From 39a9d625a2a3296e01b66beacc78d6cd7c9bc442 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Wed, 13 Dec 2023 14:43:19 -0700 Subject: [PATCH] vault backup: 2023-12-13 14:43:19 --- education/statistics/Correlation and Regression.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index 79aea81..4953c26 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -8,15 +8,15 @@ If a scatter diagram is football shaped, it can be summarized using the 5-number | Variable | Description | | -- | -- | -| $\mu_x$ | The average of the set graphed along the X axis | +| $\bar{x}$ | The average of the set graphed along the X axis | | $\sigma_x$| The standard deviation of set graphed along the X axis | -| $\mu_y$ | The average of the set graphed along the Y axis | +| $\bar{y}$ | The average of the set graphed along the Y axis | | $\sigma_y$ | The standard deviation of the set graphed along the Y axis | | $r$ | The correlation coefficient, or how closely clustered the datapoints are in a line | The intersection of the averages of x and y will be the center of an oval shaped scatter diagram. Draw lines $2\sigma$ (will contain ~95% of all data) from the center along each axis to generalize the shape of a scatter plot. -You can approximate the mean by trying to find the upper bound and the lower bound of $2\sigma$ deviation to either side of the mean, then finding the middle of those two points to find $\mu$. You can divide the range between the two points by 4 to find $\sigma$. +You can approximate the mean by trying to find the upper bound and the lower bound of $2\sigma$ deviation to either side of the mean, then finding the middle of those two points to find $\bar{x}$. You can divide the range between the two points by 4 to find $\sigma$. ### Association - Positive association is demonstrated when the dots are trend upward as $x$ increases ($r$ is positive). - Negative association is demonstrated when the the dots trend downward as $x$ increases ($r$ is negative). @@ -28,12 +28,12 @@ Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, ## Calculating $r$ by hand Put the $x$ values into $L1$, put the $y$ values into $L2$. -1. Convert the $x$ values to standard units ($z$). Convert the $y$ values to standard units. +1. Convert the $x$ each x value in the list to standard units($z$). Convert each $y$ value to standard units. $$ z = \frac{x-\bar{x}}{\sigma_x} $$ -2. Multiply the standard units for each ($x$, $y$) pair in the sets -$$ x * y = $$ +2. Multiply the standard units for each ($x$, $y$) pair in the sets, giving you a third list, named $p$ in this example. +$$ x * y = p$$ 3. Find the average of the values from step 3, this is $r$. -$$ z_x = \frac{L_1-\bar{x}}{\sigma_x} $$ +$$ \bar{x}(p) $$ https://www.thoughtco.com/how-to-calculate-the-correlation-coefficient-3126228 # Terminology