mirror of
https://github.com/jackyzha0/quartz.git
synced 2025-12-24 05:14:06 -06:00
out with the pocket
This commit is contained in:
jaden
parent
156d3bf249
commit
f302f6db4a
1
.gitignore
vendored
1
.gitignore
vendored
@ -7,3 +7,4 @@ assets/indices/linkIndex.json
|
||||
assets/indices/contentIndex.json
|
||||
content/Obsidian\ Vault/textbooks/
|
||||
content/Obsidian\ Vault/private/
|
||||
content/Obsidian\ Vault/pocket/
|
||||
|
||||
@ -7,6 +7,7 @@ disablePathToLower = true
|
||||
ignoreFiles = [
|
||||
"/content/templates/*",
|
||||
"/content/private/*",
|
||||
"/content/Obsidian Vault/templates/*"
|
||||
]
|
||||
summaryLength = 20
|
||||
paginate = 10
|
||||
|
||||
32
content/Obsidian Vault/.obsidian/workspace
vendored
32
content/Obsidian Vault/.obsidian/workspace
vendored
@ -9,7 +9,7 @@
|
||||
"state": {
|
||||
"type": "markdown",
|
||||
"state": {
|
||||
"file": "Goals.md",
|
||||
"file": "econometrics/stats-econ-lecture-notes-plus.md",
|
||||
"mode": "source"
|
||||
}
|
||||
},
|
||||
@ -21,7 +21,7 @@
|
||||
"state": {
|
||||
"type": "markdown",
|
||||
"state": {
|
||||
"file": "Goals.md",
|
||||
"file": "econometrics/stats-econ-lecture-notes-plus.md",
|
||||
"mode": "preview"
|
||||
}
|
||||
},
|
||||
@ -52,7 +52,7 @@
|
||||
"state": {
|
||||
"type": "search",
|
||||
"state": {
|
||||
"query": "eternalfamiliesall",
|
||||
"query": "{{q}",
|
||||
"matchingCase": true,
|
||||
"explainSearch": false,
|
||||
"collapseAll": false,
|
||||
@ -101,7 +101,7 @@
|
||||
"state": {
|
||||
"type": "backlink",
|
||||
"state": {
|
||||
"file": "Goals.md",
|
||||
"file": "econometrics/stats-econ-lecture-notes-plus.md",
|
||||
"collapseAll": false,
|
||||
"extraContext": false,
|
||||
"sortOrder": "alphabetical",
|
||||
@ -118,7 +118,7 @@
|
||||
"state": {
|
||||
"type": "outgoing-link",
|
||||
"state": {
|
||||
"file": "Goals.md",
|
||||
"file": "econometrics/stats-econ-lecture-notes-plus.md",
|
||||
"linksCollapsed": false,
|
||||
"unlinkedCollapsed": true
|
||||
}
|
||||
@ -130,7 +130,7 @@
|
||||
"state": {
|
||||
"type": "outline",
|
||||
"state": {
|
||||
"file": "Goals.md"
|
||||
"file": "econometrics/stats-econ-lecture-notes-plus.md"
|
||||
}
|
||||
}
|
||||
},
|
||||
@ -154,15 +154,15 @@
|
||||
},
|
||||
"active": "e6ce38905c7e26b9",
|
||||
"lastOpenFiles": [
|
||||
"Goals.md",
|
||||
"Eternalfamiliesall.md",
|
||||
"binomial series.md",
|
||||
"taylor.md",
|
||||
"power series.md",
|
||||
"orthogonal.md",
|
||||
"Series.md",
|
||||
"strategies for computing sum of series.md",
|
||||
"remnote backup/taxes.md",
|
||||
"remnote backup/why square and then square root when getting standard deviation??.md"
|
||||
"econometrics/stats-econ-lecture-notes-plus.md",
|
||||
"recovered stats lecture notes.md",
|
||||
"econometrics/stats-econ-lecture-notes.md",
|
||||
"LinearAlgebra1.md",
|
||||
"mean value theorem.md",
|
||||
"Integration by Parts.md",
|
||||
"systems of linear equations and matrices..md",
|
||||
"ss12.md",
|
||||
"ss15.md",
|
||||
"ss16.md"
|
||||
]
|
||||
}
|
||||
@ -1,4 +1,4 @@
|
||||
not yaml
|
||||
#church
|
||||
- Required Readings Study Guide
|
||||
- Reminder: In order to protect the integrity of our class quizzes and exams no questions from our study guides, quizzes, midterm, or final may be posted on-line in any public venue/format. This includes Google Docs as well as the various quizzing websites/apps like Quizlet, StudyBlue, etc. You are obviously free (and encouraged) to use any and all such sites, but if you include any questions from our class material, they must be made private so no one else can see them and they cannot be shared with others in or out of BYU. Besides the associated copyright laws (yep - weird but a teachers materials such as study guides et al. are actually copyright protected). this policy also pertains to BYU's Academic Honesty Policy and will be treated as such.
|
||||
-
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
not yaml
|
||||
#todo
|
||||
- meditation 3x/day
|
||||
- deep scripture study 1hr 1x/day
|
||||
- workout 2x/week
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
---
|
||||
date: [[2022-05-03]]
|
||||
day: [[2022-05-03]]
|
||||
---
|
||||
|
||||
#math/calculus
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
cards-deck: default_obsidian
|
||||
date: [[2022-04-27]]
|
||||
day: [[2022-04-27]]
|
||||
tags: #linear_algebra
|
||||
---
|
||||
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#todo
|
||||
- air filter
|
||||
- taxes
|
||||
- car registration
|
||||
|
||||
@ -3579,7 +3579,7 @@ Sample Variance
|
||||
|
||||
2. Wages gap between men and women:
|
||||
|
||||
> $n_{w} = 40$, ${{}_{w} = \$ 32,\ \sigma_{w} = \$ 13,\ \ n}_{m} = 45$,
|
||||
> $n_{w} = 40$, ${q}_{w}} = \$ 32,\ \sigma_{w} = \$ 13,\ \ n}_{m} = 45$,
|
||||
> ${}_{m} = \$ 35$, $\sigma_{m} = \$ 15$.
|
||||
|
||||
1. 95% confidence intervals for men
|
||||
@ -3804,7 +3804,7 @@ $\sim \chi^{2}\left( n - 1 \right) + \chi^{2}\left( 1 \right) + 0$
|
||||
2. Critical value $90.53$
|
||||
|
||||
3. Test statistic
|
||||
> $\left( n - 1 \right)\frac{S^{2}}{\sigma^{2}} = 70\left( \frac{{5.3}^{2}}{4^{2}} \right) = 122.9$,
|
||||
> $\left( n - 1 \right)\frac{S^{2}}{\sigma^{2}} = 70\left( \frac{5.3^{2}}{4^{2}} \right) = 122.9$,
|
||||
> reject $H_{0}$ (from Excel, p-value is $10^{- 5}$)
|
||||
|
||||
# L22 Regression Estimation (WMS 11.1-3)
|
||||
@ -4050,7 +4050,7 @@ Intercept estimator
|
||||
> unbiased ☺!
|
||||
|
||||
> It can be shown that
|
||||
> $V\left( {\widehat{\beta}}_{0} \right) = \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{{}^{2}}{\left( n - 1 \right)s_{x}^{2}} \right) \rightarrow 0$;
|
||||
> $V\left( {\widehat{\beta}}_{0} \right) = \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{q}^{2}}{\left( n - 1 \right)s_{x}^{2}} \right) \rightarrow 0$;
|
||||
> consistent ☺!
|
||||
|
||||
1. \[For those curious,
|
||||
@ -4063,7 +4063,7 @@ Intercept estimator
|
||||
>
|
||||
> $= V\left( \right) + {}^{2}V\left( {\widehat{\beta}}_{1} \right) - 2\text{Cov}\left( ,{\widehat{\beta}}_{1} \right)$
|
||||
>
|
||||
> $= \frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 = \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{{}^{2}}{\left( n - 1 \right)s_{x}^{2}} \right) \rightarrow 0$
|
||||
> $= \frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 = \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{q}^{2}}{\left( n - 1 \right)s_{x}^{2}} \right) \rightarrow 0$
|
||||
>
|
||||
> Note: $C\left( ,{\widehat{\beta}}_{1} \right) = 0$ because…
|
||||
>
|
||||
@ -4097,7 +4097,7 @@ Prediction estimator
|
||||
|
||||
> \[$V\left( \widehat{\beta_{0} + \beta_{1}x_{i}} \right) = V\left( {\widehat{\beta}}_{0} \right) + x_{i}^{2}V\left( {\widehat{\beta}}_{1} \right) + 2Cov\left( {\widehat{\beta}}_{0},{\widehat{\beta}}_{1}x_{i} \right)$
|
||||
>
|
||||
> $= \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{{}^{2}}{S_{\text{xx}}} \right) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$
|
||||
> $= \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{q}^{2}}{S_{\text{xx}}} \right) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$
|
||||
> (since
|
||||
> $\text{Cov}\left( {\widehat{\beta}}_{0},{\widehat{\beta}}_{1} \right) = Cov\left( - {\widehat{\beta}}_{1},{\widehat{\beta}}_{1} \right) = 0 - \frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$)
|
||||
> $= \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{\left( x_{i} - \right)^{2}}{S_{\text{xx}}} \right) = \sigma_{\varepsilon}^{2}\left( \frac{1}{n} + \frac{\left( x_{i} - \right)^{2}}{S_{\text{xx}}} \right)$\]
|
||||
|
||||
@ -347,7 +347,7 @@ ii. Excel: use VAR.S or STDEV.S, not =VAR.P or =STDEV.P
|
||||
- Relating quantitative and binary variables: conditional distributions, conditional means $E(X = 0)$, $E(X = 1)$
|
||||
|
||||
- Wages gap between men and women:
|
||||
$n_{w} = 40$, ${{}_{w} =\$ 32,\sigma_{w} =\$ 13,n}_{m} = 45$, ${}_{m} =\$ 35$, $\sigma_{m} =\$ 15$.
|
||||
$n_{w} = 40$, ${q_{w} =\$ 32,\sigma_{w} =\$ 13,n}_{m} = 45$, ${}_{m} =\$ 35$, $\sigma_{m} =\$ 15$.
|
||||
|
||||
- 95% confidence intervals for men $\lbrack\$ 30.62,\$ 39.38\rbrack$ and women $\lbrack\$ 27.97,\$ 36.03\rbrack$ overlap, making it difficult to tell true size of wage gap (if any)
|
||||
|
||||
@ -464,7 +464,7 @@ $\sim\chi^{2}(n - 1) +\chi^{2}(1) + 0$
|
||||
- Hypothesis test
|
||||
1. $H_{a}:\sigma^{2} > 4^{2}$, $\alpha = .05$
|
||||
2. Critical value $90.53$
|
||||
3. Test statistic $(n - 1)\frac{S^{2}}{\sigma^{2}} = 70(\frac{{5.3}^{2}}{4^{2}}) = 122.9$, reject $H_{0}$ (from Excel, p-value is $10^{- 5}$)
|
||||
3. Test statistic $(n - 1)\frac{S^{2}}{\sigma^{2}} = 70(\frac{5.3^{2}}{4^{2}}) = 122.9$, reject $H_{0}$ (from Excel, p-value is $10^{- 5}$)
|
||||
|
||||
# L22 Regression Estimation (WMS 11.1-3)
|
||||
|
||||
@ -606,10 +606,10 @@ Slope estimator
|
||||
Intercept estimator
|
||||
|
||||
1. It can be shown that $E({\widehat{\beta}}_{0}) =\ldots =\beta_{0}$; unbiased ☺!
|
||||
It can be shown that $V({\widehat{\beta}}_{0}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{(n - 1)s_{x}^{2}})arrow 0$; consistent ☺!
|
||||
It can be shown that $V({\widehat{\beta}}_{0}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q^{2}}{(n - 1)s_{x}^{2}})arrow 0$; consistent ☺!
|
||||
|
||||
-\[For those curious,
|
||||
$E({\widehat{\beta}}_{0}) = E(\frac{1}{n}Y_{i} - {\widehat{\beta}}_{1}) =\frac{1}{n}\lbrack\beta_{0} +\beta_{1}x_{i} + E(\varepsilon_{i})\rbrack - E({\widehat{\beta}}_{1})$ $=\frac{n\beta_{0}}{n} +\beta_{1}\frac{1}{n}x_{i} -\beta_{1} =\beta_{0}$ $V({\widehat{\beta}}_{0}) = V(- {\widehat{\beta}}_{1})$ $= V() + {}^{2}V({\widehat{\beta}}_{1}) - 2\text{Cov}(,{\widehat{\beta}}_{1})$ $=\frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{(n - 1)s_{x}^{2}})arrow 0$ Note: $C(,{\widehat{\beta}}_{1}) = 0$ because... $C(\frac{1}{n}Y_{i},\frac{1}{S_{\text{xx}}}(x_{i} -)Y_{j}) =\frac{1}{nS_{\text{xx}}}C(Y_{i},(x_{i} -)Y_{j})$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)C(Y_{i},Y_{i}) +(x_{i} -)C(Y_{i},Y_{j})\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)V(Y_{i}) +(x_{i} -)0\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack\sigma_{y}^{2}(x_{i} -)\rbrack$ $=\frac{\sigma_{y}^{2}}{nS_{\text{xx}}}\lbrack 0\rbrack$\]
|
||||
$E({\widehat{\beta}}_{0}) = E(\frac{1}{n}Y_{i} - {\widehat{\beta}}_{1}) =\frac{1}{n}\lbrack\beta_{0} +\beta_{1}x_{i} + E(\varepsilon_{i})\rbrack - E({\widehat{\beta}}_{1})$ $=\frac{n\beta_{0}}{n} +\beta_{1}\frac{1}{n}x_{i} -\beta_{1} =\beta_{0}$ $V({\widehat{\beta}}_{0}) = V(- {\widehat{\beta}}_{1})$ $= V() + {}^{2}V({\widehat{\beta}}_{1}) - 2\text{Cov}(,{\widehat{\beta}}_{1})$ $=\frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q^{2}}{(n - 1)s_{x}^{2}})arrow 0$ Note: $C(,{\widehat{\beta}}_{1}) = 0$ because... $C(\frac{1}{n}Y_{i},\frac{1}{S_{\text{xx}}}(x_{i} -)Y_{j}) =\frac{1}{nS_{\text{xx}}}C(Y_{i},(x_{i} -)Y_{j})$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)C(Y_{i},Y_{i}) +(x_{i} -)C(Y_{i},Y_{j})\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)V(Y_{i}) +(x_{i} -)0\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack\sigma_{y}^{2}(x_{i} -)\rbrack$ $=\frac{\sigma_{y}^{2}}{nS_{\text{xx}}}\lbrack 0\rbrack$\]
|
||||
|
||||
2. Note two pieces: small error in identifying $(\mu_{x},\mu_{y})$ and larger error in identifying slope (which matters more when ${}^{2}$ high).
|
||||
|
||||
@ -622,7 +622,7 @@ Prediction estimator
|
||||
2. $E(\widehat{\beta_{0} +\beta_{1}x_{i}}) = E({\widehat{\beta}}_{0} + {\widehat{\beta}}_{1}x_{i}) =\beta_{0} +\beta_{1}x_{i}$; unbiased ☺!
|
||||
|
||||
3. $V(\widehat{\beta_{0} +\beta_{1}x_{i}}) =\ldots =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})arrow 0$; consistent ☺!
|
||||
\[$V(\widehat{\beta_{0} +\beta_{1}x_{i}}) = V({\widehat{\beta}}_{0}) + x_{i}^{2}V({\widehat{\beta}}_{1}) + 2Cov({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}x_{i})$ $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{S_{\text{xx}}}) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$ (since $\text{Cov}({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}) = Cov(- {\widehat{\beta}}_{1},{\widehat{\beta}}_{1}) = 0 -\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$) $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})$\] Note: most precise close to $$; can still make predictions far away from $$, but more noisy
|
||||
\[$V(\widehat{\beta_{0} +\beta_{1}x_{i}}) = V({\widehat{\beta}}_{0}) + x_{i}^{2}V({\widehat{\beta}}_{1}) + 2Cov({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}x_{i})$ $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q^{2}}{S_{\text{xx}}}) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$ (since $\text{Cov}({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}) = Cov(- {\widehat{\beta}}_{1},{\widehat{\beta}}_{1}) = 0 -\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$) $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})$\] Note: most precise close to $$; can still make predictions far away from $$, but more noisy
|
||||
|
||||
4. $\frac{\widehat{(\beta_{0} +\beta_{1}x_{i})} -(\beta_{0} +\beta_{1}x_{i})}{}\sim N(0,1)$
|
||||
$\frac{\widehat{(\beta_{0} +\beta_{1}x_{i})} -(\beta_{0} +\beta_{1}x_{i})}{}\sim t(n - 2)$
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
---
|
||||
date: [[2022-05-03]]
|
||||
day: [[2022-05-03]]
|
||||
---
|
||||
#math/calculus
|
||||
|
||||
|
||||
@ -1,7 +1,5 @@
|
||||
---
|
||||
title: |
|
||||
Econ 378 Lecture Notes\
|
||||
Joseph McMurray
|
||||
title: Econ 378 Lecture Notes \ Joseph McMurray
|
||||
---
|
||||
|
||||
# L0 Introduction
|
||||
@ -2109,7 +2107,7 @@ ii. Excel: use VAR.S or STDEV.S, not =VAR.P or =STDEV.P
|
||||
- Relating quantitative and binary variables: conditional distributions, conditional means $E(X = 0)$, $E(X = 1)$
|
||||
|
||||
- Wages gap between men and women:
|
||||
$n_{w} = 40$, ${{}_{w} =\$ 32,\sigma_{w} =\$ 13,n}_{m} = 45$, ${}_{m} =\$ 35$, $\sigma_{m} =\$ 15$.
|
||||
$n_{w} = 40$, ${q}_{w} =\$ 32,\sigma_{w} =\$ 13,n}_{m} = 45$, ${}_{m} =\$ 35$, $\sigma_{m} =\$ 15$.
|
||||
|
||||
- 95% confidence intervals for men $\lbrack\$ 30.62,\$ 39.38\rbrack$ and women $\lbrack\$ 27.97,\$ 36.03\rbrack$ overlap, making it difficult to tell true size of wage gap (if any)
|
||||
|
||||
@ -2226,7 +2224,7 @@ $\sim\chi^{2}(n - 1) +\chi^{2}(1) + 0$
|
||||
- Hypothesis test
|
||||
1. $H_{a}:\sigma^{2} > 4^{2}$, $\alpha = .05$
|
||||
2. Critical value $90.53$
|
||||
3. Test statistic $(n - 1)\frac{S^{2}}{\sigma^{2}} = 70(\frac{{5.3}^{2}}{4^{2}}) = 122.9$, reject $H_{0}$ (from Excel, p-value is $10^{- 5}$)
|
||||
3. Test statistic $(n - 1)\frac{S^{2}}{\sigma^{2}} = 70(\frac{5.3^{2}}{4^{2}}) = 122.9$, reject $H_{0}$ (from Excel, p-value is $10^{- 5}$)
|
||||
|
||||
# L22 Regression Estimation (WMS 11.1-3)
|
||||
|
||||
@ -2368,10 +2366,10 @@ Slope estimator
|
||||
Intercept estimator
|
||||
|
||||
1. It can be shown that $E({\widehat{\beta}}_{0}) =\ldots =\beta_{0}$; unbiased ☺!
|
||||
It can be shown that $V({\widehat{\beta}}_{0}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{(n - 1)s_{x}^{2}})arrow 0$; consistent ☺!
|
||||
It can be shown that $V({\widehat{\beta}}_{0}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q}^{2}}{(n - 1)s_{x}^{2}})arrow 0$; consistent ☺!
|
||||
|
||||
-\[For those curious,
|
||||
$E({\widehat{\beta}}_{0}) = E(\frac{1}{n}Y_{i} - {\widehat{\beta}}_{1}) =\frac{1}{n}\lbrack\beta_{0} +\beta_{1}x_{i} + E(\varepsilon_{i})\rbrack - E({\widehat{\beta}}_{1})$ $=\frac{n\beta_{0}}{n} +\beta_{1}\frac{1}{n}x_{i} -\beta_{1} =\beta_{0}$ $V({\widehat{\beta}}_{0}) = V(- {\widehat{\beta}}_{1})$ $= V() + {}^{2}V({\widehat{\beta}}_{1}) - 2\text{Cov}(,{\widehat{\beta}}_{1})$ $=\frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{(n - 1)s_{x}^{2}})arrow 0$ Note: $C(,{\widehat{\beta}}_{1}) = 0$ because... $C(\frac{1}{n}Y_{i},\frac{1}{S_{\text{xx}}}(x_{i} -)Y_{j}) =\frac{1}{nS_{\text{xx}}}C(Y_{i},(x_{i} -)Y_{j})$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)C(Y_{i},Y_{i}) +(x_{i} -)C(Y_{i},Y_{j})\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)V(Y_{i}) +(x_{i} -)0\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack\sigma_{y}^{2}(x_{i} -)\rbrack$ $=\frac{\sigma_{y}^{2}}{nS_{\text{xx}}}\lbrack 0\rbrack$\]
|
||||
$E({\widehat{\beta}}_{0}) = E(\frac{1}{n}Y_{i} - {\widehat{\beta}}_{1}) =\frac{1}{n}\lbrack\beta_{0} +\beta_{1}x_{i} + E(\varepsilon_{i})\rbrack - E({\widehat{\beta}}_{1})$ $=\frac{n\beta_{0}}{n} +\beta_{1}\frac{1}{n}x_{i} -\beta_{1} =\beta_{0}$ $V({\widehat{\beta}}_{0}) = V(- {\widehat{\beta}}_{1})$ $= V() + {}^{2}V({\widehat{\beta}}_{1}) - 2\text{Cov}(,{\widehat{\beta}}_{1})$ $=\frac{\sigma_{\varepsilon}^{2}}{n} + {}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 0 =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q}^{2}}{(n - 1)s_{x}^{2}})arrow 0$ Note: $C(,{\widehat{\beta}}_{1}) = 0$ because... $C(\frac{1}{n}Y_{i},\frac{1}{S_{\text{xx}}}(x_{i} -)Y_{j}) =\frac{1}{nS_{\text{xx}}}C(Y_{i},(x_{i} -)Y_{j})$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)C(Y_{i},Y_{i}) +(x_{i} -)C(Y_{i},Y_{j})\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack(x_{i} -)V(Y_{i}) +(x_{i} -)0\rbrack$ $=\frac{1}{nS_{\text{xx}}}\lbrack\sigma_{y}^{2}(x_{i} -)\rbrack$ $=\frac{\sigma_{y}^{2}}{nS_{\text{xx}}}\lbrack 0\rbrack$\]
|
||||
|
||||
2. Note two pieces: small error in identifying $(\mu_{x},\mu_{y})$ and larger error in identifying slope (which matters more when ${}^{2}$ high).
|
||||
|
||||
@ -2384,7 +2382,7 @@ Prediction estimator
|
||||
2. $E(\widehat{\beta_{0} +\beta_{1}x_{i}}) = E({\widehat{\beta}}_{0} + {\widehat{\beta}}_{1}x_{i}) =\beta_{0} +\beta_{1}x_{i}$; unbiased ☺!
|
||||
|
||||
3. $V(\widehat{\beta_{0} +\beta_{1}x_{i}}) =\ldots =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})arrow 0$; consistent ☺!
|
||||
\[$V(\widehat{\beta_{0} +\beta_{1}x_{i}}) = V({\widehat{\beta}}_{0}) + x_{i}^{2}V({\widehat{\beta}}_{1}) + 2Cov({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}x_{i})$ $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{{}^{2}}{S_{\text{xx}}}) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$ (since $\text{Cov}({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}) = Cov(- {\widehat{\beta}}_{1},{\widehat{\beta}}_{1}) = 0 -\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$) $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})$\] Note: most precise close to $$; can still make predictions far away from $$, but more noisy
|
||||
\[$V(\widehat{\beta_{0} +\beta_{1}x_{i}}) = V({\widehat{\beta}}_{0}) + x_{i}^{2}V({\widehat{\beta}}_{1}) + 2Cov({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}x_{i})$ $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{q}^{2}}{S_{\text{xx}}}) + {(x_{i})}^{2}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}} - 2x_{i}\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$ (since $\text{Cov}({\widehat{\beta}}_{0},{\widehat{\beta}}_{1}) = Cov(- {\widehat{\beta}}_{1},{\widehat{\beta}}_{1}) = 0 -\frac{\sigma_{\varepsilon}^{2}}{S_{\text{xx}}}$) $=\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}}) =\sigma_{\varepsilon}^{2}(\frac{1}{n} +\frac{(x_{i} -)^{2}}{S_{\text{xx}}})$\] Note: most precise close to $$; can still make predictions far away from $$, but more noisy
|
||||
|
||||
4. $\frac{\widehat{(\beta_{0} +\beta_{1}x_{i})} -(\beta_{0} +\beta_{1}x_{i})}{}\sim N(0,1)$
|
||||
$\frac{\widehat{(\beta_{0} +\beta_{1}x_{i})} -(\beta_{0} +\beta_{1}x_{i})}{}\sim t(n - 2)$
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#econ
|
||||
- Why Does the Aggregate-Demand Curve Slope Downward?
|
||||
-
|
||||
- The Wealth Effect↔A lower price level increases real wealth, stimulating spending on consumption.
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#church
|
||||
- Gospel Authors
|
||||
- Mark
|
||||
- written by/for→Jew, gentiles
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#todo
|
||||
- March 12th, 2022
|
||||
- March 8th, 2022
|
||||
- November 12th, 2021
|
||||
|
||||
@ -1,4 +0,0 @@
|
||||
--------------------- Portal ---------------------
|
||||
-- Avoided infinite recursion -- --------------------- Portal ---------------------
|
||||
-
|
||||
-- Avoided infinite recursion --
|
||||
@ -1,4 +1,5 @@
|
||||
- #econ
|
||||
|
||||
#econ
|
||||
- 1
|
||||
- nutshell
|
||||
- The fundamental lessons about individual decision making are that people face trade-offs among alternative goals, that the cost of any action is measured in terms of forgone opportunities, that rational people make decisions by comparing marginal costs and marginal benefits, and that people change their behavior in response to the incentives they face.
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#church
|
||||
- Well, first of all, buy a big bag of flower and whatnot. Brush up on your first aid.
|
||||
- Primitive technology vid
|
||||
- https://youtu.be/NT0EmAgP-_k
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#church
|
||||
- [[https://www.churchofjesuschrist.org/study/general-conference/2015/04/why-marriage-why-family?lang=eng]]
|
||||
- According to Elder Christofferson, why is marriage more than the love couples feel for each other?↔It's a post/ office in the kingdom of God. Best setting for God's plan to thrive.
|
||||
- Why can no person or government alter the divine order of matrimony?↔It is not a human invention. Such marriage is indeed “from above, from God” and is as much a part of the plan of happiness as the Fall and the Atonement.
|
||||
|
||||
@ -1,4 +1,5 @@
|
||||
#code
|
||||
|
||||
- ` import multiprocessing, tqdm # for loading bar`
|
||||
- ```python
|
||||
collect_results = []
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#econ
|
||||
- Types of Capital
|
||||
- Human Capital per Worker↔Skills gained and expertise had within people ^693237
|
||||
- Natural Resources per Worker↔Ratio of natural resources to population. Brazil is big on this.
|
||||
|
||||
@ -1,2 +1,3 @@
|
||||
#tools
|
||||
- wagtail.io
|
||||
-
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#econ
|
||||
- [Marriage in the Lord’s Way, Part Two ](https://www.churchofjesuschrist.org/study/ensign/1998/06/marriage-in-the-lords-way-part-one?lang=eng)
|
||||
- [Marriage in the Lord’s Way, Part One ](https://www.churchofjesuschrist.org/study/ensign/1998/06/marriage-in-the-lords-way-part-one?lang=eng)
|
||||
- What did Elder Kofford say he believes sealing refers to?→the “sealing ordinance” or “being sealed” rather than just “being married in the temple.”
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#people
|
||||
- commands
|
||||
- tmux
|
||||
- ctrl-b, d
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#econ
|
||||
- [[firms in competitive markets]] vs monopolies
|
||||
- 
|
||||
- 
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#church
|
||||
- Required Readings Study Guide
|
||||
- Reminder: In order to protect the integrity of our class quizzes and exams no questions from our study guides, quizzes, midterm, or final may be posted on-line in any public venue/format. This includes Google Docs as well as the various quizzing websites/apps like Quizlet, StudyBlue, etc. You are obviously free (and encouraged) to use any and all such sites, but if you include any questions from our class material, they must be made private so no one else can see them and they cannot be shared with others in or out of BYU. Besides the associated copyright laws (yep - weird but a teachers materials such as study guides et al. are actually copyright protected). this policy also pertains to BYU's Academic Honesty Policy and will be treated as such.
|
||||
- 0. Course Introduction
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
- #econ
|
||||
#econ
|
||||
- non-excludable→people benefit but do not pay for it. Can't exclude people from using it.
|
||||
- non-rival→no marginal cost of use. basically unlimited people can use it.
|
||||
- Public Goods↔[[externalities/non-rival]] and [[externalities/non-excludable]]
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#church
|
||||
- has→
|
||||
- market power→when it's not perfectly competitive, somebody has market power and can choose the quantity/price
|
||||
- total revenue→all revenue, price X quantitiy.
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
-
|
||||
#church
|
||||
- Required Readings Study Guide
|
||||
- Reminder: In order to protect the integrity of our class quizzes and exams no questions from our study guides, quizzes, midterm, or final may be posted on-line in any public venue/format. This includes Google Docs as well as the various quizzing websites/apps like Quizlet, StudyBlue, etc. You are obviously free (and encouraged) to use any and all such sites, but if you include any questions from our class material, they must be made private so no one else can see them and they cannot be shared with others in or out of BYU. Besides the associated copyright laws (yep - weird but a teachers materials such as study guides et al. are actually copyright protected). this policy also pertains to BYU's Academic Honesty Policy and will be treated as such.
|
||||
-
|
||||
|
||||
@ -1,2 +1,3 @@
|
||||
#econ
|
||||
- [[Econ textbook#^78b82c]]
|
||||
- 
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#math
|
||||
- the alternative is called mean absolute deviation - $\frac {\sum (x- \bar x)}{n}$
|
||||
- instead of standard deviation - $\sqrt \frac{\sum (x- \bar x)^2}{n-1}$
|
||||
- reasons:
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-10-18]]
|
||||
Study: Luke 16-18
|
||||
Study: "Luke 16-18"
|
||||
---
|
||||
|
||||
Last class really resonated, especially the part of class about having to replace a demon with something else. Of course, by demon, I can mean just about anything bad, like a habit, an acivity, a set of thoughts, an attitude, even people and time. I thought about habits that I'm trying to form right now. I need to find things that replace the bad thought patterns that lead me to wasting so much time on social media and such. Like, I'm stressed about how much I need to do, so often I feel like I need to take some sort of break. If that's the case, I can think up better ways to take a break, really. It's not so hard, I just go on a walk or eat something or use duolingo or watch some good youtube videos. I can think about homework in a positive way, filling my need for ease and positivity by having it in my everyday work.
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-10-20]]
|
||||
Study: John 1-4, BD: John; John, Gospel of
|
||||
Study: "John 1-4, BD: John; John, Gospel of"
|
||||
---
|
||||
|
||||
These chapters reminded me aton of the first seasons of The Chosen. Like, more so than the others. Is it because both the Gospel of John and the tv show are focused on the perspective of the apostles? That would certainly be cool if it was the case. Neat observation, I guess. It comes from the order of the stories, I think, yet I may ask prof. whether it's the unique stories found in the gospel of John. It reminds me that I intend on really studying the comparison between the different gospels. I sincerely want to know the different perspectives and purposes between the four accounts.
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-10-25]]
|
||||
Study: John 5-8
|
||||
Study: "John 5-8"
|
||||
---
|
||||
|
||||
Question: I heard online that the idea that Jesus even claimed to be the messiah or God is in historical dispute. That makes sense, too, considering that both the Jews and the Muslims believe many things about him, but can exclude the idea that he is literally God. It was said that many of the records of the more grandiose claims happened much later than the rest.
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-10-27]]
|
||||
Study: John 9-12
|
||||
Study: "John 9-12"
|
||||
---
|
||||
|
||||
What's with that light metaphor??
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-01]]
|
||||
Study: BD; Bethphage; Caesar; Fig tree; Frontlets or Phylacteries; Herodians; Levirate Marriage Videos: The Lord's Triumphal Entry into Jerusalem (1:07); Jesus Cleanses the Temple (1:35) Scripture Reading: Matthew 21-23; Mark 11-12; Luke 19-20
|
||||
Study: "BD; Bethphage; Caesar; Fig tree; Frontlets or Phylacteries; Herodians; Levirate Marriage Videos: The Lord's Triumphal Entry into Jerusalem (1:07); Jesus Cleanses the Temple (1:35) Scripture Reading: Matthew 21-23; Mark 11-12; Luke 19-20"
|
||||
---
|
||||
|
||||
I always thought that Caesar was actually a name. No, it was a title, apparently.
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-03]]
|
||||
Study: BD Abomination of Desolation Olives, Mount of, or Olivet Matthew 24-25 Mark 13 Luke 21
|
||||
Study: "BD Abomination of Desolation Olives, Mount of, or Olivet Matthew 24-25 Mark 13 Luke 21"
|
||||
---
|
||||
|
||||
Abomination of Desolation sounds pretty evil, but also pretty vague. It's timing is the only thing that's clear. Perhaps it points toward the general trend of wickedness increasing nowadays, and towards it inevitable consequences of the quality of life going down. People will likely less charitable and more demanding. Idk, it sounds like you'd be able to see it better if you studied the histories of societies that once were particularly degenerate.
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-15]]
|
||||
Study: Mark 15; Matthew 27; Luke 23; John 18-19
|
||||
Study: "Mark 15; Matthew 27; Luke 23; John 18-19"
|
||||
---
|
||||
Wow even the ones crucified with Christ reviled him.
|
||||
To choose your own time of death. Amazing. Did they really kill him, then? Or did he choose to die? Does only he have the authority to do so? Like, suicide is a sin because you are taking a decision away from God, right? So, can only Christ choose to die? Should a dying old man be allowed to choose to die? If Christ was the one to give up the ghost, why is it that they shouldn't be allowed to as well, if they spiritually feel like their work is done? Is there an essential difference between killing yourself, letting yourself be killed, and giving up the ghost?
|
||||
|
||||
@ -1,9 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-27]]
|
||||
Study:
|
||||
- BD: Ascension; Emmaus; Miracles; Resurrection
|
||||
- Videos: Christ Appears on the Road to Emmaus (3:33); Feed My Sheep (5:45)
|
||||
- Mark 16; Matt 28; Luke 24; John 20-21
|
||||
Study: "- BD: Ascension; Emmaus; Miracles; Resurrection - Videos: Christ Appears on the Road to Emmaus (3:33); Feed My Sheep (5:45)- Mark 16; Matt 28; Luke 24; John 20-21"
|
||||
---
|
||||
Are all angels young? I imagine that they didn't mean a teenager, but that the angel appeared as a person at optimal health, which by my best guess is the early 20s. I say that because an angel probably wouldn't have any symptoms of aging, but would still be fully grown. A full hairline, not a single wrinkle, smooth and healthy skin, and all of that. They would look like a young man or woman.
|
||||
|
||||
|
||||
@ -1,8 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-27]]
|
||||
Study:
|
||||
- Videos: Peter and John Heal a Man Crippled Since Birth (3:22); Peter and John Continue Preaching the Gospel (5:38); Peter's Revelation to Take the Gospel to the Gentiles (9:03)
|
||||
- Acts 1-5; 10, 12, 3 Nephi 11
|
||||
Study: "- Videos: Peter and John Heal a Man Crippled Since Birth (3:22); Peter and John Continue Preaching the Gospel (5:38); Peters Revelation to Take the Gospel to the Gentiles (9:03)- Acts 1-5; 10, 12, 3 Nephi 11"
|
||||
---
|
||||
|
||||
You got to wonder, if the Jews in Jerusalem had experienced a great disaster, and then seeing Christ coming down from heaven, they might have believed him. Maybe they're challenge was truly supposed to be harder, as far as actually believing in Jesus Christ. I hope they get another chance in the next life. Before they're judged finally. Of course, in the nephites case, they were only the people that were left after the wicked were destroyed. So, only people that would probably have believed in Jesus Christ remained.
|
||||
|
||||
@ -1,9 +1,6 @@
|
||||
---
|
||||
Date: [[2021-11-29]]
|
||||
Study:
|
||||
- BD: Paul
|
||||
- Videos: The Road to Damascus (5:21); Unity of the Faith (3:32);I Have Kept the Faith (1:48)
|
||||
- Acts 9; Acts 22; Romans 1, 5-6, 8; 2 Timothy 1-4
|
||||
Study: "- BD: Paul - Videos: The Road to Damascus (5:21); Unity of the Faith (3:32);I Have Kept the Faith (1:48)- Acts 9; Acts 22; Romans 1, 5-6, 8; 2 Timothy 1-4"
|
||||
---
|
||||
Was there really some substance on saul's eyes?? Gross.
|
||||
Did saul personally know nicodemos?
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
---
|
||||
date: [[2022-05-02]]
|
||||
day: [[2022-05-02]]
|
||||
tags: #linear_algebra
|
||||
cards-deck: default_obsidian
|
||||
---
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
#todo
|
||||
- [ ] do econ hw
|
||||
- [ ] model healthcare data and stuff
|
||||
- [ ] find dataset for brasil
|
||||
|
||||
Loading…
Reference in New Issue
Block a user