Finding the Correlation Coefficient Manually:
The correlation coefficient, denoted by the symbol "r", is calculated using the following formula:
r = ( Σ(xy) ) / (√(Σx² * Σy²))
where:

Σ (sigma) represents the sum of all the values.

x and y are the corresponding data points for each variable.

Σxy is the sum of the product of each x value and its corresponding y value (x multiplied by y for each pair).

Σx² is the sum of all the squared x values (each x value squared).

Σy² is the sum of all the squared y values (each y value squared).
Here's a stepbystep process to find the correlation coefficient manually:

Prepare your data: Have your data points for both variables (x and y) organized in separate lists or columns.

Calculate products and squares: Multiply each x value with its corresponding y value (xy) and create a new list for these products. Then, square each x value (x²) and each y value (y²) and create separate lists for these squared values.

Sum the columns: Find the sum (Σ) of each column: Σx, Σy, Σxy, Σx², and Σy².

Apply the formula: Plug the calculated sums into the formula r = ( Σ(xy) ) / (√(Σx² * Σy²)) and solve for r.
Finding the Correlation Coefficient with a Spreadsheet Program:
Most spreadsheet programs like Microsoft Excel or Google Sheets have builtin functions to calculate the correlation coefficient. Here's a general process (specific steps might vary slightly depending on the program):

Input your data: Enter your data points for both variables (x and y) into separate columns in your spreadsheet.

Use the CORREL function: Locate the function for calculating the correlation coefficient. In Excel, it's the CORREL function, and in Google Sheets, it's also called CORREL.

Provide cell references: Within the function arguments, specify the cell ranges containing your x data and y data. The function will automatically calculate the correlation coefficient based on your data.
Remember:

The correlation coefficient value falls between 1 and +1.

A positive value indicates a positive correlation (as one variable increases, the other tends to increase as well).

A negative value indicates a negative correlation (as one variable increases, the other tends to decrease).

A value close to 0 indicates little to no correlation.
If you're working with a smaller dataset or prefer a manual approach, calculating the correlation coefficient by hand can be a good learning experience. However, for larger datasets or repetitive calculations, using a spreadsheet program is much faster and more efficient.