The correlation coefficient (often denoted as rrr) measures the strength and direction of a linear relationship between two variables. Here's how to find it, particularly using the Pearson correlation coefficient:

1. Identify your two data sets as variables xxx and yyy.
2. Calculate the mean of each variable (xˉ\bar{x}xˉ and yˉ\bar{y}yˉ​).
3. Calculate the standard deviation of each variable (sxs_xsx​ and sys_ysy​).
4. For each pair of values (xi,yi)(x_i,y_i)(xi​,yi​), calculate the deviation from the mean, (xi−xˉ)(x_i-\bar{x})(xi​−xˉ) and (yi−yˉ)(y_i-\bar{y})(yi​−yˉ​).
5. Multiply these deviations for each pair and sum the products: ∑(xi−xˉ)(yi−yˉ)\sum (x_i-\bar{x})(y_i-\bar{y})∑(xi​−xˉ)(yi​−yˉ​).
6. Calculate the correlation coefficient using the formula:

r=∑(xi−xˉ)(yi−yˉ)(n−1)sxsyr=\frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{(n-1)s_xs_y}r=(n−1)sx​sy​∑(xi​−xˉ)(yi​−yˉ​)​

where nnn is the number of pairs. This formula gives a value between -1 and 1, where close to 1 means a strong positive linear correlation, close to -1 means a strong negative linear correlation, and around 0 means little or no linear correlation. There are other types like Spearman and Kendall correlation coefficients for different kinds of data relationships, but Pearson is the most common for linear associations. This explanation includes both the conceptual understanding and the step-by-step calculation method.