Final answer:
The statement is true, and an r² value of 0.20 means that the regression model explains 20% of the variation in the dependent variable with the independent variables accounted for in the model.
Step-by-step explanation:
The statement is true. An r² value of 0.20 (or 20% when expressed as a percentage) indicates that approximately 20% of the variation in the dependent variable is explained by the independent variables in the regression model.
It's important to understand that this means 80% of the variation is not explained by the model, which is represented by 1 - r². The remaining variation could be due to other variables not included in the model or inherent variability in the data.
To provide an example, suppose a student's final exam grade (the dependent variable, y) is being predicted by the number of study hours (the independent variable, x).
If the r² of the regression model is 0.20, it means that the number of study hours explains 20% of the variation in the final exam grades, while the other 80% might depend on factors like the student's prior knowledge, test-taking skills, or the difficulty of the exam.