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zc=*-RKK`8+FHyHD{?gxXdZUlaqinq3AEIYo81+FMn@~c~S zk zypdnpG-=O+pV;26ntJ~DVj6>z#w;eENXtV zkUf&E_EhqNH8mhRR#Tl>OysGdT4(i0->PE+7y?e?>p`sJHKy}>OAQBVG~Q8@t$B?5Dm>=w3J2P!HvgJ09l`V* z?aRdA@XY2rG%(F!z}0kr{$RF*37M{*D*lI>I}3Xo4tK$?b-;rLtL1v72NU$s{dqJZ Vtk5_WJ3wi~HaOh>u6p;H{|801sWbop diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek37.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek37.doctree index 6fb5ac1d6fd94d8cc1b652755e206880b86e3b42..4c2740d6389d651928e2f75f0f3865ac2ab9a354 100644 GIT binary patch delta 123 zcmeC3%eZAOBTED8)Rh}q9_TT;P1ev?n#``xFOZ*;Qe2svl%G=_layMLSUXu#ztLSj d1}K0KM`nZ6)K1A@kDZbs*h4_w=HvRu\(\boldsymbol{X}\boldsymbo \[ \mathbb{E}(\boldsymbol{\hat{\beta}}) = \boldsymbol{\beta}. \] -

Show finally that the variance of \(\boldsymbol{\beta}\) is

+

Show finally that the variance of \(\boldsymbol{\boldsymbol{\beta}}\) is

\[ \mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}. diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb index f5cfe5ddf..cc9e06cfc 100644 --- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ebfc874e", + "id": "cfebae03", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "8ecf95b0", + "id": "353ebb07", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "7940e437", + "id": "c02815dd", "metadata": { "editable": true }, @@ -45,7 +45,7 @@ }, { "cell_type": "markdown", - "id": "964cf4c4", + "id": "fb152043", "metadata": { "editable": true }, @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "bc8b093a", + "id": "9aba7a46", "metadata": { "editable": true }, @@ -68,7 +68,7 @@ }, { "cell_type": "markdown", - "id": "bc1907b5", + "id": "be52c097", "metadata": { "editable": true }, @@ -80,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "c7d29897", + "id": "c54979e5", "metadata": { "editable": true }, @@ -90,7 +90,7 @@ }, { "cell_type": "markdown", - "id": "e45dbe57", + "id": "4b1eb811", "metadata": { "editable": true }, @@ -102,7 +102,7 @@ }, { "cell_type": "markdown", - "id": "0331d3dd", + "id": "036a5440", "metadata": { "editable": true }, @@ -114,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "51159839", + "id": "f7fb8094", "metadata": { "editable": true }, @@ -125,7 +125,7 @@ }, { "cell_type": "markdown", - "id": "6df6ca33", + "id": "d7d92995", "metadata": { "editable": true }, @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "6bf812e3", + "id": "29eb9701", "metadata": { "editable": true }, @@ -150,7 +150,7 @@ }, { "cell_type": "markdown", - "id": "1e04714b", + "id": "aa106511", "metadata": { "editable": true }, @@ -162,17 +162,17 @@ }, { "cell_type": "markdown", - "id": "621afaa2", + "id": "58be1091", "metadata": { "editable": true }, "source": [ - "Show finally that the variance of $\\boldsymbol{\\beta}$ is" + "Show finally that the variance of $\\boldsymbol{\\boldsymbol{\\beta}}$ is" ] }, { "cell_type": "markdown", - "id": "b7aa535d", + "id": "4cb58e41", "metadata": { "editable": true }, @@ -184,7 +184,7 @@ }, { "cell_type": "markdown", - "id": "45ea3a92", + "id": "a04df28d", "metadata": { "editable": true }, @@ -195,7 +195,7 @@ }, { "cell_type": "markdown", - "id": "3851ded2", + "id": "c095c96a", "metadata": { "editable": true }, @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "c759e617", + "id": "5d425a79", "metadata": { "editable": true }, @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "c16482df", + "id": "fb89cfab", "metadata": { "editable": true }, @@ -233,7 +233,7 @@ }, { "cell_type": "markdown", - "id": "2e2cda9b", + "id": "aea8801c", "metadata": { "editable": true }, @@ -245,7 +245,7 @@ }, { "cell_type": "markdown", - "id": "d69a45ab", + "id": "0e885693", "metadata": { "editable": true },