What do we mean when we say that a simple linear regression model is "statistically" useful?
A)All the statistics computed from the sample make sense.
B)The model is an excellent predictor of Y.
C)The model is "practically" useful for predicting Y.
D)The model is a better predictor of Y than the sample mean, .

Question

What do we mean when we say that a simple linear regression model is "statistically" useful?
A)All the statistics computed from the sample make sense. 
B)The model is an excellent predictor of Y. 
C)The model is "practically" useful for predicting Y. 
D)The model is a better predictor of Y than the sample mean, .

Quizplus · Accepted Answer

A simple linear regression model is statistically useful if it is a better predictor of Y than the sample mean. This means that the model explains more of the variability in Y than just using the mean value of Y. While practical usefulness is important, it is not the only criterion for determining statistical usefulness. A model may be practically useful but not necessarily statistically useful if it does not significantly outperform the sample mean. Similarly, just because all the statistics computed from the sample make sense does not necessarily mean that the model is statistically useful.

What Do We Mean When We Say That a Simple