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 considered "statistically" useful if it is a better predictor of Y than the sample mean. This means that the model has a lower error rate in predicting Y than simply using the mean of the Y values. While A is true for any statistically sound analysis, and B and C may or may not be true depending on the specific model and its context, D is the most accurate explanation for a "statistically" useful simple linear regression model.

What Do We Mean When We Say That a Simple