Some Statistics that you may need:

Correlation

A correlation exists between two variables when one of them is related to the other in some way.

A scatter plot is a graph in which the paired $(x,y)$ sample data are plotted with a horizontal $x$-axis and a vertical $y$-axis.

Linear Correlation means our plot looks like a line

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The Linear Correlation Coefficient or Pearson Product Moment Correlation Coefficient is a way to look at the variances of our data and come up with $r$, a number which tells us how strong the correlation is.

$$r = \frac{1}{n-1}\Sigma \left( \frac{x-\bar{x}}{s_x}\right)\left( \frac{y-\bar{y}}{s_y}\right)$$

where the sum ∑ is over all ordered pairs (x,y), s_x is the standard deviation of the x values, s_y is the standard deviation of the y values, and

and

are the sample means of x and y respectively.

Covariance

Covariance is another way of measuring correlation, but can also look at some non-linear relationships. It is defined by:

$$cov(X, Y) = \frac{1}{n}\Sigma (x_i-\bar{x})(y_i-\bar{y})$$

where the sum ∑ is over all ordered pairs (x,y),

Fun fact! When you take the same set of data twice, you get the following identities:

$$cov(X, X)=\sigma^2$$

$$r=corr(X,X)=1$$

Correlation vs. Causation

In the following chart, we can see a clear correlation between the number of people who drowned by falling in a swimming pool in the USA and number of films that Nicholas Cage appeared in in that year.

CAUSATION: Do you think Nicholas Cage causes drowning?

Or: Does smoking cause lung cancer? It’s harder than you think to prove.

Remember….. CORRELATION does not imply CAUSATION