1. Spearman’s Rho Correlation
Example1: If you have the bellow data construct regression model:

2. Spearman’s Rho Correlation1.

3. Spearman’s Rho Correlation2.

4. Spearman’s Rho Correlation
Introduction
Spearman’s correlation coefficient is a statistical measure of the strength of monotonic relationship between paired data.

5. Spearman’s Rho Correlation

6. Spearman’s Rho Correlation
Spearman Rho or ranked correlation
If we have two variables Y and X for each case that is observed, the rank of the case for each of the variable X and Y is determined by ordering the values from low to high or from high to low.
For each case I , the difference in rank on variables X and on variable Y is determined and given a symbol D, and then D will be squared if there are n cases, The spearman rank correlation between X and Y is defined as:

7. Spearman’s Rho Correlation
Also Rho can be approximated by a t distribution
with degree of freedom = n – 2
The null hypothesis is

8. Spearman’s Rho Correlation
The standardized t can be calculated as:
Note: n should be greater than 15

9. Spearman’s Rho Correlation
Example: Find the Spearman’s Rho correlation for the below data (here n = 10 just for easing)

10. Spearman’s Rho Correlation

11. Spearman’s Rho Correlation
Hypothesis at alpha = 0.05
Tabulated t

12. Spearman’s Rho Correlation
Calculated t
Then we reject null hypothesis.