative density function\n", + "p3 = plot(0:0.01:1, x->quantile(dist,x), xlims=(0,1), ylims=(0,2), color = :green, linewidth=2, xlabel=(L\"u\"), ylabel=(L\"F^{-1}(u)\"))\n", + "plot(p1,p2,p3, layout=(1,3),legend = false,size = (1200,300), margin = 0.6Plots.cm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Histogram\n", + "Generate a sample of 100 datas from the triangular distribution and plot on the same graph the histogram of the simple and the PDF function" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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rand(dist,100)\n", + "histogram(t) \n", + "histogram(t,normalize=true) # normalize=true pour ajouter la fonction de densité\n", + "plot!(a-0.5:0.1:b+0.5, x->pdf.(dist,x), linewidth=2, xlabel=(L\"x\"), ylabel=(L\"f(x)\")) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Question\n", + "What is the problem ?\n", + "\n", + "1. Use the normalize=true parameter in the histogram function for solving the problem\n", + "2. Execute for a sample of N = 10000 datas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example of discret distribution : the binomial distribution\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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theorem : \n", + "\n", + "Suppose $X_1,X_2,\\ldots$ is a sequence of Independent and identically distributed random variables with $E(X_i)=\\mu$ and $Var(X_i)=\\sigma^2 < +\\infty$. Then, as $n$ approaches infinity, the random variables $\\sqrt{n}(\\bar{X}_n - \\mu)$ converge in distribution to a normal distribution $\\mathcal{N}(0,\\sigma^2)$\n", + "\n", + "\n", + "### Exercise\n", + "1. Choose a distribution law dist, compute its mean $\\mu$ and its variance $\\sigma^2$ and $N$ the number of sanple\n", + "2. For $n$ in (1,2,5,20)\n", + " 1. Generate N=10000 samples of lenght n from the dist distribution\n", + " 2. Compute the means of the $N$ samples and the $N$ values $\\sqrt{n}(\\bar{X}_n - \\mu)$\n", + " 3. Plot the histogram of these $N$ values and the normal distribution $\\mathcal{N}(0,\\sigma^2)$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.0874056079526329 1.6998045658400844 1.6806046431067263; 0.5501782806508928 1.2933867363767768 1.2738051760050584]\n" + ] + }, + { + "data": { + "text/plain": [ + "1×3 Matrix{Float64}:\n", + " 0.818792 1.4966 1.4772" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = rand(dist,(2,3))\n", + "println(X)\n", + "(mean(X,dims=1))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "$\\mu = $6.0\n", + "$\\sigma = $3.4641016151377544\n", + "Any[Plot{Plots.GRBackend() n=2}, Plot{Plots.GRBackend() n=2}, Plot{Plots.GRBackend() n=2}, Plot{Plots.GRBackend() n=2}]\n" + ] + }, + { + "data": { + "image/png": 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"outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.10.5", + "language": "julia", + "name": "julia-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/M2/TP2-linear-regression-sol.ipynb b/M2/TP2-linear-regression-sol.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..0b17ffb05e3be142657311c02175b6af9a01fa5c --- /dev/null +++ b/M2/TP2-linear-regression-sol.ipynb @@ -0,0 +1,20860 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# TP2 : Linear regression\n", + "## Parameters estimation by least square\n", + "\n", + "### Datas : Cholesterol $(y_i)_{i=1,\\ldots,n}$ level versus ages variable $(x)_{i=1,\\ldots,n}$\n", + "\n", + "### Assumptions\n", + "We suppose that for $i=1,\\ldots,n$\n", + "$$Y_i=\\beta_0+\\beta_1 x+\\varepsilon_i$$\n", + "\n", + "with\n", + "- $E(\\varepsilon_i)=0$\n", + "- The $(\\varepsilon_i)_{i=1,\\dots,n}$ are i.i.d.\n", + "- The distributions of $(\\varepsilon_i)_{i=1,\\dots,n}$ are $\\mathcal{N}(0,\\sigma^2)$\n", + "\n", + "### Mean square estimations\n", + "\n", + "We use the mean square estimation of the parameters $\\beta_0$ and $\\beta_1$: \n", + "\n", + "\\begin{array}{ll}\n", + "Min\\quad\n", + "f(\\beta)=\\frac{1}{2}\\sum_{i=1}^{n}r_{i}^{2}(\\beta)& =\\frac{1}{2}\\|r(\\beta)\\|^2\\\\\n", + "\\beta \\in \\mathbf{R}^{2}&\n", + "\\end{array}\n", + "\n", + "where $r$ is the residual function\n", + "$$r:\\mathbf{R}^2\\rightarrow \\mathbf{R}^n$$\n", + "$$r_i(\\beta) = y_i - \\beta_{0}+\\beta_{1}x_{i}$$\n", + "\n", + "So we can write\n", + "$$r(\\beta) = y - X\\beta,$$\n", + "where\n", + "\n", + "$$y = \\begin{pmatrix} y_1\\\\ \\vdots \\\\ y_n\\end{pmatrix}\\;\\,\\texttt{and}\\;\\;\n", + " X = \\begin{pmatrix} 1 & x_1\\\\ \\vdots & \\vdots \\\\ 1 & x_n\\end{pmatrix}$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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LaTeXStrings\n", + "using Statistics\n", + "using DataFrames\n", + "using GLM\n", + "\n", + "y=[1.8, 2.3, 2, 2.4, 2, 2.5, 2.6, 2.6, 2.9, 2.3, 2.4, 2.1, 2.5, 2.7, 2.7, 3, 3.1, 2.3, 2.5, 3, 3.3, 2.7, 3.1, 2.9, 3.4, 2.4, 3.4, 3.7, 2.8, 3.3, 3.5, 3.3, 2.6]\n", + "x=[25, 25, 25, 25, 25, 25, 25, 35, 35, 35, 35, 35, 35, 35, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 65, 65, 65, 65, 65, 65]\n", + "n = length(x)\n", + "\n", + "p = plot(x,y, seriestype = :scatter, xlabel = (L\"x\"), ylabel = (L\"y\"))\n", + "a , b = .5 , 0.04\n", + "plot!(p,x,a .+ b*x)\n", + "\n", + "r(a,b) = y - (a .+ b*x)\n", + "\n", + "r(a,b)\n", + "\n", + "i = 11\n", + "plot!(p, [x[i],x[i]], [y[i],a+b*x[i]],linewidth=3)\n", + "annotate!(p,x[i],mean([y[i],a+b*x[i]]),text(L\"r_{11}(a,b)\", :left, :green))\n", + "plot(p,legend=false)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For solving the optimization problem we have to sole the linear system $X^TX\\beta = X^Ty$\n", + "\n", + "Use the \\ operator for solving linear equation" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.639575381679391, 0.024909351145038124]\n", + "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}\n", + "\n", + "chol ~ 1 + age\n", + "\n", + "Coefficients:\n", + "────────────────────────────────────────────────────────────────────────\n", + " Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95%\n", + "────────────────────────────────────────────────────────────────────────\n", + "(Intercept) 1.63958 0.189994 8.63 <1e-09 1.25208 2.02707\n", + "age 0.0249094 0.00413632 6.02 <1e-05 0.0164733 0.0333454\n", + "────────────────────────────────────────────────────────────────────────\n", + "Normal equation : βhat₀, βhat₁ = 1.6395753816793879, 0.0249093511450382\n", + "\\ of julia : βhat₀, βhat₁ = 1.6395753816793897, 0.02490935114503816\n", + "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m\n" + ] + } + ], + "source": [ + "# \n", + "# Use of the GLM Package\n", + "datas = DataFrame(age=x, chol = y)\n", + "lm1 = lm(@formula(chol ~ age), datas)\n", + "println(coef(lm1))\n", + "println(lm1)\n", + "\n", + "# ... To complete\n", + "X = [ones(n) x]\n", + "\n", + "βhat₀, βhat₁ = (X'*X)\\(X'*y)\n", + "βhat = [βhat₀, βhat₁]\n", + "println(\"Normal equation : βhat₀, βhat₁ = \", βhat₀, \", \", βhat₁)\n", + "βhat₀, βhat₁ = X\\y\n", + "println(\"\\\\ of julia : βhat₀, βhat₁ = \", βhat₀, \", \", βhat₁)\n", + "p = plot(x,y, seriestype = :scatter, xlabel = (L\"x\"), ylabel = (L\"y\"))\n", + "plot!(p,x,βhat₀ .+ βhat₁*x)\n", + "\n", + "println(@test βhat ≈ coef(lm1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Confidence intervals of the parameters\n", + "\n", + "- We note $r_i = y_i - (\\hat{\\beta}_0 + \\hat{\\beta}_1x_i)$, then the unbiased estimation of the variance $\\sigma^2$ is\n", + "\n", + "$$\\hat{\\sigma}^2\\frac{\\sum_ir_i^2}{n-2}$$\n", + "\n", + "- As $\\hat{\\beta} = (X^TX)^{-1}X^Ty$ the statistic $B=(X^TX)^{-1}X^TY = (X^TX)^{-1}X^T(X\\beta+\\varepsilon)=\\beta +(X^TX)^{-1}X^T\\varepsilon$ as the $\\mathcal{N}(\\beta,\\sigma^2(X^TX)^{-1})$ distribution. \n", + "\n", + "Si les postulats sont vérifiés alors les\n", + "intervalles de confiances de $\\beta _{0},\\beta _{1}$ et $\\sigma ^{2}$ au\n", + "seuil $(1-\\alpha )$ sont:\n", + "\n", + "\n", + "- \n", + "$$\n", + "\\sigma ^{2}\\in \\left[ \\frac{\\sum_{i=1}^{n}r_{i}^{2}}{\\chi _{1-\\alpha /2}};%\n", + "\\frac{\\sum_{i=1}^{n}r_{i}^{2}}{\\chi _{\\alpha /2}}\\right] \n", + "$$\n", + "\n", + "where $\\chi _{1-\\alpha /2}$ and $\\chi _{\\alpha /2}$ sont lues\n", + "dans le table du Khi-2 à $\\nu =n-2$ ddl.\n", + "\n", + "\\item \n", + "$$\n", + "\\begin{array}{ccc}\n", + "\\beta _{1} & \\in & [\\hat{\\beta}_{1}-t_{1-\\alpha /2}\\hat{\\sigma}%\n", + "_{B_{1}}^{{}};\\hat{\\beta}_{1}+t_{1-\\alpha /2}\\hat{\\sigma}_{B_{1}}^{{}}] \\\\ \n", + "\\beta _{0} & \\in & [\\hat{\\beta}_{0}-t_{1-\\alpha /2}\\hat{\\sigma}%\n", + "_{B_{0}}^{{}};\\hat{\\beta}_{0}+t_{1-\\alpha /2}\\hat{\\sigma}_{B_{0}}^{{}}]\n", + "\\end{array}\n", + "$$\n", + "\n", + "où \n", + "- $\\hat{\\sigma}_{B_{1}}^{2} = \\dfrac{\\hat{\\sigma}^{2}}{SCE_{x}} $\n", + "- $\\hat{\\sigma}_{B_{0}}^{2} = \\hat{\\sigma}^{2}(\\dfrac{1}{n}+\\dfrac{\\bar{x}^{2}}{SCE_{x}})$\n", + "- $t_{1-\\alpha /2}$ from the Student law with $n-2$ degrees of freedom\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise\n", + "1. Compute the $n$ residuals in the vector res\n", + "2. Compute the estimation of residual variance $\\sigma^2$ and of the standard error $\\sigma$\n", + "3. Compute the estimation of the variance, covariance matrix $\\Sigma$.\n", + "4. Compute the estimation of the standard error of $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$.\n", + "5. Compute the confidence intervalle of $\\beta_0$ and $\\beta_1$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test residuals : \u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m\n", + "σ²hat = 0.10866889312977099\n", + "σ²hat = 0.10866889312977099\n", + "Σ = [0.03609767024885643 -0.0007491724741055301; -0.0007491724741055301 1.710912916642387e-5]\n", + "Test Variance, covariance matrix : \u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m\n", + "test of the variance of σhat₀ : \u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m\n", + "test of the variance of σhat₁ : \u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m\n", + "β₀ ∈ [1.2520803311678832,2.027070432190896]\n", + "β₁ ∈ [0.016473274332038396,0.033345427958037924]\n" + ] + } + ], + "source": [ + "# Compute the residuals\n", + "res = y-X*βhat \n", + "println(\"Test residuals : \",@test res ≈ residuals(lm1))\n", + "\n", + "# estimation of σ²\n", + "σ²hat = sum(res.^2)/(n-2) \n", + "σhat = sqrt(σ²hat)\n", + "println(\"σ²hat = \", σ²hat)\n", + "\n", + "\n", + "println(\"σ²hat = \", σ²hat)\n", + "\n", + "\n", + "# Variances, covariances matrix of B\n", + "Σ = σ²hat*inv(X'*X) \n", + "println(\"Σ = \", Σ)\n", + "covB = vcov(lm1) # GLM Package\n", + "println(\"Test Variance, covariance matrix : \", @test Σ ≈ covB)\n", + "\n", + "using Distributions\n", + "using HypothesisTests\n", + "α = 0.05\n", + "\n", + "t_crit = quantile(TDist(n-2),1-α/2)\n", + "\n", + "σhat₀ = sqrt(Σ[1,1])\n", + "σhat₁ = sqrt(Σ[2,2])\n", + "println(\"test of the variance of σhat₀ : \", @test σhat₀ ≈ stderror(lm1)[1])\n", + "println(\"test of the variance of σhat₁ : \", @test σhat₁ ≈ stderror(lm1)[2])\n", + "\n", + "println(\"β₀ ∈ [\", βhat₀ - t_crit*σhat₀, \",\",βhat₀ + t_crit*σhat₀,\"]\")\n", + "println(\"β₁ ∈ [\", βhat₁ - t_crit*σhat₁, \",\",βhat₁ + t_crit*σhat₁,\"]\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Confidence Bands and Prediction Bands\n", + "- The condidence band for the mean is\n", + "$$\\hat{\\beta}_0 +\\hat{\\beta}_1x \\pm t_{1-\\alpha/2}\\hat{\\sigma}\\sqrt{\\frac{1}{n}+\\frac{(x-\\bar{x})^2}{SCE_x}}$$\n", + "- The Prediction band is \n", + "$$\\hat{\\beta}_0 +\\hat{\\beta}_1x \\pm t_{1-\\alpha/2}\\hat{\\sigma}\\sqrt{1+\\frac{1}{n}+\\frac{(x-\\bar{x})^2}{SCE_x}}$$\n", + "\n", + "### Exercice\n", + "Plot these confidence and prevision bands on the graph p" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n= 33\n", + "x = [25, 25, 25, 25, 25, 25, 25, 35, 35, 35, 35, 35, 35, 35, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 65, 65, 65, 65, 65, 65]\n" + ] + }, + { + "data": { + "image/png": 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fill-opacity=\"1\" /></svg>\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "println(\"n= \", n)\n", + "println(\"x = \", x)\n", + "\n", + "\n", + "t_crit = quantile(TDist(n-2),1-α/2)\n", + "xbar = mean(x)\n", + "SCE = sum((x .- xbar).^2)\n", + "xx = 20:1:70\n", + "p = plot(x,y, seriestype = :scatter, xlabel = (L\"x\"), ylabel = (L\"y\"), label=\"\")\n", + "plot!(p,xx,βhat₀ .+ βhat₁*xx, label=\"\")\n", + "\n", + "# Confidence Bands\n", + "\n", + "yy_sup = βhat₀ .+ βhat₁*xx + t_crit*σhat*sqrt.(1/n .+ (xx .-xbar).^2/SCE)\n", + "plot!(p, xx, yy_sup, c=:green, label = \"Confidence bands\")\n", + "yy_inf = βhat₀ .+ βhat₁*xx - t_crit*σhat*sqrt.(1/n .+ (xx .-xbar).^2/SCE)\n", + "plot!(p, xx, yy_inf, c=:green, label = \"\")\n", + "\n", + "# Prevision Bands\n", + "xx = 20:1:70\n", + "yy_sup = βhat₀ .+ βhat₁*xx + t_crit*σhat*sqrt.(1 .+ 1/n .+ (xx .-xbar).^2/SCE)\n", + "plot!(p, xx, yy_sup, c=:blue, label = \"Prevision bands\")\n", + "yy_inf = βhat₀ .+ βhat₁*xx - t_crit*σhat*sqrt.(1 .+ 1/n .+ (xx .-xbar).^2/SCE)\n", + "plot!(p, xx, yy_inf, c=:blue, label = \"\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulation of the distribution the estimates of $\\beta_0$ and $\\beta_1$\n", + "\n", + "We consider the model\n", + "$$Y_i = \\beta_0 + \\beta_1 x_i + \\varepsilon_i$$\n", + "with\n", + "- $(\\varepsilon_i)_{i=1,\\ldots,n}$ i.i.d.\n", + "- The $\\varepsilon_i$ have the $\\mathcal{N}(0,\\sigma^2)$ distribution\n", + "- $(x_1,\\ldots,x_n) = (1,2,\\ldots,10)$\n", + "- $\\beta_0 = 2.0, \\beta_1 = 1.5$ and $\\sigma = 1.5$\n", + "\n", + "We recall that the statistic $B$ which estimate the parameter $\\beta$ follows the $\\mathcal{N}(\\beta,\\Sigma)$ distribution, with $\\Sigma=\\sigma^2(X^TX)^{-1}$.\n", + "\n", + "### Exercise (more difficult)\n", + "1. Define a function coefEst() with return the estimation of the parameters $\\beta_0$ and $\\beta_1$.\n", + " We generate a sample of size $n=10$ of the $(y_i)_{i=1,\\ldots,n}$ inside the fonction \n", + "2. Compute $N$ samples of the estimation $\\hat{\\beta}$\n", + "3. Compute $\\Sigma^{-1}$\n", + "4. " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Percentage of points inside the ellipse : 0.9495\n" + ] + }, + { + "data": { + "image/png": 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coeff(model)\n", + " \"\"\"\n", + " yVals = β₀ .+ β₁*xVals +rand(Normal(0,σ),n) # genetating a sample\n", + " data = DataFrame([xVals,yVals], [:x, :y]) # create a DataFrame from the datas\n", + " model = lm(@formula(y ~ x), data) # linear regresseion\n", + " return (coef(model)) # return the estimation of β₀ and β₁\n", + "end\n", + "\n", + "ests = [coefEst() for _ in 1:N] # generating N sample of the parameters (in an array)\n", + "\n", + "# The statistic B which estimate β follows the N(β,Σ) distribution with, Σ = σ²(XᵀX)⁻¹\n", + "Σ⁻¹ = (1/σ^2)*X'*X # Compute the inverse of the variance, covariance matrix \n", + "A = cholesky(Σ⁻¹).U # Z = A(B-β) follows the N(0,I) distribution\n", + "A⁻¹ = inv(A)\n", + "# The radius of a standard bidimensional normal distribution follows a Rayleigh law\n", + "radius = quantile(Rayleigh(),1-α) # Z₁² + Z₂² follows a χ^2 with 2 dof distribution\n", + "isInEllipse(b) = norm(A*(b-β)) <= radius # function which indicate if b is in the ellipse or not.\n", + " # A*(b-β) transform an ellipse to a circle\n", + "estIn = isInEllipse.(ests) # Vectorize the function\n", + "\n", + "println(\"Percentage of points inside the ellipse : \", sum(estIn)/N)\n", + "scatter(first.(ests[estIn]), last.(ests[estIn]), color = :green, ms=2, msw=0) # display points inside the ellipse \n", + "scatter!(first.(ests[.!estIn]), last.(ests[.!estIn]), color = :red, ms=2, msw=0) # display points outside the ellipse\n", + "# Calculus of the ellipse\n", + "ellipsePts = [radius*A⁻¹*[cos(t),sin(t)] + β for t in 0:0.01:2*pi] # compute the ellipse\n", + "scatter!([β₀], [β₁], c=:red, ms=5, msw=2) # display the center of the ellipse\n", + "plot!(first.(ellipsePts), last.(ellipsePts), c=:blue, lw=2, legend=false,xlabel=L\"\\hat{\\beta}_0\", ylabel=L\"\\hat{\\beta}_1\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.10.5", + "language": "julia", + "name": "julia-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}