Is correlation coefficient r or r2

How do we actually calculate the correlation coefficient?

The sample correlation coefficient can be represented with a formula:

$$ r=\frac{\sum\left[\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)\right]}{\sqrt{\mathrm{\Sigma}\left(x_i-\overline{x}\right)^2\
\ast\ \mathrm{\Sigma}(y_i\ -\overline{y})^2}} $$

View Annotated Formula

Let’s step through how to calculate the correlation coefficient using an example with a small set of simple numbers, so that it’s easy to follow the operations.

Let’s imagine that we’re interested in whether we can expect there to be more ice cream sales in our city on hotter days.

Ice cream shops start to open in the spring; perhaps people buy more ice cream on days when it’s hot outside. On the other hand, perhaps people simply buy ice cream at a steady rate because they like it so much.

We start to answer this question by gathering data on average daily ice cream sales and the highest daily temperature.

Ice Cream Sales and Temperature are therefore the two variables which we’ll use to calculate the correlatio

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