diff --git a/.nojekyll b/.nojekyll
index 3f4518c..18c06fd 100644
--- a/.nojekyll
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+0fb35371
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diff --git a/schedule/slides/02-lm-example.html b/schedule/slides/02-lm-example.html
index 4f1fcf3..a0c380e 100644
--- a/schedule/slides/02-lm-example.html
+++ b/schedule/slides/02-lm-example.html
@@ -398,7 +398,7 @@
02 Linear model example
Stat 406
Geoff Pleiss, Trevor Campbell
-Last modified – 10 December 2023
+Last modified – 13 September 2024
\[
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
@@ -491,9 +491,9 @@ Analysis
set.seed (20220914 )<- mobility[complete.cases (mobility), ]<- nrow (mob)<- mob |> select (- Name, - ID, - State)<- mobility[complete.cases (mobility), ] |> select (- Name, - ID, - State)<- nrow (mob)<- sample.int (n, floor (n * .75 ), FALSE )<- mob[set, ]<- mob[setdiff (1 : n, set), ]Analysis
Results
+(dispatch happening here!)
@@ -582,8 +583,19 @@
Results
Diagnostic plots
-
par (mar = c (5 , 3 , 0 , 0 ))plot (full, 1 )
+
<- tibble (residuals = residuals (full),fitted = fitted (full),stdresiduals = rstandard (full)ggplot (stuff, aes (fitted, residuals)) + geom_point () + geom_smooth (se = FALSE ,colour = "steelblue" ,linewidth = 2 + ggtitle ("Residuals vs Fitted" )
@@ -595,7 +607,14 @@
Diagnostic plots
-
+
ggplot (stuff, aes (sample = stdresiduals)) + geom_qq (size = 2 ) + geom_qq_line (linewidth = 2 , color = "steelblue" ) + labs (x = "Theoretical quantiles" ,y = "Standardized residuals" ,title = "Normal Q-Q"
@@ -606,25 +625,11 @@
Diagnostic plots
-
-(Those were plot methods for objects of class lm)
-Same thing in ggplot
+
+Can also just use dispatched plot
-
<- tibble (residuals = residuals (full),fitted = fitted (full),stdresiduals = rstandard (full)ggplot (stuff, aes (fitted, residuals)) + geom_point (colour = "salmon" ) + geom_smooth (se = FALSE ,colour = "steelblue" ,linewidth = 2 + ggtitle ("Residuals vs Fitted" )
+
-
ggplot (stuff, aes (sample = stdresiduals)) + geom_qq (colour = "purple" , size = 2 ) + geom_qq_line (colour = "peachpuff" , linewidth = 2 ) + labs (x = "Theoretical quantiles" ,y = "Standardized residuals" ,title = "Normal Q-Q"
+
+
summary (reduced)$ coefficients
-
# A tibble: 9 × 4
- Estimate `Std. Error` `t value` `Pr(>|t|)`
- <dbl> <dbl> <dbl> <dbl>
-1 0.166 0.0178 9.36 1.83e-18
-2 0.0637 0.0149 4.27 2.62e- 5
-3 -0.109 0.0390 -2.79 5.64e- 3
-4 0.000500 0.000256 1.95 5.19e- 2
-5 -0.216 0.0820 -2.64 8.81e- 3
-6 -0.159 0.0202 -7.89 5.65e-14
-7 -0.389 0.172 -2.26 2.42e- 2
-8 0.0436 0.0105 4.16 4.08e- 5
-9 -0.286 0.0466 -6.15 2.44e- 9
+
Estimate Std. Error t value Pr(>|t|)
+(Intercept) 0.1663344179 0.017769995 9.360409 1.829270e-18
+Commute 0.0637329409 0.014926382 4.269819 2.618234e-05
+Gini_99 -0.1086058241 0.038958986 -2.787696 5.642726e-03
+Test_scores 0.0004997645 0.000256038 1.951915 5.186618e-02
+HS_dropout -0.2162067301 0.082003195 -2.636565 8.805228e-03
+Manufacturing -0.1594229237 0.020215791 -7.886059 5.647668e-14
+Migration_in -0.3891567027 0.171839168 -2.264657 2.423771e-02
+Religious 0.0435673365 0.010463920 4.163577 4.084854e-05
+Single_mothers -0.2864269552 0.046578928 -6.149282 2.444903e-09|> :: glance () |>
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-12-1.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-12-1.svg
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-13-1.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-13-1.svg
index d3ba892..385a248 100644
--- a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-13-1.svg
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-4-1.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-4-1.svg
index 671b2de..58ff0ed 100644
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-4-2.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-4-2.svg
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-5-1.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-5-1.svg
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diff --git a/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-6-1.svg b/schedule/slides/02-lm-example_files/figure-revealjs/unnamed-chunk-6-1.svg
index ed8b113..cd9c2b9 100644
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index 0338bf6..7a79d6a 100644
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index 20858dc..0464ddd 100644
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diff --git a/schedule/slides/03-regression-function.html b/schedule/slides/03-regression-function.html
index 4f65b37..e66513e 100644
--- a/schedule/slides/03-regression-function.html
+++ b/schedule/slides/03-regression-function.html
@@ -398,7 +398,7 @@
03 The regression function
Stat 406
Geoff Pleiss, Trevor Campbell
-Last modified – 18 September 2023
+Last modified – 14 September 2024
\[
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
@@ -418,6 +418,15 @@ 03 The regression function
\newcommand{\R}{\mathbb{R}}
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\snorm}[1]{\lVert #1 \rVert}
+\newcommand{\tr}[1]{\mbox{tr}(#1)}
+\newcommand{\brt}{\widehat{\beta}^R_{s}}
+\newcommand{\brl}{\widehat{\beta}^R_{\lambda}}
+\newcommand{\bls}{\widehat{\beta}_{ols}}
+\newcommand{\blt}{\widehat{\beta}^L_{s}}
+\newcommand{\bll}{\widehat{\beta}^L_{\lambda}}
+\newcommand{\U}{\mathbf{U}}
+\newcommand{\D}{\mathbf{D}}
+\newcommand{\V}{\mathbf{V}}
\]
@@ -462,10 +471,10 @@ Statistical models 101
Some examples:
-\(\P = \{ 0 < p < 1 : P(z=1)=p,\ P(z=0)=1-p\}\) .\(\P = \{ \beta \in \R^p,\ \sigma>0 : Y \sim N(X^\top\beta,\sigma^2),\ X\mbox{ fixed}\}\) .\(\P = \{\mbox{all CDF's }F\}\) .\(\P = \{\mbox{all smooth functions } f: \R^p \rightarrow \R : Z_i = (X_i, Y_i),\ E[Y_i] = f(X_i) \}\) \(\P = \{P : P(Z=1)=p,\ P(Z=0)=1-p, 0 \leq p \leq 1\}\) .\(\P = \{P : Y | X \sim N(X^\top\beta,\sigma^2),\ \beta \in \R^p,\ \sigma>0\}\) (here \(Z = (Y,X)\) )\(\P = \{P \mbox{ given by any CDF }F\}\) .\(\P = \{P : E[Y | X] = f(X) \mbox{ for some smooth } f: \R^p \rightarrow \R\}\) (here \(Z = (Y,X)\) )
@@ -474,7 +483,7 @@ Statistical models
My model:
\[
-\P = \{ P(z=1)=p,\ P(z=0)=1-p,\ 0 < p < 1 \}
+\P = \{P: P(z=1)=p,\ P(z=0)=1-p,\ 0 < p < 1 \}
\]
To completely characterize \(P\) , I just need to estimate \(p\) .
My model:
Statistical models
-We observe data \(Z_i=(Y_i,X_i)\) generated by some probability distribution \(P\) . We want to use the data to learn about \(P\) .
+We observe data \((Y, X)\) generated by some probability distribution \(P\) on \(\R \times \R^p\) . We want to use the data to learn about \(P\) .
My model
\[
-\P = \{ \beta \in \R^p, \sigma>0 : Y_i \given X_i=x_i \sim N(x_i^\top\beta,\ \sigma^2) \}.
+\P = \{P : Y | X \sim N(X^\top\beta,\ \sigma^2), \beta \in \R^p, \sigma>0\}.
\]
-To completely characterize \(P\) , I just need to estimate \(\beta\) and \(\sigma\) .
To completely characterize the \(Y|X\) -conditional of \(P\) , I just need to estimate \(\beta\) and \(\sigma\) .
+
+I’m not interested in learning the \(X\) -marginal of \(P\)
+ Need to assume that \(P\in\P\) .
This time, I have to assume a lot more: (conditional) Linearity, independence, conditional Gaussian noise, no ignored variables, no collinearity, etc.
This time, I have to assume a lot more: (conditional) linearity, independence, conditional Gaussian noise, no ignored variables, no collinearity, etc.
Statistical models, unfamiliar example
-We observe data \(Z_i \in \R\) generated by some probability distribution \(P\) . We want to use the data to learn about \(P\) .
+We observe data \(Z \in \R\) generated by some probability distribution \(P\) . We want to use the data to learn about \(P\) .
My model
\[
-\P = \{ Z_i \textrm{ has a density function } f \}.
+\P = \{P : Z \textrm{ has a density function } f \}.
\]
To completely characterize \(P\) , I need to estimate \(f\) .
In fact, we can’t hope to do this.
-Revised Model 1 - \(\P=\{ Z_i \textrm{ has a density function } f : \int (f'')^2 dx < M \}\)
-Revised Model 2 - \(\P=\{ Z_i \textrm{ has a density function } f : \int (f'')^2 dx < K < M \}\)
-Revised Model 3 - \(\P=\{ Z_i \textrm{ has a density function } f : \int |f'| dx < M \}\)
+Revised Model 1 - \(\P=\{ Z \textrm{ has a density function } f : \int (f'')^2 dx < M \}\)
+Revised Model 2 - \(\P=\{ Z \textrm{ has a density function } f : \int (f'')^2 dx < K < M \}\)
+Revised Model 3 - \(\P=\{ Z \textrm{ has a density function } f : \int |f'| dx < M \}\)
Each of these suggests different ways of estimating \(f\)
diff --git a/schedule/slides/03-regression-function_files/figure-revealjs/unnamed-chunk-1-1.svg b/schedule/slides/03-regression-function_files/figure-revealjs/unnamed-chunk-1-1.svg
index e3e4249..de46afd 100644
--- a/schedule/slides/03-regression-function_files/figure-revealjs/unnamed-chunk-1-1.svg
+++ b/schedule/slides/03-regression-function_files/figure-revealjs/unnamed-chunk-1-1.svg
@@ -1,276 +1,269 @@
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diff --git a/search.json b/search.json
index 73118ad..e230521 100644
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+++ b/search.json
@@ -3028,7 +3028,7 @@
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"title": "UBC Stat406 2024W",
"section": "03 The regression function",
- "text": "03 The regression function\nStat 406\nGeoff Pleiss, Trevor Campbell\nLast modified – 18 September 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\]"
+ "text": "03 The regression function\nStat 406\nGeoff Pleiss, Trevor Campbell\nLast modified – 14 September 2024\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\newcommand{\\U}{\\mathbf{U}}\n\\newcommand{\\D}{\\mathbf{D}}\n\\newcommand{\\V}{\\mathbf{V}}\n\\]"
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- "text": "Statistical models 101\nWe observe data \\(Z_1,\\ Z_2,\\ \\ldots,\\ Z_n\\) generated by some probability distribution \\(P\\). We want to use the data to learn about \\(P\\).\n\nA statistical model is a set of distributions \\(\\mathcal{P}\\).\n\nSome examples:\n\n\\(\\P = \\{ 0 < p < 1 : P(z=1)=p,\\ P(z=0)=1-p\\}\\).\n\\(\\P = \\{ \\beta \\in \\R^p,\\ \\sigma>0 : Y \\sim N(X^\\top\\beta,\\sigma^2),\\ X\\mbox{ fixed}\\}\\).\n\\(\\P = \\{\\mbox{all CDF's }F\\}\\).\n\\(\\P = \\{\\mbox{all smooth functions } f: \\R^p \\rightarrow \\R : Z_i = (X_i, Y_i),\\ E[Y_i] = f(X_i) \\}\\)"
+ "text": "Statistical models 101\nWe observe data \\(Z_1,\\ Z_2,\\ \\ldots,\\ Z_n\\) generated by some probability distribution \\(P\\). We want to use the data to learn about \\(P\\).\n\nA statistical model is a set of distributions \\(\\mathcal{P}\\).\n\nSome examples:\n\n\\(\\P = \\{P : P(Z=1)=p,\\ P(Z=0)=1-p, 0 \\leq p \\leq 1\\}\\).\n\\(\\P = \\{P : Y | X \\sim N(X^\\top\\beta,\\sigma^2),\\ \\beta \\in \\R^p,\\ \\sigma>0\\}\\) (here \\(Z = (Y,X)\\))\n\\(\\P = \\{P \\mbox{ given by any CDF }F\\}\\).\n\\(\\P = \\{P : E[Y | X] = f(X) \\mbox{ for some smooth } f: \\R^p \\rightarrow \\R\\}\\) (here \\(Z = (Y,X)\\))"
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+ "text": "Statistical models\nWe want to use the data to select a distribution \\(P\\) that probably generated the data.\n\nMy model:\n\\[\n\\P = \\{P: P(z=1)=p,\\ P(z=0)=1-p,\\ 0 < p < 1 \\}\n\\]\n\nTo completely characterize \\(P\\), I just need to estimate \\(p\\).\nNeed to assume that \\(P \\in \\P\\).\nThis assumption is mostly empty: need independent, can’t see \\(z=12\\)."
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- "text": "Statistical models\nWe observe data \\(Z_i=(Y_i,X_i)\\) generated by some probability distribution \\(P\\). We want to use the data to learn about \\(P\\).\n\nMy model\n\\[\n\\P = \\{ \\beta \\in \\R^p, \\sigma>0 : Y_i \\given X_i=x_i \\sim N(x_i^\\top\\beta,\\ \\sigma^2) \\}.\n\\]\n\nTo completely characterize \\(P\\), I just need to estimate \\(\\beta\\) and \\(\\sigma\\).\nNeed to assume that \\(P\\in\\P\\).\nThis time, I have to assume a lot more: (conditional) Linearity, independence, conditional Gaussian noise, no ignored variables, no collinearity, etc."
+ "text": "Statistical models\nWe observe data \\((Y, X)\\) generated by some probability distribution \\(P\\) on \\(\\R \\times \\R^p\\). We want to use the data to learn about \\(P\\).\n\nMy model\n\\[\n\\P = \\{P : Y | X \\sim N(X^\\top\\beta,\\ \\sigma^2), \\beta \\in \\R^p, \\sigma>0\\}.\n\\]\n\nTo completely characterize the \\(Y|X\\)-conditional of \\(P\\), I just need to estimate \\(\\beta\\) and \\(\\sigma\\).\n\nI’m not interested in learning the \\(X\\)-marginal of \\(P\\)\n\nNeed to assume that \\(P\\in\\P\\).\nThis time, I have to assume a lot more: (conditional) linearity, independence, conditional Gaussian noise, no ignored variables, no collinearity, etc."
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"section": "Statistical models, unfamiliar example",
- "text": "Statistical models, unfamiliar example\nWe observe data \\(Z_i \\in \\R\\) generated by some probability distribution \\(P\\). We want to use the data to learn about \\(P\\).\nMy model\n\\[\n\\P = \\{ Z_i \\textrm{ has a density function } f \\}.\n\\]\n\nTo completely characterize \\(P\\), I need to estimate \\(f\\).\nIn fact, we can’t hope to do this.\n\nRevised Model 1 - \\(\\P=\\{ Z_i \\textrm{ has a density function } f : \\int (f'')^2 dx < M \\}\\)\nRevised Model 2 - \\(\\P=\\{ Z_i \\textrm{ has a density function } f : \\int (f'')^2 dx < K < M \\}\\)\nRevised Model 3 - \\(\\P=\\{ Z_i \\textrm{ has a density function } f : \\int |f'| dx < M \\}\\)\n\nEach of these suggests different ways of estimating \\(f\\)"
+ "text": "Statistical models, unfamiliar example\nWe observe data \\(Z \\in \\R\\) generated by some probability distribution \\(P\\). We want to use the data to learn about \\(P\\).\nMy model\n\\[\n\\P = \\{P : Z \\textrm{ has a density function } f \\}.\n\\]\n\nTo completely characterize \\(P\\), I need to estimate \\(f\\).\nIn fact, we can’t hope to do this.\n\nRevised Model 1 - \\(\\P=\\{ Z \\textrm{ has a density function } f : \\int (f'')^2 dx < M \\}\\)\nRevised Model 2 - \\(\\P=\\{ Z \\textrm{ has a density function } f : \\int (f'')^2 dx < K < M \\}\\)\nRevised Model 3 - \\(\\P=\\{ Z \\textrm{ has a density function } f : \\int |f'| dx < M \\}\\)\n\nEach of these suggests different ways of estimating \\(f\\)"
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"section": "02 Linear model example",
- "text": "02 Linear model example\nStat 406\nGeoff Pleiss, Trevor Campbell\nLast modified – 10 December 2023\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\newcommand{\\U}{\\mathbf{U}}\n\\newcommand{\\D}{\\mathbf{D}}\n\\newcommand{\\V}{\\mathbf{V}}\n\\]"
+ "text": "02 Linear model example\nStat 406\nGeoff Pleiss, Trevor Campbell\nLast modified – 13 September 2024\n\\[\n\\DeclareMathOperator*{\\argmin}{argmin}\n\\DeclareMathOperator*{\\argmax}{argmax}\n\\DeclareMathOperator*{\\minimize}{minimize}\n\\DeclareMathOperator*{\\maximize}{maximize}\n\\DeclareMathOperator*{\\find}{find}\n\\DeclareMathOperator{\\st}{subject\\,\\,to}\n\\newcommand{\\E}{E}\n\\newcommand{\\Expect}[1]{\\E\\left[ #1 \\right]}\n\\newcommand{\\Var}[1]{\\mathrm{Var}\\left[ #1 \\right]}\n\\newcommand{\\Cov}[2]{\\mathrm{Cov}\\left[#1,\\ #2\\right]}\n\\newcommand{\\given}{\\ \\vert\\ }\n\\newcommand{\\X}{\\mathbf{X}}\n\\newcommand{\\x}{\\mathbf{x}}\n\\newcommand{\\y}{\\mathbf{y}}\n\\newcommand{\\P}{\\mathcal{P}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\norm}[1]{\\left\\lVert #1 \\right\\rVert}\n\\newcommand{\\snorm}[1]{\\lVert #1 \\rVert}\n\\newcommand{\\tr}[1]{\\mbox{tr}(#1)}\n\\newcommand{\\brt}{\\widehat{\\beta}^R_{s}}\n\\newcommand{\\brl}{\\widehat{\\beta}^R_{\\lambda}}\n\\newcommand{\\bls}{\\widehat{\\beta}_{ols}}\n\\newcommand{\\blt}{\\widehat{\\beta}^L_{s}}\n\\newcommand{\\bll}{\\widehat{\\beta}^L_{\\lambda}}\n\\newcommand{\\U}{\\mathbf{U}}\n\\newcommand{\\D}{\\mathbf{D}}\n\\newcommand{\\V}{\\mathbf{V}}\n\\]"
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"section": "Analysis",
- "text": "Analysis\n\nRandomly split into a training (say 3/4) and a test set (1/4)\nUse training set to fit a model\nFit the “full” model\n“Look” at the fit\n\n\n\nset.seed(20220914)\nmob <- mobility[complete.cases(mobility), ]\nn <- nrow(mob)\nmob <- mob |> select(-Name, -ID, -State)\nset <- sample.int(n, floor(n * .75), FALSE)\ntrain <- mob[set, ]\ntest <- mob[setdiff(1:n, set), ]\nfull <- lm(Mobility ~ ., data = train)\n\n\nWhy don’t we include Name or ID?"
+ "text": "Analysis\n\nRandomly split into a training (say 3/4) and a test set (1/4)\nUse training set to fit a model\nFit the “full” model\n“Look” at the fit\n\n\n\nset.seed(20220914)\nmob <- mobility[complete.cases(mobility), ] |>\n select(-Name, -ID, -State)\nn <- nrow(mob)\nset <- sample.int(n, floor(n * .75), FALSE)\ntrain <- mob[set, ]\ntest <- mob[setdiff(1:n, set), ]\nfull <- lm(Mobility ~ ., data = train)\n\n\nWhy don’t we include Name or ID?"
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- "text": "Results\n\nsummary(full)\n\n\nCall:\nlm(formula = Mobility ~ ., data = train)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.072092 -0.010256 -0.001452 0.009170 0.090428 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 1.849e-01 8.083e-02 2.288 0.022920 * \nPopulation 3.378e-09 2.478e-09 1.363 0.173916 \nUrban 2.853e-03 3.892e-03 0.733 0.464202 \nBlack 7.807e-02 2.859e-02 2.731 0.006735 ** \nSeg_racial -5.626e-02 1.780e-02 -3.160 0.001754 ** \nSeg_income 8.677e-01 9.355e-01 0.928 0.354453 \nSeg_poverty -7.416e-01 5.014e-01 -1.479 0.140316 \nSeg_affluence -2.224e-01 4.763e-01 -0.467 0.640874 \nCommute 6.313e-02 2.838e-02 2.225 0.026915 * \nIncome 4.207e-07 6.997e-07 0.601 0.548112 \nGini 3.592e+00 3.357e+00 1.070 0.285578 \nShare01 -3.635e-02 3.357e-02 -1.083 0.279925 \nGini_99 -3.657e+00 3.356e+00 -1.090 0.276704 \nMiddle_class 1.031e-01 4.835e-02 2.133 0.033828 * \nLocal_tax_rate 2.268e-01 2.620e-01 0.866 0.387487 \nLocal_gov_spending 1.273e-07 3.016e-06 0.042 0.966374 \nProgressivity 4.983e-03 1.324e-03 3.764 0.000205 ***\nEITC -3.324e-04 4.528e-04 -0.734 0.463549 \nSchool_spending -9.019e-04 2.272e-03 -0.397 0.691658 \nStudent_teacher_ratio -1.639e-03 1.123e-03 -1.459 0.145748 \nTest_scores 2.487e-04 3.137e-04 0.793 0.428519 \nHS_dropout -1.698e-01 9.352e-02 -1.816 0.070529 . \nColleges -2.811e-02 7.661e-02 -0.367 0.713942 \nTuition 3.459e-07 4.362e-07 0.793 0.428417 \nGraduation -1.702e-02 1.425e-02 -1.194 0.233650 \nLabor_force_participation -7.850e-02 5.405e-02 -1.452 0.147564 \nManufacturing -1.605e-01 2.816e-02 -5.700 3.1e-08 ***\nChinese_imports -5.165e-04 1.004e-03 -0.514 0.607378 \nTeenage_labor -1.019e+00 2.111e+00 -0.483 0.629639 \nMigration_in 4.490e-02 3.480e-01 0.129 0.897436 \nMigration_out -4.475e-01 4.093e-01 -1.093 0.275224 \nForeign_born 9.137e-02 5.494e-02 1.663 0.097454 . \nSocial_capital -1.114e-03 2.728e-03 -0.408 0.683245 \nReligious 4.570e-02 1.298e-02 3.520 0.000506 ***\nViolent_crime -3.393e+00 1.622e+00 -2.092 0.037373 * \nSingle_mothers -3.590e-01 9.442e-02 -3.802 0.000177 ***\nDivorced 1.707e-02 1.603e-01 0.107 0.915250 \nMarried -5.894e-02 7.246e-02 -0.813 0.416720 \nLongitude -4.239e-05 2.239e-04 -0.189 0.850001 \nLatitude 6.725e-04 5.687e-04 1.182 0.238037 \n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.02128 on 273 degrees of freedom\nMultiple R-squared: 0.7808, Adjusted R-squared: 0.7494 \nF-statistic: 24.93 on 39 and 273 DF, p-value: < 2.2e-16"
+ "text": "Results\n(dispatch happening here!)\n\nsummary(full)\n\n\nCall:\nlm(formula = Mobility ~ ., data = train)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.072092 -0.010256 -0.001452 0.009170 0.090428 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 1.849e-01 8.083e-02 2.288 0.022920 * \nPopulation 3.378e-09 2.478e-09 1.363 0.173916 \nUrban 2.853e-03 3.892e-03 0.733 0.464202 \nBlack 7.807e-02 2.859e-02 2.731 0.006735 ** \nSeg_racial -5.626e-02 1.780e-02 -3.160 0.001754 ** \nSeg_income 8.677e-01 9.355e-01 0.928 0.354453 \nSeg_poverty -7.416e-01 5.014e-01 -1.479 0.140316 \nSeg_affluence -2.224e-01 4.763e-01 -0.467 0.640874 \nCommute 6.313e-02 2.838e-02 2.225 0.026915 * \nIncome 4.207e-07 6.997e-07 0.601 0.548112 \nGini 3.592e+00 3.357e+00 1.070 0.285578 \nShare01 -3.635e-02 3.357e-02 -1.083 0.279925 \nGini_99 -3.657e+00 3.356e+00 -1.090 0.276704 \nMiddle_class 1.031e-01 4.835e-02 2.133 0.033828 * \nLocal_tax_rate 2.268e-01 2.620e-01 0.866 0.387487 \nLocal_gov_spending 1.273e-07 3.016e-06 0.042 0.966374 \nProgressivity 4.983e-03 1.324e-03 3.764 0.000205 ***\nEITC -3.324e-04 4.528e-04 -0.734 0.463549 \nSchool_spending -9.019e-04 2.272e-03 -0.397 0.691658 \nStudent_teacher_ratio -1.639e-03 1.123e-03 -1.459 0.145748 \nTest_scores 2.487e-04 3.137e-04 0.793 0.428519 \nHS_dropout -1.698e-01 9.352e-02 -1.816 0.070529 . \nColleges -2.811e-02 7.661e-02 -0.367 0.713942 \nTuition 3.459e-07 4.362e-07 0.793 0.428417 \nGraduation -1.702e-02 1.425e-02 -1.194 0.233650 \nLabor_force_participation -7.850e-02 5.405e-02 -1.452 0.147564 \nManufacturing -1.605e-01 2.816e-02 -5.700 3.1e-08 ***\nChinese_imports -5.165e-04 1.004e-03 -0.514 0.607378 \nTeenage_labor -1.019e+00 2.111e+00 -0.483 0.629639 \nMigration_in 4.490e-02 3.480e-01 0.129 0.897436 \nMigration_out -4.475e-01 4.093e-01 -1.093 0.275224 \nForeign_born 9.137e-02 5.494e-02 1.663 0.097454 . \nSocial_capital -1.114e-03 2.728e-03 -0.408 0.683245 \nReligious 4.570e-02 1.298e-02 3.520 0.000506 ***\nViolent_crime -3.393e+00 1.622e+00 -2.092 0.037373 * \nSingle_mothers -3.590e-01 9.442e-02 -3.802 0.000177 ***\nDivorced 1.707e-02 1.603e-01 0.107 0.915250 \nMarried -5.894e-02 7.246e-02 -0.813 0.416720 \nLongitude -4.239e-05 2.239e-04 -0.189 0.850001 \nLatitude 6.725e-04 5.687e-04 1.182 0.238037 \n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.02128 on 273 degrees of freedom\nMultiple R-squared: 0.7808, Adjusted R-squared: 0.7494 \nF-statistic: 24.93 on 39 and 273 DF, p-value: < 2.2e-16"
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"section": "Diagnostic plots",
- "text": "Diagnostic plots\n\n\npar(mar = c(5, 3, 0, 0))\nplot(full, 1)\n\n\n\n\n\n\n\n\n\n\n\nplot(full, 2)"
+ "text": "Diagnostic plots\n\n\nstuff <- tibble(\n residuals = residuals(full),\n fitted = fitted(full),\n stdresiduals = rstandard(full)\n)\nggplot(stuff, aes(fitted, residuals)) +\n geom_point() +\n geom_smooth(\n se = FALSE,\n colour = \"steelblue\",\n linewidth = 2\n ) +\n ggtitle(\"Residuals vs Fitted\")\n\n\n\n\n\n\n\n\n\n\n\nggplot(stuff, aes(sample = stdresiduals)) +\n geom_qq(size = 2) +\n geom_qq_line(linewidth = 2, color = \"steelblue\") +\n labs(\n x = \"Theoretical quantiles\",\n y = \"Standardized residuals\",\n title = \"Normal Q-Q\"\n )"
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- "objectID": "schedule/slides/02-lm-example.html#section-1",
- "href": "schedule/slides/02-lm-example.html#section-1",
+ "objectID": "schedule/slides/02-lm-example.html#can-also-just-use-dispatched-plot",
+ "href": "schedule/slides/02-lm-example.html#can-also-just-use-dispatched-plot",
"title": "UBC Stat406 2024W",
- "section": "",
- "text": "(Those were plot methods for objects of class lm)\nSame thing in ggplot\n\n\nstuff <- tibble(\n residuals = residuals(full),\n fitted = fitted(full),\n stdresiduals = rstandard(full)\n)\nggplot(stuff, aes(fitted, residuals)) +\n geom_point(colour = \"salmon\") +\n geom_smooth(\n se = FALSE,\n colour = \"steelblue\",\n linewidth = 2\n ) +\n ggtitle(\"Residuals vs Fitted\")\n\n\n\n\n\n\n\n\n\n\n\nggplot(stuff, aes(sample = stdresiduals)) +\n geom_qq(colour = \"purple\", size = 2) +\n geom_qq_line(colour = \"peachpuff\", linewidth = 2) +\n labs(\n x = \"Theoretical quantiles\",\n y = \"Standardized residuals\",\n title = \"Normal Q-Q\"\n )"
+ "section": "Can also just use dispatched plot",
+ "text": "Can also just use dispatched plot\n\n\nplot(full, 1)\n\n\n\n\n\n\n\n\n\n\n\nplot(full, 2)"
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"section": "Fit a reduced model",
- "text": "Fit a reduced model\n\nreduced <- lm(\n Mobility ~ Commute + Gini_99 + Test_scores + HS_dropout +\n Manufacturing + Migration_in + Religious + Single_mothers,\n data = train\n)\n\nsummary(reduced)$coefficients |> as_tibble()\n\n# A tibble: 9 × 4\n Estimate `Std. Error` `t value` `Pr(>|t|)`\n <dbl> <dbl> <dbl> <dbl>\n1 0.166 0.0178 9.36 1.83e-18\n2 0.0637 0.0149 4.27 2.62e- 5\n3 -0.109 0.0390 -2.79 5.64e- 3\n4 0.000500 0.000256 1.95 5.19e- 2\n5 -0.216 0.0820 -2.64 8.81e- 3\n6 -0.159 0.0202 -7.89 5.65e-14\n7 -0.389 0.172 -2.26 2.42e- 2\n8 0.0436 0.0105 4.16 4.08e- 5\n9 -0.286 0.0466 -6.15 2.44e- 9\n\nreduced |>\n broom::glance() |>\n print(width = 120)\n\n# A tibble: 1 × 12\n r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC\n <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>\n1 0.718 0.711 0.0229 96.9 5.46e-79 8 743. -1466. -1429.\n deviance df.residual nobs\n <dbl> <int> <int>\n1 0.159 304 313"
+ "text": "Fit a reduced model\n\nreduced <- lm(\n Mobility ~ Commute + Gini_99 + Test_scores + HS_dropout +\n Manufacturing + Migration_in + Religious + Single_mothers,\n data = train\n)\n\nsummary(reduced)$coefficients \n\n Estimate Std. Error t value Pr(>|t|)\n(Intercept) 0.1663344179 0.017769995 9.360409 1.829270e-18\nCommute 0.0637329409 0.014926382 4.269819 2.618234e-05\nGini_99 -0.1086058241 0.038958986 -2.787696 5.642726e-03\nTest_scores 0.0004997645 0.000256038 1.951915 5.186618e-02\nHS_dropout -0.2162067301 0.082003195 -2.636565 8.805228e-03\nManufacturing -0.1594229237 0.020215791 -7.886059 5.647668e-14\nMigration_in -0.3891567027 0.171839168 -2.264657 2.423771e-02\nReligious 0.0435673365 0.010463920 4.163577 4.084854e-05\nSingle_mothers -0.2864269552 0.046578928 -6.149282 2.444903e-09\n\nreduced |>\n broom::glance() |>\n print(width = 120)\n\n# A tibble: 1 × 12\n r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC\n <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>\n1 0.718 0.711 0.0229 96.9 5.46e-79 8 743. -1466. -1429.\n deviance df.residual nobs\n <dbl> <int> <int>\n1 0.159 304 313"
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diff --git a/sitemap.xml b/sitemap.xml
index c6d267a..53b3320 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -2,194 +2,194 @@
https://UBC-STAT.github.io/stat-406/schedule/slides/00-r-review.html
- 2024-09-12T14:52:23.522Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/handouts/keras-nnet.html
- 2024-09-12T14:52:23.518Z
+ 2024-09-14T15:54:43.952Z
https://UBC-STAT.github.io/stat-406/schedule/slides/11-kernel-smoothers.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/09-l1-penalties.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/18-the-bootstrap.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.964Z
https://UBC-STAT.github.io/stat-406/schedule/slides/23-nnets-other.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.964Z
https://UBC-STAT.github.io/stat-406/schedule/slides/25-pca-issues.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.964Z
https://UBC-STAT.github.io/stat-406/schedule/slides/24-pca-intro.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.964Z
https://UBC-STAT.github.io/stat-406/schedule/slides/15-LDA-and-QDA.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/08-ridge-regression.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/00-quiz-0-wrap.html
- 2024-09-12T14:52:23.522Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/27-kmeans.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.964Z
https://UBC-STAT.github.io/stat-406/schedule/slides/14-classification-intro.html
- 2024-09-12T14:52:23.526Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/04-bias-variance.html
- 2024-09-12T14:52:23.522Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/00-cv-for-many-models.html
- 2024-09-12T14:52:23.522Z
+ 2024-09-14T15:54:43.960Z
https://UBC-STAT.github.io/stat-406/schedule/slides/01-lm-review.html
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