The formula to calculate the Sample Correlation Coefficient R is:
R=∑(xi−ˉx)(yi−ˉy)√∑(xi−ˉx)2∑(yi−ˉy)2
The Sample Correlation Coefficient R, also known as Pearson’s correlation coefficient, is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.
Let's assume the following data points:
Step 1: Calculate the means:
ˉx=2+4+6+84=5
ˉy=1+3+5+74=4
Step 2: Calculate the numerator:
∑(xi−ˉx)(yi−ˉy)=(2−5)(1−4)+(4−5)(3−4)+(6−5)(5−4)+(8−5)(7−4)=20
Step 3: Calculate the denominator:
√∑(xi−ˉx)2∑(yi−ˉy)2=√20×20=20
Therefore, the Sample Correlation Coefficient R is:
R=2020=1