To calculate the linear correlation coefficient $r$, we use the formula:

[ r = \frac{n\sum{xy} - \sum{x}\sum{y}}{\sqrt{\left[n\sum{x^2} - (\sum{x})^2\right] \left[n\sum{y^2} - (\sum{y})^2\right]}} ]

Here’s the step-by-step process:

Step 1: Organize and Label the Data

The given dataset should have corresponding $x$ and $y$ values. If this isn't provided, we assume the dataset is one set of numbers, and we treat them as a single variable for analysis. Clarify if $x$ and $y$ pairs are available.

Step 2: Calculate Necessary Summations

Using the dataset:

1. $\sum{x}$: Sum of all $x$-values.
2. $\sum{y}$: Sum of all $y$-values.
3. $\sum{xy}$: Sum of products of $x$- and $y$-values.
4. $\sum{x^2}$: Sum of squares of $x$-values.
5. $\sum{y^2}$: Sum of squares of $y$-values.

Step 3: Calculate $r$

Substitute the above values into the formula.

If there’s a specific clarification on whether this is a paired dataset or single variable analysis (using lag or time-series methods), let me know. Do you want me to compute $r$ using this dataset, or should I organize $x$ and $y$ for you?