Make a five-column table of your values with a pen and paper. The column heads will be in the order of X, X^2, Y, Y^2, and XY. The bottom of each column will contain the sum of the values for that particular column.
Data set:
X | Y
1 | 2
3 | 4
5 | 6
Five-column table:
X| X^2| Y| Y^2| XY|
1| 1| 2| 4| 2|
3| 9| 4| 16| 12|
5| 25| 6| 36| 30|
9| 35| 12| 56| 44|
Start your calculations to find the numerator of the correlation coefficient
formula.
The numerator:
Sum of XY column = 44
Sum of X column multiplied by the sum of the Y column / by number of data sets = (9 * 12) / 3 = 36
Numerator = (44 -- 36) = 4
Calculate the denominator of the correlation coefficient formula.
The denominator:
Sum of X^2 column = 35
Sum of (X column)^2 / number of value sets = 27
Sum of Y^2 column = 56
Sum of (Y column)^2 = 48
Denominator = square root of ((35-27)(56-48)) = about 7.483
Calculate the correlation coefficient by dividing the numerator by the denominator.
r = 4 / 7.483 = .535