A bivariate relationship has a correlation coefficient ( � ) (r) of 0.7. 0.7. Identify the % of variation in the response variable that can be explained by response in the explanatory variable:
Question
A bivariate relationship has a correlation coefficient ( � ) (r) of 0.7. 0.7.
Identify the % of variation in the response variable that can be explained by response in the explanatory variable:
Solution
The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship.
The square of the correlation coefficient (r^2), also known as the coefficient of determination, is a measure of the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is a key output of regression analysis.
In this case, the correlation coefficient (r) is 0.7. To find the coefficient of determination (r^2), we square the correlation coefficient:
r^2 = (0.7)^2 = 0.49
Therefore, 49% of the variation in the response variable can be explained by the response in the explanatory variable.
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