Question

A regression relationship has been established between two variables X and Y, in which X is the independent variable. The coefficient of correlation between X and Y is 0.55. What percentage of the variation in Y is not explained by the regression relationship?

Answer 1

The connections between signs can be weak and strong (close). Their criteria are assessed on the Chaddock scale:

0.1 <rxy <0.3: weak;

0.3 <rxy <0.5: moderate;

0.5 <rxy <0.7: noticeable;

0.7 <rxy <0.9: high;

0.9 <rxy <1: very high.

In this case noticeable.

The percentage of the variation in Y is not explained by the regression relationship is

$$(1-0.55)\times100=45$$