From 24584b63e384f7c355f946783249b81917b6a163 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Sat, 16 Dec 2023 10:44:37 -0700 Subject: [PATCH 01/21] vault backup: 2023-12-16 10:44:37 --- .obsidian/plugins/obsidian-git/data.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json index 7b1247f..4bc189e 100644 --- a/.obsidian/plugins/obsidian-git/data.json +++ b/.obsidian/plugins/obsidian-git/data.json @@ -2,7 +2,7 @@ "commitMessage": "vault backup: {{date}}", "autoCommitMessage": "vault backup: {{date}}", "commitDateFormat": "YYYY-MM-DD HH:mm:ss", - "autoSaveInterval": 1, + "autoSaveInterval": 5, "autoPushInterval": 0, "autoPullInterval": 5, "autoPullOnBoot": false, From 9021b20ca434f4d5f96e5cea0cbb26ac0d9f1a3d Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 09:31:06 -0700 Subject: [PATCH 02/21] vault backup: 2023-12-18 09:31:06 --- education/statistics/Correlation and Regression.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 444471f..cc649fb 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -87,5 +87,9 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70 $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ - You can find the regression line by multiplying $\sigma_y$ by $r$, for the rise, then using $\sigma_x$ for the run from the point of averages. -$$ z_x = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ -This formula finds the $z$ score for $x$, transforms by $r$, and uses the equation $x = z * \sigma + \bar{x}$ to predict a value for one axis given another axis. \ No newline at end of file +The below formula can be used to predict a y value given a 5 number summary of a set. +$$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ +# Terminology +| Term | Definition | +| -- | -- | +| $\hat{y}$ | The predicted value | From 14b9ba3ea2bf66360488c6e8970cdaaddb16fbda Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 10:07:15 -0700 Subject: [PATCH 03/21] vault backup: 2023-12-18 10:07:15 --- education/math/Inverse Functions.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 education/math/Inverse Functions.md diff --git a/education/math/Inverse Functions.md b/education/math/Inverse Functions.md new file mode 100644 index 0000000..bf9e23b --- /dev/null +++ b/education/math/Inverse Functions.md @@ -0,0 +1 @@ +For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function. \ No newline at end of file From 802a064cc0fa9e2e04368bf9a6b0fc73f829a5a7 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 10:12:15 -0700 Subject: [PATCH 04/21] vault backup: 2023-12-18 10:12:15 --- education/math/Inverse Functions.md | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/education/math/Inverse Functions.md b/education/math/Inverse Functions.md index bf9e23b..13dc21a 100644 --- a/education/math/Inverse Functions.md +++ b/education/math/Inverse Functions.md @@ -1 +1,8 @@ -For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function. \ No newline at end of file +For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function. To get the inverse, you can switch the x and y of a function, and it will mirror the graph over the line $y = x$. + +# Examles +Given the below function: +$$ y = \frac{1}{2}x + 3 $$ +You can find the inverse by switching the $x$ and $y$ values and solving for $y$: +$$ x = \frac{1}{2}y + 3 $$ +The range of the inver \ No newline at end of file From 77565add5cd04557129dde7987c06ccf99382253 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 10:17:15 -0700 Subject: [PATCH 05/21] vault backup: 2023-12-18 10:17:15 --- education/math/Inverse Functions.md | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/education/math/Inverse Functions.md b/education/math/Inverse Functions.md index 13dc21a..acfc17e 100644 --- a/education/math/Inverse Functions.md +++ b/education/math/Inverse Functions.md @@ -1,8 +1,13 @@ For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function. To get the inverse, you can switch the x and y of a function, and it will mirror the graph over the line $y = x$. -# Examles +# Examples Given the below function: $$ y = \frac{1}{2}x + 3 $$ You can find the inverse by switching the $x$ and $y$ values and solving for $y$: $$ x = \frac{1}{2}y + 3 $$ -The range of the inver \ No newline at end of file +The range of the inverse is the same as the domain of the original. +You can verify by taking $f \circ g$, and simplifying. + + +Given the below function: +$$ f(x) = \frac{x+ \ No newline at end of file From 24521f2a701167564d947b8321362e446f50b8bf Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 10:22:15 -0700 Subject: [PATCH 06/21] vault backup: 2023-12-18 10:22:15 --- education/math/Inverse Functions.md | 3 --- 1 file changed, 3 deletions(-) diff --git a/education/math/Inverse Functions.md b/education/math/Inverse Functions.md index acfc17e..47a4db7 100644 --- a/education/math/Inverse Functions.md +++ b/education/math/Inverse Functions.md @@ -8,6 +8,3 @@ $$ x = \frac{1}{2}y + 3 $$ The range of the inverse is the same as the domain of the original. You can verify by taking $f \circ g$, and simplifying. - -Given the below function: -$$ f(x) = \frac{x+ \ No newline at end of file From add067cc57661602e8b7117b0497b4673f87638f Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 11:18:07 -0700 Subject: [PATCH 07/21] vault backup: 2023-12-18 11:18:07 --- education/english/Media Bias.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 education/english/Media Bias.md diff --git a/education/english/Media Bias.md b/education/english/Media Bias.md new file mode 100644 index 0000000..e69de29 From 5d9d270fae2625d2f94c0992839d2e3ae4e7ccdc Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 11:23:07 -0700 Subject: [PATCH 08/21] vault backup: 2023-12-18 11:23:07 --- education/english/Media Bias.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/education/english/Media Bias.md b/education/english/Media Bias.md index e69de29..d430d31 100644 --- a/education/english/Media Bias.md +++ b/education/english/Media Bias.md @@ -0,0 +1,2 @@ +# Fake News +Fake news is defined as fabricated information presented as news. It is not accurate or credible. Fake news overlaps with other information disorders, like misinformation (false or misleading information), and disinformation (false information intentionally spread to deceive people). \ No newline at end of file From 7e883a0ce71b863adfadaa38564504f60c63c324 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 11:54:58 -0700 Subject: [PATCH 09/21] vault backup: 2023-12-18 11:54:58 --- education/english/Media Bias.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/education/english/Media Bias.md b/education/english/Media Bias.md index d430d31..ea505ec 100644 --- a/education/english/Media Bias.md +++ b/education/english/Media Bias.md @@ -1,2 +1,5 @@ # Fake News -Fake news is defined as fabricated information presented as news. It is not accurate or credible. Fake news overlaps with other information disorders, like misinformation (false or misleading information), and disinformation (false information intentionally spread to deceive people). \ No newline at end of file +Fake news is defined as fabricated information presented as news. It is not accurate or credible. Fake news overlaps with other information disorders, like misinformation (false or misleading information), and disinformation (false information intentionally spread to deceive people). + +# Accountability +Use news sources with explicit editorial polcies and ethical standards. \ No newline at end of file From 6d447012b4e14bccf580ba8a7833f74620a3a0fb Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 12:06:48 -0700 Subject: [PATCH 10/21] vault backup: 2023-12-18 12:06:48 --- education/english/Media Bias.md | 5 ----- 1 file changed, 5 deletions(-) delete mode 100644 education/english/Media Bias.md diff --git a/education/english/Media Bias.md b/education/english/Media Bias.md deleted file mode 100644 index ea505ec..0000000 --- a/education/english/Media Bias.md +++ /dev/null @@ -1,5 +0,0 @@ -# Fake News -Fake news is defined as fabricated information presented as news. It is not accurate or credible. Fake news overlaps with other information disorders, like misinformation (false or misleading information), and disinformation (false information intentionally spread to deceive people). - -# Accountability -Use news sources with explicit editorial polcies and ethical standards. \ No newline at end of file From e99b4adbcb57c5cdc38a170a0cfe29ebbbc434fd Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 13:54:40 -0700 Subject: [PATCH 11/21] vault backup: 2023-12-18 13:54:40 --- education/statistics/Correlation and Regression.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index cc649fb..423f2ee 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -83,12 +83,18 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70 ### The Regression Line/Least Squared Regression Line (LSRL) - This line has a more moderate slope than the SD line. it does not go through the peaks of the "football" - The regression line is *used to predict* the y variable when the x variable is given -- The regression line also goes through the point of averages +- The regression line goes through the point of averages $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ - You can find the regression line by multiplying $\sigma_y$ by $r$, for the rise, then using $\sigma_x$ for the run from the point of averages. The below formula can be used to predict a y value given a 5 number summary of a set. $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ +1. Find $z_x$ +2. Multiply $z_x$ by $r$ +3. Multiply that by $\sigma_y$ +4. Add the average of $y$ + + # Terminology | Term | Definition | | -- | -- | From 82181e5c22cb52e9eb187387b180718371ac787c Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 13:59:40 -0700 Subject: [PATCH 12/21] vault backup: 2023-12-18 13:59:40 --- education/statistics/Correlation and Regression.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 423f2ee..7cfc444 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -83,7 +83,8 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70 ### The Regression Line/Least Squared Regression Line (LSRL) - This line has a more moderate slope than the SD line. it does not go through the peaks of the "football" - The regression line is *used to predict* the y variable when the x variable is given -- The regression line goes through the point of averages +- In regression, the $x$ variable is the known variable, and $y$ is the value being solved for. +- The regression line goes through the point of averages, and can be positive or negative $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ - You can find the regression line by multiplying $\sigma_y$ by $r$, for the rise, then using $\sigma_x$ for the run from the point of averages. From 511a7633c1235a06906d53f88480b11524fd3099 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 14:09:40 -0700 Subject: [PATCH 13/21] vault backup: 2023-12-18 14:09:40 --- education/statistics/Correlation and Regression.md | 1 + 1 file changed, 1 insertion(+) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 7cfc444..78c3d5f 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -95,6 +95,7 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 3. Multiply that by $\sigma_y$ 4. Add the average of $y$ +- For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y. # Terminology | Term | Definition | From 52420d77d78450a542b3a5a6b219b87e1c7db6f7 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 14:14:40 -0700 Subject: [PATCH 14/21] vault backup: 2023-12-18 14:14:40 --- education/statistics/Correlation and Regression.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 78c3d5f..6e22735 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -95,7 +95,7 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 3. Multiply that by $\sigma_y$ 4. Add the average of $y$ -- For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y. +- For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x # Terminology | Term | Definition | From b687be1ebf49ac801af15a255b6a6b97aba51404 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 14:19:40 -0700 Subject: [PATCH 15/21] vault backup: 2023-12-18 14:19:40 --- education/statistics/Correlation and Regression.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 6e22735..fa165f9 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -96,7 +96,8 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 4. Add the average of $y$ - For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x - +### The Regression Effect +In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest. # Terminology | Term | Definition | | -- | -- | From 01260becd722adb21c53f94fdf708f53addda645 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 14:24:40 -0700 Subject: [PATCH 16/21] vault backup: 2023-12-18 14:24:40 --- education/statistics/Correlation and Regression.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index fa165f9..fe9f94e 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -96,8 +96,12 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 4. Add the average of $y$ - For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x +- Being asked to interpret the slope: __slope__ means that for every _unit_ ### The Regression Effect -In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest. +- In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest. +- The regression *fallacy* is contributing this to something other than chance error. + +--- # Terminology | Term | Definition | | -- | -- | From 9eecc310e6cbc5c96862abb11cca3e99ba19ff80 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 14:29:40 -0700 Subject: [PATCH 17/21] vault backup: 2023-12-18 14:29:40 --- education/statistics/Correlation and Regression.md | 1 - 1 file changed, 1 deletion(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index fe9f94e..fcaeb68 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -96,7 +96,6 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 4. Add the average of $y$ - For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x -- Being asked to interpret the slope: __slope__ means that for every _unit_ ### The Regression Effect - In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest. - The regression *fallacy* is contributing this to something other than chance error. From 1afeb7fd57409c0d2da0bb5f7909b450777d8a0a Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 19 Dec 2023 10:51:37 -0700 Subject: [PATCH 18/21] vault backup: 2023-12-19 10:51:37 --- education/math/Standard forms of circles.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/education/math/Standard forms of circles.md b/education/math/Standard forms of circles.md index 3d37236..9e04b67 100644 --- a/education/math/Standard forms of circles.md +++ b/education/math/Standard forms of circles.md @@ -3,7 +3,7 @@ For $(f\circ g)(x)$ for two sets, you look for $x$ from $f$ and an equivalent $y$ value from $g$, and leftover coordinates are the answer. The order of $f$ and $g$ does matter. # Formulae The general equation for a circle: -$$ (x - h)^2 + (y - k)^2 =r $$ +$$ (x - h)^2 + (y - k)^2 =r^2 $$ Distance formula: $$ \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} $$ Midpoint foruma: From 77a2b9bb60deb87e3019f631e8eeec6fbdcfe9b9 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 19 Dec 2023 13:55:29 -0700 Subject: [PATCH 19/21] vault backup: 2023-12-19 13:55:29 --- education/statistics/Correlation and Regression.md | 1 + 1 file changed, 1 insertion(+) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index fcaeb68..ae98578 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -82,6 +82,7 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70 ### The Regression Line/Least Squared Regression Line (LSRL) - This line has a more moderate slope than the SD line. it does not go through the peaks of the "football" +- Predictions can only be made if the data displays a linear association (is a football shape). - The regression line is *used to predict* the y variable when the x variable is given - In regression, the $x$ variable is the known variable, and $y$ is the value being solved for. - The regression line goes through the point of averages, and can be positive or negative From 7a62975e727df3129ccc5e3504524de98b253331 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 19 Dec 2023 14:05:30 -0700 Subject: [PATCH 20/21] vault backup: 2023-12-19 14:05:30 --- education/statistics/Correlation and Regression.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index ae98578..722d99d 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -29,9 +29,9 @@ If $x$ is above average, we expect the $y$ to be above average if there's a stro ## Calculating $r$ by hand Put the $x$ values into $L1$, put the $y$ values into $L2$. -1. Convert the $x$ each x value in the list to standard units($z$). Convert each $y$ value to standard units. +1. Convert the $x$ each x value in the list to standard units($z$). Convert each $y$ value to standard units. This will create two new tables containing $z_x$ and $z_y$. $$ z = \frac{x-\bar{x}}{\sigma_x} $$ -2. Multiply the standard units for each ($x$, $y$) pair in the sets, giving you a third list, named $p$ in this example. +2. Multiply the standard units for each ($z_x$, $z_y$) pair in the sets, giving you a fifth list, named $p$ in this example. $$ x * y = p$$ 3. Find the average of the values from step 3, this is $r$. $$ \bar{x}(p) $$ From a23f8dfc5812aa063522f2119f3c0b1a5d7fe34d Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 19 Dec 2023 14:20:30 -0700 Subject: [PATCH 21/21] vault backup: 2023-12-19 14:20:30 --- education/statistics/Correlation and Regression.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 722d99d..f05cfa4 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -97,6 +97,8 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ 4. Add the average of $y$ - For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x +- There are two separate regression lines, one for predicting $y$ from $x$, and one for predicting $x$ from $y$ +- Do not extrapolate outside of the graph ### The Regression Effect - In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest. - The regression *fallacy* is contributing this to something other than chance error.