vault backup: 2023-12-13 14:03:19

education/math/Standard forms of circles.md

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+# Notes
+## Composition of functions
+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:
+$$ (x - h)^2 + (y - k)^2 =r $$
+Distance formula:
+$$ \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} $$
+Midpoint foruma:
+$$ (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) $$
+Adding functions:
+$$ (f + g)(x) = f(x) + g(x) $$
+Multiplying functions:
+$$ (f*g)(x)=f(g(x)) $$
+
+# Examples
+Given the function $f = \{(0, 2), (3, -1), (5, 4), (2, 1)\}$, and $g=\{(2, 0), (3, -1), (4, -2), (5, 2)\}$, and applying $(f+g(x)$, If the same $x$ value exists in both the sets $f$ and $g$, then you can solve for that value by adding $y$ values for the matching x coordinates together. 
+
+
+# Terminology
+
+| Term | Definition |
+|--|--|
+| $h$ | How far left or right something is shifted from the origin |
+| $k$| How far up or down something is shifted from the origin |
+| $r$ | The radius of a circle |

education/statistics/Correlation and Regression.md

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 ## Scatter Diagrams
 A scatter diagram or scatter plot shows the relationship between two variables. One variable is on the X axis, the other on the Y axis. 
 ### Association
-- Positive association is demonstrated when the dots are trend upward as `x` increases. 
-- Negative association is demonstrated when the the dots trend downward as `x` increases.
+- Positive association is demonstrated when the dots are trend upward as $x$ increases. 
+- Negative association is demonstrated when the the dots trend downward as $x$ increases.
 - Strong association is demonstrated when dots are clustered tightly together along a line.
 - Weak association is demonstrated when dots are not clustered tightly. 
 ## Correlation
-Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering. 
+Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering.  $r$ is -1 if the points are on a line with negative slope, $r$ is positive 1 if the points are on a line with a positive slope. As $|r|$ gets closer to 1, the line points cluster more tightly around a line.
 
 # Terminology
 | Term | Definition |
-| `r` | Correlation Coefficient |
+| -- | -- |
+| $r$ | Correlation Coefficient |
+| Linear Correlation | Measures the strength of a line |