diff --git a/doc/pub/week35/html/._week35-bs045.html b/doc/pub/week35/html/._week35-bs045.html index e2c994e45..57965c4a3 100644 --- a/doc/pub/week35/html/._week35-bs045.html +++ b/doc/pub/week35/html/._week35-bs045.html @@ -350,16 +350,17 @@ $$

which gives us, using the orthogonality of the matrix \( \boldsymbol{V} \),

$$ -\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, +\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, $$ +

which is not the same as \( \tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y} \), which due to the orthogonality of \( \boldsymbol{U} \) would have given us that the model equals the output.

+

It means that the ordinary least square model (with the optimal parameters) \( \boldsymbol{\tilde{y}} \), corresponds to an orthogonal transformation of the output (or target) vector \( \boldsymbol{y} \) by the vectors of the matrix \( \boldsymbol{U} \). Note that the summation ends at \( p-1 \), that is \( \boldsymbol{\tilde{y}}\ne \boldsymbol{y} \). We can thus not use the -orthogonality relation for the matrix \( \boldsymbol{U} \). This can already be -when we multiply the matrices \( \boldsymbol{\Sigma}^T\boldsymbol{U}^T \). +orthogonality relation for the matrix \( \boldsymbol{U} \).

diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html index 1e819dcec..9a5fc265a 100644 --- a/doc/pub/week35/html/week35-reveal.html +++ b/doc/pub/week35/html/week35-reveal.html @@ -2189,17 +2189,18 @@ $$

 
$$ -\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, +\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, $$

 
+

which is not the same as \( \tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y} \), which due to the orthogonality of \( \boldsymbol{U} \) would have given us that the model equals the output.

+

It means that the ordinary least square model (with the optimal parameters) \( \boldsymbol{\tilde{y}} \), corresponds to an orthogonal transformation of the output (or target) vector \( \boldsymbol{y} \) by the vectors of the matrix \( \boldsymbol{U} \). Note that the summation ends at \( p-1 \), that is \( \boldsymbol{\tilde{y}}\ne \boldsymbol{y} \). We can thus not use the -orthogonality relation for the matrix \( \boldsymbol{U} \). This can already be -when we multiply the matrices \( \boldsymbol{\Sigma}^T\boldsymbol{U}^T \). +orthogonality relation for the matrix \( \boldsymbol{U} \).

diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html index ae4055a7f..7c8cb8843 100644 --- a/doc/pub/week35/html/week35-solarized.html +++ b/doc/pub/week35/html/week35-solarized.html @@ -2062,16 +2062,17 @@ $$

which gives us, using the orthogonality of the matrix \( \boldsymbol{V} \),

$$ -\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, +\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, $$ +

which is not the same as \( \tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y} \), which due to the orthogonality of \( \boldsymbol{U} \) would have given us that the model equals the output.

+

It means that the ordinary least square model (with the optimal parameters) \( \boldsymbol{\tilde{y}} \), corresponds to an orthogonal transformation of the output (or target) vector \( \boldsymbol{y} \) by the vectors of the matrix \( \boldsymbol{U} \). Note that the summation ends at \( p-1 \), that is \( \boldsymbol{\tilde{y}}\ne \boldsymbol{y} \). We can thus not use the -orthogonality relation for the matrix \( \boldsymbol{U} \). This can already be -when we multiply the matrices \( \boldsymbol{\Sigma}^T\boldsymbol{U}^T \). +orthogonality relation for the matrix \( \boldsymbol{U} \).











diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html index d2cce1874..f74afd161 100644 --- a/doc/pub/week35/html/week35.html +++ b/doc/pub/week35/html/week35.html @@ -2139,16 +2139,17 @@ $$

which gives us, using the orthogonality of the matrix \( \boldsymbol{V} \),

$$ -\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, +\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y}, $$ +

which is not the same as \( \tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y} \), which due to the orthogonality of \( \boldsymbol{U} \) would have given us that the model equals the output.

+

It means that the ordinary least square model (with the optimal parameters) \( \boldsymbol{\tilde{y}} \), corresponds to an orthogonal transformation of the output (or target) vector \( \boldsymbol{y} \) by the vectors of the matrix \( \boldsymbol{U} \). Note that the summation ends at \( p-1 \), that is \( \boldsymbol{\tilde{y}}\ne \boldsymbol{y} \). We can thus not use the -orthogonality relation for the matrix \( \boldsymbol{U} \). This can already be -when we multiply the matrices \( \boldsymbol{\Sigma}^T\boldsymbol{U}^T \). +orthogonality relation for the matrix \( \boldsymbol{U} \).











diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz index 21143a638..b3bcd3921 100644 Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb index 93790600c..01ae64c94 100644 --- a/doc/pub/week35/ipynb/week35.ipynb +++ b/doc/pub/week35/ipynb/week35.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "82c2f725", + "id": "f0622ebb", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "d2fc786b", + "id": "3fe98f20", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "77512f33", + "id": "8e604e3c", "metadata": { "editable": true }, @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "41516757", + "id": "c7f0b40a", "metadata": { "editable": true }, @@ -69,7 +69,7 @@ }, { "cell_type": "markdown", - "id": "d3703d2f", + "id": "507709a4", "metadata": { "editable": true }, @@ -102,7 +102,7 @@ }, { "cell_type": "markdown", - "id": "f22b90af", + "id": "bb3b5f67", "metadata": { "editable": true }, @@ -118,7 +118,7 @@ }, { "cell_type": "markdown", - "id": "3fe305bb", + "id": "14444be5", "metadata": { "editable": true }, @@ -130,7 +130,7 @@ }, { "cell_type": "markdown", - "id": "f2f38355", + "id": "4edc5258", "metadata": { "editable": true }, @@ -140,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "c3d9a4b6", + "id": "4d6f9c43", "metadata": { "editable": true }, @@ -152,7 +152,7 @@ }, { "cell_type": "markdown", - "id": "ff3ba043", + "id": "fb52f7f5", "metadata": { "editable": true }, @@ -173,7 +173,7 @@ }, { "cell_type": "markdown", - "id": "5de294d5", + "id": "4fff6b39", "metadata": { "editable": true }, @@ -185,7 +185,7 @@ }, { "cell_type": "markdown", - "id": "5721942a", + "id": "54a4cabb", "metadata": { "editable": true }, @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "2b2aa843", + "id": "d383a507", "metadata": { "editable": true }, @@ -210,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "2b12c06f", + "id": "498fe31e", "metadata": { "editable": true }, @@ -222,7 +222,7 @@ }, { "cell_type": "markdown", - "id": "276d4eba", + "id": "7bbbdcd2", "metadata": { "editable": true }, @@ -232,7 +232,7 @@ }, { "cell_type": "markdown", - "id": "4751c9b4", + "id": "405a61ac", "metadata": { "editable": true }, @@ -244,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "dd00bf4b", + "id": "e7c07f57", "metadata": { "editable": true }, @@ -257,7 +257,7 @@ }, { "cell_type": "markdown", - "id": "bc9028f0", + "id": "6054782f", "metadata": { "editable": true }, @@ -269,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "d6a27e54", + "id": "7b55104f", "metadata": { "editable": true }, @@ -279,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "82f1494a", + "id": "4635525e", "metadata": { "editable": true }, @@ -291,7 +291,7 @@ }, { "cell_type": "markdown", - "id": "d6427a35", + "id": "11f6ffc7", "metadata": { "editable": true }, @@ -303,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "38c78421", + "id": "820ddc3f", "metadata": { "editable": true }, @@ -314,7 +314,7 @@ }, { "cell_type": "markdown", - "id": "f23ac12e", + "id": "9aa4b864", "metadata": { "editable": true }, @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "88fd9c03", + "id": "c542e149", "metadata": { "editable": true }, @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "a953b1a3", + "id": "7be13194", "metadata": { "editable": true }, @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "19eb0838", + "id": "aad2641f", "metadata": { "editable": true }, @@ -368,7 +368,7 @@ }, { "cell_type": "markdown", - "id": "a4f910a4", + "id": "9dfe7e22", "metadata": { "editable": true }, @@ -380,7 +380,7 @@ }, { "cell_type": "markdown", - "id": "5060e089", + "id": "852c82a9", "metadata": { "editable": true }, @@ -390,7 +390,7 @@ }, { "cell_type": "markdown", - "id": "8542c5a3", + "id": "84163c68", "metadata": { "editable": true }, @@ -402,7 +402,7 @@ }, { "cell_type": "markdown", - "id": "475e1436", + "id": "5bfb8965", "metadata": { "editable": true }, @@ -412,7 +412,7 @@ }, { "cell_type": "markdown", - "id": "88abf4ad", + "id": "3822fa25", "metadata": { "editable": true }, @@ -424,7 +424,7 @@ }, { "cell_type": "markdown", - "id": "62f558d9", + "id": "2c0f9f09", "metadata": { "editable": true }, @@ -435,7 +435,7 @@ }, { "cell_type": "markdown", - "id": "99cc5104", + "id": "7ce9a08c", "metadata": { "editable": true }, @@ -447,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "29043759", + "id": "3efb75ba", "metadata": { "editable": true }, @@ -457,7 +457,7 @@ }, { "cell_type": "markdown", - "id": "e9d0f067", + "id": "8c4ceb9d", "metadata": { "editable": true }, @@ -469,7 +469,7 @@ }, { "cell_type": "markdown", - "id": "c34bfdd2", + "id": "53a5a827", "metadata": { "editable": true }, @@ -479,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "3533f92e", + "id": "12d309d7", "metadata": { "editable": true }, @@ -491,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "135631d4", + "id": "16fdbfbe", "metadata": { "editable": true }, @@ -511,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "cf25f4a7", + "id": "b5651e23", "metadata": { "editable": true }, @@ -538,7 +538,7 @@ }, { "cell_type": "markdown", - "id": "5d82400a", + "id": "e3289213", "metadata": { "editable": true }, @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "00d8d123", + "id": "db9c8386", "metadata": { "editable": true }, @@ -562,7 +562,7 @@ }, { "cell_type": "markdown", - "id": "cce17e14", + "id": "ea7d7d7e", "metadata": { "editable": true }, @@ -578,7 +578,7 @@ }, { "cell_type": "markdown", - "id": "65efb775", + "id": "7dace63c", "metadata": { "editable": true }, @@ -596,7 +596,7 @@ }, { "cell_type": "markdown", - "id": "2df9efd6", + "id": "b00b4a82", "metadata": { "editable": true }, @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "37b621d8", + "id": "26392bc2", "metadata": { "editable": true }, @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "297be9c9", + "id": "f5214ffc", "metadata": { "editable": true }, @@ -631,7 +631,7 @@ }, { "cell_type": "markdown", - "id": "fe288c99", + "id": "0eec52de", "metadata": { "editable": true }, @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "d4333779", + "id": "077e4fe0", "metadata": { "editable": true }, @@ -653,7 +653,7 @@ }, { "cell_type": "markdown", - "id": "f7e72c3d", + "id": "e3ff215c", "metadata": { "editable": true }, @@ -665,7 +665,7 @@ }, { "cell_type": "markdown", - "id": "3423b702", + "id": "6cb9ae59", "metadata": { "editable": true }, @@ -679,7 +679,7 @@ }, { "cell_type": "markdown", - "id": "fe66f713", + "id": "7a02062e", "metadata": { "editable": true }, @@ -691,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "43eed51b", + "id": "45f73c0f", "metadata": { "editable": true }, @@ -703,7 +703,7 @@ }, { "cell_type": "markdown", - "id": "6f943ccb", + "id": "6c9d24a2", "metadata": { "editable": true }, @@ -715,7 +715,7 @@ }, { "cell_type": "markdown", - "id": "5df09c55", + "id": "241fed59", "metadata": { "editable": true }, @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "b92d9f2a", + "id": "1c67de99", "metadata": { "editable": true }, @@ -737,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "c6cf49ab", + "id": "36af470a", "metadata": { "editable": true }, @@ -749,7 +749,7 @@ }, { "cell_type": "markdown", - "id": "3e000448", + "id": "38f9d9cf", "metadata": { "editable": true }, @@ -761,7 +761,7 @@ }, { "cell_type": "markdown", - "id": "fbaa984b", + "id": "b20c89a1", "metadata": { "editable": true }, @@ -775,7 +775,7 @@ }, { "cell_type": "markdown", - "id": "f4e444ea", + "id": "e56ba6c5", "metadata": { "editable": true }, @@ -787,7 +787,7 @@ }, { "cell_type": "markdown", - "id": "454ba5ba", + "id": "1481f969", "metadata": { "editable": true }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "c0434cd9", + "id": "fbd29e7c", "metadata": { "editable": true }, @@ -811,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "f2bcda9d", + "id": "889c22f1", "metadata": { "editable": true }, @@ -821,7 +821,7 @@ }, { "cell_type": "markdown", - "id": "aea0ba73", + "id": "5a753c31", "metadata": { "editable": true }, @@ -833,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "5a58d6e8", + "id": "4fed4676", "metadata": { "editable": true }, @@ -843,7 +843,7 @@ }, { "cell_type": "markdown", - "id": "927428aa", + "id": "e1894902", "metadata": { "editable": true }, @@ -855,7 +855,7 @@ }, { "cell_type": "markdown", - "id": "372ad443", + "id": "ddca93b1", "metadata": { "editable": true }, @@ -865,7 +865,7 @@ }, { "cell_type": "markdown", - "id": "37a99489", + "id": "5f9d8901", "metadata": { "editable": true }, @@ -877,7 +877,7 @@ }, { "cell_type": "markdown", - "id": "4872a1cd", + "id": "726c169c", "metadata": { "editable": true }, @@ -889,7 +889,7 @@ }, { "cell_type": "markdown", - "id": "b21e9cb2", + "id": "7d7715d5", "metadata": { "editable": true }, @@ -901,7 +901,7 @@ }, { "cell_type": "markdown", - "id": "442375d1", + "id": "057fedd9", "metadata": { "editable": true }, @@ -916,7 +916,7 @@ }, { "cell_type": "markdown", - "id": "aabab237", + "id": "4c06fecd", "metadata": { "editable": true }, @@ -928,7 +928,7 @@ }, { "cell_type": "markdown", - "id": "106f09df", + "id": "490e6469", "metadata": { "editable": true }, @@ -938,7 +938,7 @@ }, { "cell_type": "markdown", - "id": "73d8f824", + "id": "b6259635", "metadata": { "editable": true }, @@ -950,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "f2626be7", + "id": "0fda0191", "metadata": { "editable": true }, @@ -960,7 +960,7 @@ }, { "cell_type": "markdown", - "id": "81d89d86", + "id": "797e356f", "metadata": { "editable": true }, @@ -972,7 +972,7 @@ }, { "cell_type": "markdown", - "id": "59c2576a", + "id": "46bdaee6", "metadata": { "editable": true }, @@ -982,7 +982,7 @@ }, { "cell_type": "markdown", - "id": "4b7bf3f9", + "id": "cb1f5f36", "metadata": { "editable": true }, @@ -994,7 +994,7 @@ }, { "cell_type": "markdown", - "id": "ea1e8943", + "id": "fa70c555", "metadata": { "editable": true }, @@ -1006,7 +1006,7 @@ }, { "cell_type": "markdown", - "id": "d0425d72", + "id": "2fdb367f", "metadata": { "editable": true }, @@ -1018,7 +1018,7 @@ }, { "cell_type": "markdown", - "id": "38386834", + "id": "ced6532f", "metadata": { "editable": true }, @@ -1028,7 +1028,7 @@ }, { "cell_type": "markdown", - "id": "bfbc4bd3", + "id": "49c27708", "metadata": { "editable": true }, @@ -1040,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "3ced3cec", + "id": "27da1de0", "metadata": { "editable": true }, @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "fc6f1dec", + "id": "9ddef35d", "metadata": { "editable": true }, @@ -1065,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "699662d2", + "id": "ae006a7e", "metadata": { "editable": true }, @@ -1075,7 +1075,7 @@ }, { "cell_type": "markdown", - "id": "0991592c", + "id": "904d2486", "metadata": { "editable": true }, @@ -1087,7 +1087,7 @@ }, { "cell_type": "markdown", - "id": "450dd961", + "id": "525eda84", "metadata": { "editable": true }, @@ -1097,7 +1097,7 @@ }, { "cell_type": "markdown", - "id": "a13de0fa", + "id": "7eadfb46", "metadata": { "editable": true }, @@ -1109,7 +1109,7 @@ }, { "cell_type": "markdown", - "id": "c64bc916", + "id": "8ee45bc9", "metadata": { "editable": true }, @@ -1119,7 +1119,7 @@ }, { "cell_type": "markdown", - "id": "ab1e18bc", + "id": "73b41248", "metadata": { "editable": true }, @@ -1131,7 +1131,7 @@ }, { "cell_type": "markdown", - "id": "f1e74f34", + "id": "dc4356aa", "metadata": { "editable": true }, @@ -1141,7 +1141,7 @@ }, { "cell_type": "markdown", - "id": "1ad3ebd9", + "id": "3e2b94a9", "metadata": { "editable": true }, @@ -1153,7 +1153,7 @@ }, { "cell_type": "markdown", - "id": "37d1b4ca", + "id": "b9716f36", "metadata": { "editable": true }, @@ -1163,7 +1163,7 @@ }, { "cell_type": "markdown", - "id": "3d5fc67a", + "id": "01341a5b", "metadata": { "editable": true }, @@ -1175,7 +1175,7 @@ }, { "cell_type": "markdown", - "id": "d98472d9", + "id": "83a3f463", "metadata": { "editable": true }, @@ -1191,7 +1191,7 @@ }, { "cell_type": "markdown", - "id": "5d859f20", + "id": "c2c42203", "metadata": { "editable": true }, @@ -1203,7 +1203,7 @@ }, { "cell_type": "markdown", - "id": "e7bb91ec", + "id": "94f060b9", "metadata": { "editable": true }, @@ -1213,7 +1213,7 @@ }, { "cell_type": "markdown", - "id": "1553864b", + "id": "d0e5c32c", "metadata": { "editable": true }, @@ -1225,7 +1225,7 @@ }, { "cell_type": "markdown", - "id": "f8cc9c71", + "id": "0b464ed4", "metadata": { "editable": true }, @@ -1243,7 +1243,7 @@ }, { "cell_type": "markdown", - "id": "f1f01477", + "id": "5c952119", "metadata": { "editable": true }, @@ -1255,7 +1255,7 @@ }, { "cell_type": "markdown", - "id": "f2dea7e1", + "id": "25e4a5f3", "metadata": { "editable": true }, @@ -1267,7 +1267,7 @@ }, { "cell_type": "markdown", - "id": "76b0f99e", + "id": "4f774737", "metadata": { "editable": true }, @@ -1277,7 +1277,7 @@ }, { "cell_type": "markdown", - "id": "cfa3ca25", + "id": "59c91b82", "metadata": { "editable": true }, @@ -1289,7 +1289,7 @@ }, { "cell_type": "markdown", - "id": "9a9163d8", + "id": "33ceec0f", "metadata": { "editable": true }, @@ -1299,7 +1299,7 @@ }, { "cell_type": "markdown", - "id": "c6b54a1e", + "id": "931da8ef", "metadata": { "editable": true }, @@ -1311,7 +1311,7 @@ }, { "cell_type": "markdown", - "id": "659c98d0", + "id": "2f2516b6", "metadata": { "editable": true }, @@ -1321,7 +1321,7 @@ }, { "cell_type": "markdown", - "id": "209b5b37", + "id": "bcb56a20", "metadata": { "editable": true }, @@ -1335,7 +1335,7 @@ }, { "cell_type": "markdown", - "id": "b325d0c3", + "id": "86333a6f", "metadata": { "editable": true }, @@ -1347,7 +1347,7 @@ }, { "cell_type": "markdown", - "id": "c49a2fcd", + "id": "1513e73c", "metadata": { "editable": true }, @@ -1358,7 +1358,7 @@ }, { "cell_type": "markdown", - "id": "6978ef70", + "id": "c8c47d9a", "metadata": { "editable": true }, @@ -1371,13 +1371,10 @@ { "cell_type": "code", "execution_count": 1, - "id": "01530c39", + "id": "8ec18f31", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1401,7 +1398,7 @@ }, { "cell_type": "markdown", - "id": "90ff28d4", + "id": "b7255330", "metadata": { "editable": true }, @@ -1412,13 +1409,10 @@ { "cell_type": "code", "execution_count": 2, - "id": "1d052cbe", + "id": "9d5f3a70", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1428,7 +1422,7 @@ }, { "cell_type": "markdown", - "id": "3362efd4", + "id": "8daa4681", "metadata": { "editable": true }, @@ -1442,13 +1436,10 @@ { "cell_type": "code", "execution_count": 3, - "id": "3e9e681f", + "id": "de91ca73", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1458,7 +1449,7 @@ }, { "cell_type": "markdown", - "id": "78e4427f", + "id": "442ef680", "metadata": { "editable": true }, @@ -1469,13 +1460,10 @@ { "cell_type": "code", "execution_count": 4, - "id": "20aab659", + "id": "9b329ab4", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1484,7 +1472,7 @@ }, { "cell_type": "markdown", - "id": "326f641d", + "id": "d7ded522", "metadata": { "editable": true }, @@ -1495,13 +1483,10 @@ { "cell_type": "code", "execution_count": 5, - "id": "c8e80cf1", + "id": "34c18b8f", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1514,7 +1499,7 @@ }, { "cell_type": "markdown", - "id": "aba7b289", + "id": "229d94fa", "metadata": { "editable": true }, @@ -1525,13 +1510,10 @@ { "cell_type": "code", "execution_count": 6, - "id": "7235bf1b", + "id": "afb92eb9", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1542,7 +1524,7 @@ }, { "cell_type": "markdown", - "id": "3eaf5f8d", + "id": "8a02aaaf", "metadata": { "editable": true }, @@ -1563,7 +1545,7 @@ }, { "cell_type": "markdown", - "id": "6fc5dc26", + "id": "b64b7d81", "metadata": { "editable": true }, @@ -1573,33 +1555,13 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "98ca5627", + "execution_count": 7, + "id": "094eed3e", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 2.00000015e+00 -1.33455722e-06 5.00000368e+00 -4.56206180e-06\n", - " 3.29741124e-06 -1.41302735e-06 7.29192834e-07 -2.87627245e-07]\n", - "Training R2\n", - "0.9999999999999959\n", - "Training MSE\n", - "9.120225711002453e-15\n", - "Test R2\n", - "0.9999999999999963\n", - "Test MSE\n", - "6.3758192923440154e-15\n" - ] - } - ], + "outputs": [], "source": [ "%matplotlib inline\n", "\n", @@ -1617,19 +1579,16 @@ " return np.sum((y_data-y_model)**2)/n\n", "\n", "x = np.random.rand(100)\n", - "y = 2.0+5*x*x#+0.1*np.random.randn(100)\n", + "y = 2.0+5*x*x+0.1*np.random.randn(100)\n", "\n", "\n", "# The design matrix now as function of a fourth-order polynomial\n", - "X = np.zeros((len(x),8))\n", + "X = np.zeros((len(x),5))\n", "X[:,0] = 1.0\n", "X[:,1] = x\n", "X[:,2] = x**2\n", "X[:,3] = x**3\n", "X[:,4] = x**4\n", - "X[:,5] = x**5\n", - "X[:,6] = x**6\n", - "X[:,7] = x**7\n", "# We split the data in test and training data\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n", "# matrix inversion to find theta\n", @@ -1650,7 +1609,7 @@ }, { "cell_type": "markdown", - "id": "09f0c1c6", + "id": "76119de5", "metadata": { "editable": true }, @@ -1661,13 +1620,10 @@ { "cell_type": "code", "execution_count": 8, - "id": "02220d97", + "id": "dff69c9a", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -1689,7 +1645,7 @@ }, { "cell_type": "markdown", - "id": "5494af4d", + "id": "02285c48", "metadata": { "editable": true }, @@ -1701,7 +1657,7 @@ }, { "cell_type": "markdown", - "id": "048560ee", + "id": "71fab9ce", "metadata": { "editable": true }, @@ -1730,7 +1686,7 @@ }, { "cell_type": "markdown", - "id": "85b56c79", + "id": "424914f7", "metadata": { "editable": true }, @@ -1755,7 +1711,7 @@ }, { "cell_type": "markdown", - "id": "60937483", + "id": "e486c793", "metadata": { "editable": true }, @@ -1775,7 +1731,7 @@ }, { "cell_type": "markdown", - "id": "5d0ea6a3", + "id": "1c6a9f34", "metadata": { "editable": true }, @@ -1802,7 +1758,7 @@ }, { "cell_type": "markdown", - "id": "8f6fc4e6", + "id": "28f4300e", "metadata": { "editable": true }, @@ -1815,7 +1771,7 @@ }, { "cell_type": "markdown", - "id": "4bd392ed", + "id": "deb48c69", "metadata": { "editable": true }, @@ -1827,7 +1783,7 @@ }, { "cell_type": "markdown", - "id": "4e33d3e3", + "id": "127f4812", "metadata": { "editable": true }, @@ -1838,7 +1794,7 @@ }, { "cell_type": "markdown", - "id": "7e1c73ac", + "id": "305b4349", "metadata": { "editable": true }, @@ -1853,425 +1809,13 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "2c315558", + "execution_count": 9, + "id": "9dacf721", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, - "outputs": [ - { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
01234
0-1.7497650.3426801.153036-0.2524360.981321
10.5142190.221180-1.070043-0.1894960.255001
2-0.4580270.435163-0.5835950.8168470.672721
3-0.104411-0.5312801.029733-0.438136-1.118318
41.6189821.541605-0.251879-0.8424360.184519
50.9370820.7310001.361556-0.3262380.055676
60.222400-1.443217-0.7563520.8164540.750445
7-0.4559471.189622-1.690617-1.356399-1.232435
8-0.544439-0.6681720.007315-0.6129391.299748
9-1.733096-0.9833100.357508-1.6135791.470714
\n", - "
" - ], - "text/plain": [ - " 0 1 2 3 4\n", - "0 -1.749765 0.342680 1.153036 -0.252436 0.981321\n", - "1 0.514219 0.221180 -1.070043 -0.189496 0.255001\n", - "2 -0.458027 0.435163 -0.583595 0.816847 0.672721\n", - "3 -0.104411 -0.531280 1.029733 -0.438136 -1.118318\n", - "4 1.618982 1.541605 -0.251879 -0.842436 0.184519\n", - "5 0.937082 0.731000 1.361556 -0.326238 0.055676\n", - "6 0.222400 -1.443217 -0.756352 0.816454 0.750445\n", - "7 -0.455947 1.189622 -1.690617 -1.356399 -1.232435\n", - "8 -0.544439 -0.668172 0.007315 -0.612939 1.299748\n", - "9 -1.733096 -0.983310 0.357508 -1.613579 1.470714" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0 -0.175300\n", - "1 0.083527\n", - "2 -0.044334\n", - "3 -0.399836\n", - "4 0.331939\n", - "dtype: float64\n", - "0 1.069584\n", - "1 0.965548\n", - "2 1.018232\n", - "3 0.793167\n", - "4 0.918992\n", - "dtype: float64\n" - ] - }, - { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
01234
0-1.5744650.2591531.1973700.1474000.649382
10.6895190.137652-1.0257090.210340-0.076938
2-0.2827270.351636-0.5392611.2166830.340782
30.070889-0.6148081.074067-0.038300-1.450257
41.7942821.458078-0.207545-0.442600-0.147420
51.1123830.6474731.4058900.073598-0.276263
60.397700-1.526744-0.7120181.2162900.418506
7-0.2806471.106095-1.646283-0.956563-1.564374
8-0.369139-0.7516990.051649-0.2131030.967809
9-1.557795-1.0668370.401842-1.2137431.138775
\n", - "
" - ], - "text/plain": [ - " 0 1 2 3 4\n", - "0 -1.574465 0.259153 1.197370 0.147400 0.649382\n", - "1 0.689519 0.137652 -1.025709 0.210340 -0.076938\n", - "2 -0.282727 0.351636 -0.539261 1.216683 0.340782\n", - "3 0.070889 -0.614808 1.074067 -0.038300 -1.450257\n", - "4 1.794282 1.458078 -0.207545 -0.442600 -0.147420\n", - "5 1.112383 0.647473 1.405890 0.073598 -0.276263\n", - "6 0.397700 -1.526744 -0.712018 1.216290 0.418506\n", - "7 -0.280647 1.106095 -1.646283 -0.956563 -1.564374\n", - "8 -0.369139 -0.751699 0.051649 -0.213103 0.967809\n", - "9 -1.557795 -1.066837 0.401842 -1.213743 1.138775" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
01234
00.00.00.00.00.0
10.00.00.00.00.0
20.00.00.00.00.0
30.00.00.00.00.0
40.00.00.00.00.0
50.00.00.00.00.0
60.00.00.00.00.0
70.00.00.00.00.0
80.00.00.00.00.0
90.00.00.00.00.0
\n", - "
" - ], - "text/plain": [ - " 0 1 2 3 4\n", - "0 0.0 0.0 0.0 0.0 0.0\n", - "1 0.0 0.0 0.0 0.0 0.0\n", - "2 0.0 0.0 0.0 0.0 0.0\n", - "3 0.0 0.0 0.0 0.0 0.0\n", - "4 0.0 0.0 0.0 0.0 0.0\n", - "5 0.0 0.0 0.0 0.0 0.0\n", - "6 0.0 0.0 0.0 0.0 0.0\n", - "7 0.0 0.0 0.0 0.0 0.0\n", - "8 0.0 0.0 0.0 0.0 0.0\n", - "9 0.0 0.0 0.0 0.0 0.0" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import sklearn.linear_model as skl\n", "from sklearn.metrics import mean_squared_error\n", @@ -2300,7 +1844,7 @@ }, { "cell_type": "markdown", - "id": "aaa58775", + "id": "63596c47", "metadata": { "editable": true }, @@ -2310,7 +1854,7 @@ }, { "cell_type": "markdown", - "id": "02b198ed", + "id": "e663049c", "metadata": { "editable": true }, @@ -2325,7 +1869,7 @@ }, { "cell_type": "markdown", - "id": "4cef197d", + "id": "e2b36261", "metadata": { "editable": true }, @@ -2337,7 +1881,7 @@ }, { "cell_type": "markdown", - "id": "23b34528", + "id": "69fa292f", "metadata": { "editable": true }, @@ -2347,7 +1891,7 @@ }, { "cell_type": "markdown", - "id": "b2847956", + "id": "23b3dece", "metadata": { "editable": true }, @@ -2362,14 +1906,11 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "b8dacc33", + "execution_count": 10, + "id": "e1630ab8", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -2383,7 +1924,7 @@ }, { "cell_type": "markdown", - "id": "cd89705f", + "id": "c2d3b936", "metadata": { "editable": true }, @@ -2395,27 +1936,13 @@ }, { "cell_type": "code", - "execution_count": 12, - "id": "d35541fd", + "execution_count": 11, + "id": "355c6a66", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, - "outputs": [ - { - "data": { - "image/png": "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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", @@ -2426,8 +1953,8 @@ "\n", "\n", "np.random.seed(2018)\n", - "n = 100\n", - "maxdegree = 30\n", + "n = 50\n", + "maxdegree = 5\n", "# Make data set.\n", "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", @@ -2457,7 +1984,7 @@ }, { "cell_type": "markdown", - "id": "36014ec9", + "id": "ab553d39", "metadata": { "editable": true }, @@ -2471,7 +1998,7 @@ }, { "cell_type": "markdown", - "id": "16fb5f8f", + "id": "f439180e", "metadata": { "editable": true }, @@ -2483,7 +2010,7 @@ }, { "cell_type": "markdown", - "id": "f1ec698e", + "id": "7ba7386d", "metadata": { "editable": true }, @@ -2495,7 +2022,7 @@ }, { "cell_type": "markdown", - "id": "787f58f5", + "id": "7e0a1440", "metadata": { "editable": true }, @@ -2507,7 +2034,7 @@ }, { "cell_type": "markdown", - "id": "e23435fd", + "id": "2e7611f3", "metadata": { "editable": true }, @@ -2517,7 +2044,7 @@ }, { "cell_type": "markdown", - "id": "ccaad283", + "id": "414e53ca", "metadata": { "editable": true }, @@ -2529,7 +2056,7 @@ }, { "cell_type": "markdown", - "id": "be8092da", + "id": "31ed8899", "metadata": { "editable": true }, @@ -2539,7 +2066,7 @@ }, { "cell_type": "markdown", - "id": "6e055e08", + "id": "a66641fb", "metadata": { "editable": true }, @@ -2551,7 +2078,7 @@ }, { "cell_type": "markdown", - "id": "ff86c9bc", + "id": "28a50f9e", "metadata": { "editable": true }, @@ -2562,7 +2089,7 @@ }, { "cell_type": "markdown", - "id": "b4f2e747", + "id": "b8c5f507", "metadata": { "editable": true }, @@ -2574,7 +2101,7 @@ }, { "cell_type": "markdown", - "id": "5a9a9f87", + "id": "445744c8", "metadata": { "editable": true }, @@ -2586,7 +2113,7 @@ }, { "cell_type": "markdown", - "id": "1232e11a", + "id": "ef90b7cb", "metadata": { "editable": true }, @@ -2596,7 +2123,7 @@ }, { "cell_type": "markdown", - "id": "a807825b", + "id": "9d4c2ac7", "metadata": { "editable": true }, @@ -2608,7 +2135,7 @@ }, { "cell_type": "markdown", - "id": "4fa9855c", + "id": "84e62cfc", "metadata": { "editable": true }, @@ -2620,7 +2147,7 @@ }, { "cell_type": "markdown", - "id": "dcffefcf", + "id": "41c2ba4b", "metadata": { "editable": true }, @@ -2630,7 +2157,7 @@ }, { "cell_type": "markdown", - "id": "3c08ff3a", + "id": "beb557ef", "metadata": { "editable": true }, @@ -2642,7 +2169,7 @@ }, { "cell_type": "markdown", - "id": "c2483a13", + "id": "b3fdffce", "metadata": { "editable": true }, @@ -2652,7 +2179,7 @@ }, { "cell_type": "markdown", - "id": "9a82a8c5", + "id": "8005292a", "metadata": { "editable": true }, @@ -2664,7 +2191,7 @@ }, { "cell_type": "markdown", - "id": "743f7309", + "id": "92d9f94b", "metadata": { "editable": true }, @@ -2674,7 +2201,7 @@ }, { "cell_type": "markdown", - "id": "e6d7b31a", + "id": "17940c71", "metadata": { "editable": true }, @@ -2714,7 +2241,7 @@ }, { "cell_type": "markdown", - "id": "518d6bb4", + "id": "6ffb31dd", "metadata": { "editable": true }, @@ -2731,7 +2258,7 @@ }, { "cell_type": "markdown", - "id": "056673c8", + "id": "cc767251", "metadata": { "editable": true }, @@ -2754,7 +2281,7 @@ }, { "cell_type": "markdown", - "id": "63daba59", + "id": "347029b1", "metadata": { "editable": true }, @@ -2771,7 +2298,7 @@ }, { "cell_type": "markdown", - "id": "89b74667", + "id": "a77dda49", "metadata": { "editable": true }, @@ -2790,7 +2317,7 @@ }, { "cell_type": "markdown", - "id": "588dd662", + "id": "25a0d7d6", "metadata": { "editable": true }, @@ -2801,7 +2328,7 @@ }, { "cell_type": "markdown", - "id": "eb8348c6", + "id": "70462fa0", "metadata": { "editable": true }, @@ -2813,7 +2340,7 @@ }, { "cell_type": "markdown", - "id": "62027bc1", + "id": "f8421c8e", "metadata": { "editable": true }, @@ -2831,7 +2358,7 @@ }, { "cell_type": "markdown", - "id": "0c73c4b7", + "id": "d4ef09ac", "metadata": { "editable": true }, @@ -2847,7 +2374,7 @@ }, { "cell_type": "markdown", - "id": "a3a2d330", + "id": "fc6f8651", "metadata": { "editable": true }, @@ -2859,7 +2386,7 @@ }, { "cell_type": "markdown", - "id": "374b88cc", + "id": "ece72dfe", "metadata": { "editable": true }, @@ -2869,7 +2396,7 @@ }, { "cell_type": "markdown", - "id": "d5aa42e6", + "id": "3f900d15", "metadata": { "editable": true }, @@ -2882,7 +2409,7 @@ }, { "cell_type": "markdown", - "id": "1c01a816", + "id": "3cb45c74", "metadata": { "editable": true }, @@ -2894,7 +2421,7 @@ }, { "cell_type": "markdown", - "id": "f556eddc", + "id": "81b8790f", "metadata": { "editable": true }, @@ -2904,7 +2431,7 @@ }, { "cell_type": "markdown", - "id": "dcf14a16", + "id": "9d42c98f", "metadata": { "editable": true }, @@ -2917,7 +2444,7 @@ }, { "cell_type": "markdown", - "id": "08c37095", + "id": "ab036419", "metadata": { "editable": true }, @@ -2927,7 +2454,7 @@ }, { "cell_type": "markdown", - "id": "6815fa1b", + "id": "bba11ff3", "metadata": { "editable": true }, @@ -2939,7 +2466,7 @@ }, { "cell_type": "markdown", - "id": "daf50946", + "id": "6518184d", "metadata": { "editable": true }, @@ -2952,7 +2479,7 @@ }, { "cell_type": "markdown", - "id": "a7a60cb3", + "id": "ba89e5b0", "metadata": { "editable": true }, @@ -2965,7 +2492,7 @@ }, { "cell_type": "markdown", - "id": "38105bfd", + "id": "47325cf5", "metadata": { "editable": true }, @@ -2977,7 +2504,7 @@ }, { "cell_type": "markdown", - "id": "3d697464", + "id": "8d9036c1", "metadata": { "editable": true }, @@ -2989,7 +2516,7 @@ }, { "cell_type": "markdown", - "id": "c298d7ba", + "id": "889f801b", "metadata": { "editable": true }, @@ -2999,7 +2526,7 @@ }, { "cell_type": "markdown", - "id": "45265b59", + "id": "8a803d4a", "metadata": { "editable": true }, @@ -3012,7 +2539,7 @@ }, { "cell_type": "markdown", - "id": "ab6ce408", + "id": "ec92b840", "metadata": { "editable": true }, @@ -3024,7 +2551,7 @@ }, { "cell_type": "markdown", - "id": "ca0350a7", + "id": "6de4ce40", "metadata": { "editable": true }, @@ -3036,7 +2563,7 @@ }, { "cell_type": "markdown", - "id": "e8146e6f", + "id": "22e97024", "metadata": { "editable": true }, @@ -3048,7 +2575,7 @@ }, { "cell_type": "markdown", - "id": "05d97a86", + "id": "9cd0a124", "metadata": { "editable": true }, @@ -3060,7 +2587,7 @@ }, { "cell_type": "markdown", - "id": "f84e7118", + "id": "29b31bed", "metadata": { "editable": true }, @@ -3074,7 +2601,7 @@ }, { "cell_type": "markdown", - "id": "28be9ec4", + "id": "d1145ae7", "metadata": { "editable": true }, @@ -3086,7 +2613,7 @@ }, { "cell_type": "markdown", - "id": "b9f5a5d8", + "id": "f1479849", "metadata": { "editable": true }, @@ -3096,7 +2623,7 @@ }, { "cell_type": "markdown", - "id": "86b43b21", + "id": "0c51f5eb", "metadata": { "editable": true }, @@ -3108,7 +2635,7 @@ }, { "cell_type": "markdown", - "id": "58744172", + "id": "2cbb0f42", "metadata": { "editable": true }, @@ -3120,7 +2647,7 @@ }, { "cell_type": "markdown", - "id": "dd515e6f", + "id": "406c4098", "metadata": { "editable": true }, @@ -3132,7 +2659,7 @@ }, { "cell_type": "markdown", - "id": "e8c98bfe", + "id": "70966948", "metadata": { "editable": true }, @@ -3144,7 +2671,7 @@ }, { "cell_type": "markdown", - "id": "08cc9626", + "id": "627f3d38", "metadata": { "editable": true }, @@ -3156,7 +2683,7 @@ }, { "cell_type": "markdown", - "id": "725df93e", + "id": "129105f7", "metadata": { "editable": true }, @@ -3179,13 +2706,10 @@ { "cell_type": "code", "execution_count": 12, - "id": "8d0397cd", + "id": "bce32748", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -3258,7 +2782,7 @@ }, { "cell_type": "markdown", - "id": "dbc56c2b", + "id": "62eccb26", "metadata": { "editable": true }, @@ -3270,7 +2794,7 @@ }, { "cell_type": "markdown", - "id": "cfab477f", + "id": "675cc7de", "metadata": { "editable": true }, @@ -3285,7 +2809,7 @@ }, { "cell_type": "markdown", - "id": "bc176ed4", + "id": "ff36cd09", "metadata": { "editable": true }, @@ -3297,7 +2821,7 @@ }, { "cell_type": "markdown", - "id": "a9eef8e3", + "id": "7ae7a42a", "metadata": { "editable": true }, @@ -3307,7 +2831,7 @@ }, { "cell_type": "markdown", - "id": "c33552ec", + "id": "607325f0", "metadata": { "editable": true }, @@ -3319,7 +2843,7 @@ }, { "cell_type": "markdown", - "id": "9465d4f6", + "id": "cfb328b4", "metadata": { "editable": true }, @@ -3329,7 +2853,7 @@ }, { "cell_type": "markdown", - "id": "3cd89a35", + "id": "bc44d844", "metadata": { "editable": true }, @@ -3341,7 +2865,7 @@ }, { "cell_type": "markdown", - "id": "13a9f453", + "id": "17ddbfda", "metadata": { "editable": true }, @@ -3353,7 +2877,7 @@ }, { "cell_type": "markdown", - "id": "6c909f72", + "id": "f5658751", "metadata": { "editable": true }, @@ -3368,7 +2892,7 @@ }, { "cell_type": "markdown", - "id": "b32ee709", + "id": "2b01e674", "metadata": { "editable": true }, @@ -3379,7 +2903,7 @@ }, { "cell_type": "markdown", - "id": "e5d3f72c", + "id": "c18a65c6", "metadata": { "editable": true }, @@ -3399,7 +2923,7 @@ }, { "cell_type": "markdown", - "id": "18f488f0", + "id": "04258de2", "metadata": { "editable": true }, @@ -3411,7 +2935,7 @@ }, { "cell_type": "markdown", - "id": "93618783", + "id": "e10d0aad", "metadata": { "editable": true }, @@ -3421,7 +2945,7 @@ }, { "cell_type": "markdown", - "id": "02f57528", + "id": "d198578b", "metadata": { "editable": true }, @@ -3433,7 +2957,7 @@ }, { "cell_type": "markdown", - "id": "762833f4", + "id": "2aec2fc1", "metadata": { "editable": true }, @@ -3462,7 +2986,7 @@ }, { "cell_type": "markdown", - "id": "9ab8ec4f", + "id": "81fed6f5", "metadata": { "editable": true }, @@ -3489,7 +3013,7 @@ }, { "cell_type": "markdown", - "id": "3e526d1f", + "id": "fe7d1d49", "metadata": { "editable": true }, @@ -3500,13 +3024,10 @@ { "cell_type": "code", "execution_count": 13, - "id": "f5d258ce", + "id": "0b32041d", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -3543,7 +3064,7 @@ }, { "cell_type": "markdown", - "id": "4e4bf198", + "id": "db224b5b", "metadata": { "editable": true }, @@ -3560,7 +3081,7 @@ }, { "cell_type": "markdown", - "id": "33a42ac4", + "id": "6b988f39", "metadata": { "editable": true }, @@ -3583,7 +3104,7 @@ }, { "cell_type": "markdown", - "id": "7b5d1bbb", + "id": "1214012e", "metadata": { "editable": true }, @@ -3597,7 +3118,7 @@ }, { "cell_type": "markdown", - "id": "1fee5f54", + "id": "c7a8cd85", "metadata": { "editable": true }, @@ -3616,7 +3137,7 @@ }, { "cell_type": "markdown", - "id": "235f2975", + "id": "0f2a2211", "metadata": { "editable": true }, @@ -3626,7 +3147,7 @@ }, { "cell_type": "markdown", - "id": "fd7415b7", + "id": "e9863a0f", "metadata": { "editable": true }, @@ -3638,7 +3159,7 @@ }, { "cell_type": "markdown", - "id": "7c265b5d", + "id": "d88c8316", "metadata": { "editable": true }, @@ -3652,7 +3173,7 @@ }, { "cell_type": "markdown", - "id": "976c31a2", + "id": "643f1b6d", "metadata": { "editable": true }, @@ -3664,7 +3185,7 @@ }, { "cell_type": "markdown", - "id": "8dc8acd7", + "id": "0769ec85", "metadata": { "editable": true }, @@ -3674,7 +3195,7 @@ }, { "cell_type": "markdown", - "id": "a1dc8e8e", + "id": "f0d61e66", "metadata": { "editable": true }, @@ -3686,7 +3207,7 @@ }, { "cell_type": "markdown", - "id": "eb688af0", + "id": "0d7c9d9e", "metadata": { "editable": true }, @@ -3703,7 +3224,7 @@ }, { "cell_type": "markdown", - "id": "eeadd85e", + "id": "335fb5ed", "metadata": { "editable": true }, @@ -3713,7 +3234,7 @@ }, { "cell_type": "markdown", - "id": "e9375ad7", + "id": "1dbb3e05", "metadata": { "editable": true }, @@ -3729,7 +3250,7 @@ }, { "cell_type": "markdown", - "id": "025f1ca1", + "id": "4a535424", "metadata": { "editable": true }, @@ -3739,7 +3260,7 @@ }, { "cell_type": "markdown", - "id": "d44951a1", + "id": "512418d2", "metadata": { "editable": true }, @@ -3755,7 +3276,7 @@ }, { "cell_type": "markdown", - "id": "ecc9216b", + "id": "baa56321", "metadata": { "editable": true }, @@ -3765,7 +3286,7 @@ }, { "cell_type": "markdown", - "id": "28e2ff44", + "id": "1fd5881c", "metadata": { "editable": true }, @@ -3781,7 +3302,7 @@ }, { "cell_type": "markdown", - "id": "935324af", + "id": "546a2bf3", "metadata": { "editable": true }, @@ -3791,7 +3312,7 @@ }, { "cell_type": "markdown", - "id": "a15e7526", + "id": "4e356417", "metadata": { "editable": true }, @@ -3808,7 +3329,7 @@ }, { "cell_type": "markdown", - "id": "5d3cef55", + "id": "1f3c787b", "metadata": { "editable": true }, @@ -3820,7 +3341,7 @@ }, { "cell_type": "markdown", - "id": "0fab1783", + "id": "72018911", "metadata": { "editable": true }, @@ -3832,7 +3353,7 @@ }, { "cell_type": "markdown", - "id": "f9a8450e", + "id": "7d741e98", "metadata": { "editable": true }, @@ -3844,7 +3365,7 @@ }, { "cell_type": "markdown", - "id": "485d1023", + "id": "f2e4a67f", "metadata": { "editable": true }, @@ -3854,7 +3375,7 @@ }, { "cell_type": "markdown", - "id": "a2da5dbe", + "id": "302c8edf", "metadata": { "editable": true }, @@ -3866,7 +3387,7 @@ }, { "cell_type": "markdown", - "id": "13959099", + "id": "def3ec8a", "metadata": { "editable": true }, @@ -3878,7 +3399,7 @@ }, { "cell_type": "markdown", - "id": "23f0b903", + "id": "37150ee7", "metadata": { "editable": true }, @@ -3890,7 +3411,7 @@ }, { "cell_type": "markdown", - "id": "1c344e77", + "id": "e937a396", "metadata": { "editable": true }, @@ -3900,7 +3421,7 @@ }, { "cell_type": "markdown", - "id": "d8064053", + "id": "07e76c7b", "metadata": { "editable": true }, @@ -3912,7 +3433,7 @@ }, { "cell_type": "markdown", - "id": "714ab01f", + "id": "99f80e22", "metadata": { "editable": true }, @@ -3922,35 +3443,36 @@ }, { "cell_type": "markdown", - "id": "a3ff6988", + "id": "7a917bf2", "metadata": { "editable": true }, "source": [ "$$\n", - "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n", + "\\tilde{y}_{\\mathrm{OLS}}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n", "$$" ] }, { "cell_type": "markdown", - "id": "5c204f79", + "id": "c11ae5fe", "metadata": { "editable": true }, "source": [ + "which is not the same as $\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}$, which due to the orthogonality of $\\boldsymbol{U}$ would have given us that the model equals the output.\n", + "\n", "It means that the ordinary least square model (with the optimal\n", "parameters) $\\boldsymbol{\\tilde{y}}$, corresponds to an orthogonal\n", "transformation of the output (or target) vector $\\boldsymbol{y}$ by the\n", "vectors of the matrix $\\boldsymbol{U}$. **Note that the summation ends at**\n", "$p-1$, that is $\\boldsymbol{\\tilde{y}}\\ne \\boldsymbol{y}$. We can thus not use the\n", - "orthogonality relation for the matrix $\\boldsymbol{U}$. This can already be\n", - "when we multiply the matrices $\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T$." + "orthogonality relation for the matrix $\\boldsymbol{U}$." ] }, { "cell_type": "markdown", - "id": "78c51f10", + "id": "f300aa1b", "metadata": { "editable": true }, @@ -3962,7 +3484,7 @@ }, { "cell_type": "markdown", - "id": "2c432ed4", + "id": "8bd1e2a6", "metadata": { "editable": true }, @@ -3974,7 +3496,7 @@ }, { "cell_type": "markdown", - "id": "68a7b505", + "id": "62502292", "metadata": { "editable": true }, @@ -3984,7 +3506,7 @@ }, { "cell_type": "markdown", - "id": "14268cd5", + "id": "efca6f6c", "metadata": { "editable": true }, @@ -3996,7 +3518,7 @@ }, { "cell_type": "markdown", - "id": "f3207844", + "id": "e2cbd6f5", "metadata": { "editable": true }, @@ -4007,7 +3529,7 @@ }, { "cell_type": "markdown", - "id": "4c7f5556", + "id": "5cc9aea6", "metadata": { "editable": true }, @@ -4019,7 +3541,7 @@ }, { "cell_type": "markdown", - "id": "01bd8826", + "id": "61ad8f4c", "metadata": { "editable": true }, @@ -4029,7 +3551,7 @@ }, { "cell_type": "markdown", - "id": "cb083248", + "id": "b1cc9449", "metadata": { "editable": true }, @@ -4041,7 +3563,7 @@ }, { "cell_type": "markdown", - "id": "66bd1ec9", + "id": "a9b28652", "metadata": { "editable": true }, @@ -4051,7 +3573,7 @@ }, { "cell_type": "markdown", - "id": "b92a06bb", + "id": "f26b69cc", "metadata": { "editable": true }, @@ -4063,7 +3585,7 @@ }, { "cell_type": "markdown", - "id": "dad0b409", + "id": "53acde0e", "metadata": { "editable": true }, @@ -4074,7 +3596,7 @@ }, { "cell_type": "markdown", - "id": "75d85fa8", + "id": "512b9f17", "metadata": { "editable": true }, @@ -4086,7 +3608,7 @@ }, { "cell_type": "markdown", - "id": "d0918773", + "id": "a1c49f5f", "metadata": { "editable": true }, @@ -4104,7 +3626,7 @@ }, { "cell_type": "markdown", - "id": "65592b3b", + "id": "db70d623", "metadata": { "editable": true }, @@ -4120,7 +3642,7 @@ }, { "cell_type": "markdown", - "id": "442404b8", + "id": "95b18b06", "metadata": { "editable": true }, @@ -4132,7 +3654,7 @@ }, { "cell_type": "markdown", - "id": "50eca816", + "id": "db07fa1e", "metadata": { "editable": true }, @@ -4144,7 +3666,7 @@ }, { "cell_type": "markdown", - "id": "a27e487e", + "id": "9856cea3", "metadata": { "editable": true }, @@ -4156,7 +3678,7 @@ }, { "cell_type": "markdown", - "id": "49c74d48", + "id": "7f6cba4c", "metadata": { "editable": true }, @@ -4169,7 +3691,7 @@ }, { "cell_type": "markdown", - "id": "214feab7", + "id": "581565a5", "metadata": { "editable": true }, @@ -4185,7 +3707,7 @@ }, { "cell_type": "markdown", - "id": "e61c0669", + "id": "22b63d08", "metadata": { "editable": true }, @@ -4199,7 +3721,7 @@ }, { "cell_type": "markdown", - "id": "9f3db006", + "id": "cd6032aa", "metadata": { "editable": true }, @@ -4209,7 +3731,7 @@ }, { "cell_type": "markdown", - "id": "6dfeb8ca", + "id": "25b7936a", "metadata": { "editable": true }, @@ -4221,7 +3743,7 @@ }, { "cell_type": "markdown", - "id": "da47505d", + "id": "9c4ad4d2", "metadata": { "editable": true }, @@ -4231,7 +3753,7 @@ }, { "cell_type": "markdown", - "id": "87c1a756", + "id": "75bcfcea", "metadata": { "editable": true }, @@ -4243,7 +3765,7 @@ }, { "cell_type": "markdown", - "id": "5028dae1", + "id": "95c9cc40", "metadata": { "editable": true }, @@ -4253,7 +3775,7 @@ }, { "cell_type": "markdown", - "id": "98da161b", + "id": "33c19ed1", "metadata": { "editable": true }, @@ -4267,7 +3789,7 @@ }, { "cell_type": "markdown", - "id": "69065ef4", + "id": "c28b0a97", "metadata": { "editable": true }, @@ -4284,7 +3806,7 @@ }, { "cell_type": "markdown", - "id": "3455143e", + "id": "d4ece056", "metadata": { "editable": true }, @@ -4300,7 +3822,7 @@ }, { "cell_type": "markdown", - "id": "e322fdc8", + "id": "22360ee3", "metadata": { "editable": true }, @@ -4312,7 +3834,7 @@ }, { "cell_type": "markdown", - "id": "f50b583d", + "id": "77e8998d", "metadata": { "editable": true }, @@ -4325,7 +3847,7 @@ }, { "cell_type": "markdown", - "id": "b12b62dc", + "id": "8ef4225d", "metadata": { "editable": true }, @@ -4339,7 +3861,7 @@ }, { "cell_type": "markdown", - "id": "40355c87", + "id": "627eac2b", "metadata": { "editable": true }, @@ -4349,7 +3871,7 @@ }, { "cell_type": "markdown", - "id": "ee70666b", + "id": "f7ac0db1", "metadata": { "editable": true }, @@ -4362,7 +3884,7 @@ }, { "cell_type": "markdown", - "id": "dc6d0cc7", + "id": "e93eae5d", "metadata": { "editable": true }, @@ -4381,7 +3903,7 @@ }, { "cell_type": "markdown", - "id": "d6b6f792", + "id": "58364673", "metadata": { "editable": true }, @@ -4393,7 +3915,7 @@ }, { "cell_type": "markdown", - "id": "39c76bf5", + "id": "30541096", "metadata": { "editable": true }, @@ -4405,7 +3927,7 @@ }, { "cell_type": "markdown", - "id": "f2d754e5", + "id": "101bb217", "metadata": { "editable": true }, @@ -4415,7 +3937,7 @@ }, { "cell_type": "markdown", - "id": "77a984ab", + "id": "ba8e52b1", "metadata": { "editable": true }, @@ -4427,7 +3949,7 @@ }, { "cell_type": "markdown", - "id": "33060c1a", + "id": "67d4335e", "metadata": { "editable": true }, @@ -4440,7 +3962,7 @@ }, { "cell_type": "markdown", - "id": "ed1e8279", + "id": "06416768", "metadata": { "editable": true }, @@ -4459,7 +3981,7 @@ }, { "cell_type": "markdown", - "id": "22b40263", + "id": "dd2f405a", "metadata": { "editable": true }, @@ -4469,7 +3991,7 @@ }, { "cell_type": "markdown", - "id": "1b02469c", + "id": "40ded798", "metadata": { "editable": true }, @@ -4488,7 +4010,7 @@ }, { "cell_type": "markdown", - "id": "0660e456", + "id": "d3044a01", "metadata": { "editable": true }, @@ -4506,7 +4028,7 @@ }, { "cell_type": "markdown", - "id": "0a40e5c0", + "id": "d612ad97", "metadata": { "editable": true }, @@ -4520,7 +4042,7 @@ }, { "cell_type": "markdown", - "id": "82d7e99d", + "id": "52f27c53", "metadata": { "editable": true }, @@ -4535,13 +4057,10 @@ { "cell_type": "code", "execution_count": 14, - "id": "6f4b429b", + "id": "ca5ce77c", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -4559,7 +4078,7 @@ }, { "cell_type": "markdown", - "id": "a38f8430", + "id": "1c02019d", "metadata": { "editable": true }, @@ -4576,13 +4095,10 @@ { "cell_type": "code", "execution_count": 15, - "id": "87d44fdf", + "id": "58381fbe", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -4611,7 +4127,7 @@ }, { "cell_type": "markdown", - "id": "5f08f4dc", + "id": "a647044e", "metadata": { "editable": true }, @@ -4625,7 +4141,7 @@ }, { "cell_type": "markdown", - "id": "a25b356f", + "id": "d7bea0a6", "metadata": { "editable": true }, @@ -4638,13 +4154,10 @@ { "cell_type": "code", "execution_count": 16, - "id": "928ae649", + "id": "81d407da", "metadata": { "collapsed": false, - "editable": true, - "jupyter": { - "outputs_hidden": false - } + "editable": true }, "outputs": [], "source": [ @@ -4666,7 +4179,7 @@ }, { "cell_type": "markdown", - "id": "cab70377", + "id": "7998701a", "metadata": { "editable": true }, @@ -4678,7 +4191,7 @@ }, { "cell_type": "markdown", - "id": "22ac4a6d", + "id": "e4f65917", "metadata": { "editable": true }, @@ -4690,7 +4203,7 @@ }, { "cell_type": "markdown", - "id": "cd0697a9", + "id": "73ecb476", "metadata": { "editable": true }, @@ -4700,7 +4213,7 @@ }, { "cell_type": "markdown", - "id": "b5043405", + "id": "f4f10483", "metadata": { "editable": true }, @@ -4717,7 +4230,7 @@ }, { "cell_type": "markdown", - "id": "6a4edab6", + "id": "9e173ba2", "metadata": { "editable": true }, @@ -4727,7 +4240,7 @@ }, { "cell_type": "markdown", - "id": "e1b67496", + "id": "6b6f3d02", "metadata": { "editable": true }, @@ -4742,7 +4255,7 @@ }, { "cell_type": "markdown", - "id": "47a041cb", + "id": "69a2c9b4", "metadata": { "editable": true }, @@ -4752,7 +4265,7 @@ }, { "cell_type": "markdown", - "id": "575264b7", + "id": "41dedd73", "metadata": { "editable": true }, @@ -4766,7 +4279,7 @@ }, { "cell_type": "markdown", - "id": "7b049c58", + "id": "a7b2bb8c", "metadata": { "editable": true }, @@ -4778,7 +4291,7 @@ }, { "cell_type": "markdown", - "id": "9780789f", + "id": "dba35fc4", "metadata": { "editable": true }, @@ -4790,7 +4303,7 @@ }, { "cell_type": "markdown", - "id": "da396c4a", + "id": "0e30a645", "metadata": { "editable": true }, @@ -4802,7 +4315,7 @@ }, { "cell_type": "markdown", - "id": "87a74417", + "id": "6fa482d3", "metadata": { "editable": true }, @@ -4812,7 +4325,7 @@ }, { "cell_type": "markdown", - "id": "c5ca565a", + "id": "ae9f30ae", "metadata": { "editable": true }, @@ -4824,7 +4337,7 @@ }, { "cell_type": "markdown", - "id": "10944fc5", + "id": "67907a60", "metadata": { "editable": true }, @@ -4834,7 +4347,7 @@ }, { "cell_type": "markdown", - "id": "7b985955", + "id": "3a21fe71", "metadata": { "editable": true }, @@ -4851,7 +4364,7 @@ }, { "cell_type": "markdown", - "id": "1b748051", + "id": "3b91b5d8", "metadata": { "editable": true }, @@ -4861,7 +4374,7 @@ }, { "cell_type": "markdown", - "id": "40c1c1eb", + "id": "86de4409", "metadata": { "editable": true }, @@ -4873,7 +4386,7 @@ }, { "cell_type": "markdown", - "id": "e44c9e87", + "id": "d0c0608f", "metadata": { "editable": true }, @@ -4883,7 +4396,7 @@ }, { "cell_type": "markdown", - "id": "28abe46c", + "id": "98f544a6", "metadata": { "editable": true }, @@ -4895,7 +4408,7 @@ }, { "cell_type": "markdown", - "id": "178bc776", + "id": "24587410", "metadata": { "editable": true }, @@ -4909,7 +4422,7 @@ }, { "cell_type": "markdown", - "id": "1f0ead95", + "id": "61fb4275", "metadata": { "editable": true }, @@ -4921,7 +4434,7 @@ }, { "cell_type": "markdown", - "id": "fcce3bb5", + "id": "6d2404eb", "metadata": { "editable": true }, @@ -4943,7 +4456,7 @@ }, { "cell_type": "markdown", - "id": "5f9a7281", + "id": "22615b7e", "metadata": { "editable": true }, @@ -4955,7 +4468,7 @@ }, { "cell_type": "markdown", - "id": "d3ea695c", + "id": "bee48c87", "metadata": { "editable": true }, @@ -4970,7 +4483,7 @@ }, { "cell_type": "markdown", - "id": "edfff9e0", + "id": "7f12f53a", "metadata": { "editable": true }, @@ -4982,7 +4495,7 @@ }, { "cell_type": "markdown", - "id": "c3c83244", + "id": "a6acb75c", "metadata": { "editable": true }, @@ -4994,7 +4507,7 @@ }, { "cell_type": "markdown", - "id": "00df5ee5", + "id": "131e9d9c", "metadata": { "editable": true }, @@ -5004,7 +4517,7 @@ }, { "cell_type": "markdown", - "id": "4661cbd7", + "id": "85812d77", "metadata": { "editable": true }, @@ -5016,7 +4529,7 @@ }, { "cell_type": "markdown", - "id": "07b95265", + "id": "35007c74", "metadata": { "editable": true }, @@ -5026,7 +4539,7 @@ }, { "cell_type": "markdown", - "id": "8c9aeba4", + "id": "0100935a", "metadata": { "editable": true }, @@ -5038,7 +4551,7 @@ }, { "cell_type": "markdown", - "id": "03690a72", + "id": "7b6ff86e", "metadata": { "editable": true }, @@ -5048,7 +4561,7 @@ }, { "cell_type": "markdown", - "id": "478e2a9d", + "id": "1f452dfb", "metadata": { "editable": true }, @@ -5060,7 +4573,7 @@ }, { "cell_type": "markdown", - "id": "e997196a", + "id": "05600fbd", "metadata": { "editable": true }, @@ -5077,7 +4590,7 @@ }, { "cell_type": "markdown", - "id": "770e587e", + "id": "a2af3e04", "metadata": { "editable": true }, @@ -5090,7 +4603,7 @@ }, { "cell_type": "markdown", - "id": "5cb701c2", + "id": "0342c08c", "metadata": { "editable": true }, @@ -5102,7 +4615,7 @@ }, { "cell_type": "markdown", - "id": "dee9d948", + "id": "bdd5faeb", "metadata": { "editable": true }, @@ -5112,7 +4625,7 @@ }, { "cell_type": "markdown", - "id": "121cd014", + "id": "35873dc6", "metadata": { "editable": true }, @@ -5125,7 +4638,7 @@ }, { "cell_type": "markdown", - "id": "2ee745b4", + "id": "6ff6ab78", "metadata": { "editable": true }, @@ -5135,7 +4648,7 @@ }, { "cell_type": "markdown", - "id": "94a15fb9", + "id": "77286b5f", "metadata": { "editable": true }, @@ -5147,7 +4660,7 @@ }, { "cell_type": "markdown", - "id": "6341fe06", + "id": "0ade2616", "metadata": { "editable": true }, @@ -5160,7 +4673,7 @@ }, { "cell_type": "markdown", - "id": "5bef6925", + "id": "da22a168", "metadata": { "editable": true }, @@ -5173,7 +4686,7 @@ }, { "cell_type": "markdown", - "id": "4539e82b", + "id": "caa18da2", "metadata": { "editable": true }, @@ -5185,7 +4698,7 @@ }, { "cell_type": "markdown", - "id": "1f496d16", + "id": "f31c8084", "metadata": { "editable": true }, @@ -5197,7 +4710,7 @@ }, { "cell_type": "markdown", - "id": "ee78adfa", + "id": "53dc71a2", "metadata": { "editable": true }, @@ -5207,7 +4720,7 @@ }, { "cell_type": "markdown", - "id": "47a0c860", + "id": "753442d5", "metadata": { "editable": true }, @@ -5220,7 +4733,7 @@ }, { "cell_type": "markdown", - "id": "6b452b5d", + "id": "e0b2f58a", "metadata": { "editable": true }, @@ -5232,7 +4745,7 @@ }, { "cell_type": "markdown", - "id": "a3331a79", + "id": "e4af8e7e", "metadata": { "editable": true }, @@ -5244,7 +4757,7 @@ }, { "cell_type": "markdown", - "id": "9befd0e3", + "id": "6e353a3a", "metadata": { "editable": true }, @@ -5261,7 +4774,7 @@ }, { "cell_type": "markdown", - "id": "9d8f2ba3", + "id": "66a4056b", "metadata": { "editable": true }, @@ -5273,7 +4786,7 @@ }, { "cell_type": "markdown", - "id": "da712e9d", + "id": "ea5b3d9f", "metadata": { "editable": true }, @@ -5283,7 +4796,7 @@ }, { "cell_type": "markdown", - "id": "d91cd5f7", + "id": "db50585a", "metadata": { "editable": true }, @@ -5295,7 +4808,7 @@ }, { "cell_type": "markdown", - "id": "18940f72", + "id": "afd3cd57", "metadata": { "editable": true }, @@ -5305,7 +4818,7 @@ }, { "cell_type": "markdown", - "id": "51fe3527", + "id": "6606774b", "metadata": { "editable": true }, @@ -5317,7 +4830,7 @@ }, { "cell_type": "markdown", - "id": "2e85d1eb", + "id": "bcfd3adb", "metadata": { "editable": true }, @@ -5329,7 +4842,7 @@ }, { "cell_type": "markdown", - "id": "96c47485", + "id": "46d7227b", "metadata": { "editable": true }, @@ -5345,7 +4858,7 @@ }, { "cell_type": "markdown", - "id": "c1adcbbc", + "id": "a214b881", "metadata": { "editable": true }, @@ -5357,7 +4870,7 @@ }, { "cell_type": "markdown", - "id": "9693074c", + "id": "727c87de", "metadata": { "editable": true }, @@ -5369,7 +4882,7 @@ }, { "cell_type": "markdown", - "id": "46b05531", + "id": "5083858e", "metadata": { "editable": true }, @@ -5379,7 +4892,7 @@ }, { "cell_type": "markdown", - "id": "2e4ce02b", + "id": "973ad2fa", "metadata": { "editable": true }, @@ -5391,7 +4904,7 @@ }, { "cell_type": "markdown", - "id": "dbd3f781", + "id": "4fbd0028", "metadata": { "editable": true }, @@ -5401,7 +4914,7 @@ }, { "cell_type": "markdown", - "id": "779e1ac5", + "id": "bee26901", "metadata": { "editable": true }, @@ -5413,7 +4926,7 @@ }, { "cell_type": "markdown", - "id": "ef53f2a5", + "id": "da771d96", "metadata": { "editable": true }, @@ -5430,7 +4943,7 @@ }, { "cell_type": "markdown", - "id": "57adfaff", + "id": "8ecb8a62", "metadata": { "editable": true }, @@ -5442,7 +4955,7 @@ }, { "cell_type": "markdown", - "id": "a8f94cba", + "id": "5cf08e3d", "metadata": { "editable": true }, @@ -5454,7 +4967,7 @@ }, { "cell_type": "markdown", - "id": "d60431ff", + "id": "d984ce12", "metadata": { "editable": true }, @@ -5464,7 +4977,7 @@ }, { "cell_type": "markdown", - "id": "f78d1dfd", + "id": "837a69b7", "metadata": { "editable": true }, @@ -5476,7 +4989,7 @@ }, { "cell_type": "markdown", - "id": "445800de", + "id": "21dde5ad", "metadata": { "editable": true }, @@ -5486,7 +4999,7 @@ }, { "cell_type": "markdown", - "id": "3c54c49c", + "id": "4d49c112", "metadata": { "editable": true }, @@ -5498,7 +5011,7 @@ }, { "cell_type": "markdown", - "id": "11366dc1", + "id": "5b4eabcf", "metadata": { "editable": true }, @@ -5508,7 +5021,7 @@ }, { "cell_type": "markdown", - "id": "d68d3ac1", + "id": "28dcb3c8", "metadata": { "editable": true }, @@ -5520,7 +5033,7 @@ }, { "cell_type": "markdown", - "id": "63fedbd6", + "id": "f315a306", "metadata": { "editable": true }, @@ -5530,7 +5043,7 @@ }, { "cell_type": "markdown", - "id": "470b20a8", + "id": "7b4f990c", "metadata": { "editable": true }, @@ -5542,7 +5055,7 @@ }, { "cell_type": "markdown", - "id": "f3277c65", + "id": "197daa81", "metadata": { "editable": true }, @@ -5551,25 +5064,7 @@ ] } ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt index 4661992f2..8f07a83f9 100644 --- a/doc/src/week35/week35.do.txt +++ b/doc/src/week35/week35.do.txt @@ -1630,17 +1630,17 @@ which gives us, using the orthogonality of the matrix $\bm{V}$, !bt \[ -\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{U}^T\bm{y}=\sum_{i=0}^{p-1}\bm{u}_i\bm{u}^T_i\bm{y}, +\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\bm{u}_i\bm{u}^T_i\bm{y}, \] !et +which is not the same as $\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{U}^T\bm{y}$, which due to the orthogonality of $\bm{U}$ would have given us that the model equals the output. It means that the ordinary least square model (with the optimal parameters) $\bm{\tilde{y}}$, corresponds to an orthogonal transformation of the output (or target) vector $\bm{y}$ by the vectors of the matrix $\bm{U}$. _Note that the summation ends at_ $p-1$, that is $\bm{\tilde{y}}\ne \bm{y}$. We can thus not use the -orthogonality relation for the matrix $\bm{U}$. This can already be -when we multiply the matrices $\bm{\Sigma}^T\bm{U}^T$. +orthogonality relation for the matrix $\bm{U}$. !split ===== Further properties (important for our analyses later) =====