Final answer:
The statement that a low r² value indicates the regression line is not useful in describing the relationship is true. A low r² value means that the regression line does not effectively explain the variance in the dependent variable and hence, is not useful for making predictions.
Step-by-step explanation:
The student asked if a low value of r² indicates that the regression line is not useful in describing the relationship. The short answer to this question is true. When we have a low r² value, it indicates that a relatively small percentage of the variance in the dependent variable (y) can be explained by the independent variable (x) using the regression line. In other words, the regression line does not well-explain the relationship between x and y.
As an example, let's interpret an r² value in the context of a given example: If we have an r² value of .4397, as in the third exam/final exam example provided, this means approximately 44 percent of the variation in the final exam grades can be explained by the variation in the grades on the third exam using the regression line. A lower r² would indicate an even less useful model for prediction.
It's important to note that while a significant r (with a significance level, typically 0.05) and a linear trend in the scatter plot are prerequisites for using the regression line for prediction, r² represents how well the regression line fits the data. Hence, a low r² value suggests that the regression model may not be the most appropriate choice for making predictions.