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education/statistics/Correlation and Regression.md
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@ -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 ## Calculating $r$ by hand
Put the $x$ values into $L1$, put the $y$ values into $L2$. 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 $z_y$.
$$ z = \frac{x-\bar{x}}{\sigma_x} $$ $$ z = \frac{x-\bar{x}}{\sigma_x} $$
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.
$$ x * y = p$$ $$ x * y = p$$
3. Find the average of the values from step 3, this is $r$. 3. Find the average of the values from step 3, this is $r$.
$$ \bar{x}(p) $$ $$ \bar{x}(p) $$