use the table of values to calculate the linear correlation coefficient r
you see why no one is going to help with this, right?
To calculate the linear correlation coefficient (also known as Pearson's correlation coefficient) using a table of values, you need the following steps:
Step 1: Gather the Data
Collect the data pairs for which you want to calculate the linear correlation coefficient. Ensure that you have a set of paired observations.
Step 2: Calculate the Sum of X values
Add up all the values from the X column of the table and denote the sum as ΣX.
Step 3: Calculate the Sum of Y values
Add up all the values from the Y column of the table and denote the sum as ΣY.
Step 4: Calculate the Sum of the Product of X and Y values
Multiply each X value by its corresponding Y value and add up all these products to get the sum ΣXY.
Step 5: Calculate the Square of Each X Value
Square each X value and add up all the squared values to get the sum of squares (ΣX^2).
Step 6: Calculate the Square of Each Y Value
Square each Y value and add up all the squared values to get the sum of squares (ΣY^2).
Step 7: Calculate the Cross-Product Sum of X and Y Values
Multiply ΣX by ΣY, and then divide it by the number of data pairs (n).
Step 8: Calculate the Cross-Product Sum of X Squares
Multiply ΣX^2 by n and subtract the square of ΣX.
Step 9: Calculate the Cross-Product Sum of Y Squares
Multiply ΣY^2 by n and subtract the square of ΣY.
Step 10: Calculate the Linear Correlation Coefficient
Divide the cross-product sum of X and Y values (from step 7) by the square root of the cross-product sums of X squares (from step 8) multiplied by the cross-product sums of Y squares (from step 9).
The result will be the linear correlation coefficient (r) ranging between -1 and +1. A positive value indicates a positive correlation, a negative value indicates a negative correlation, and a value close to zero indicates a weak or no correlation.