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 provides a better prediction of the dependent variable (Y) than simply using the sample mean. Therefore, option D is the best choice. Option A simply implies that the statistics computed from the sample are sensible, but this does not necessarily mean that the model is useful for prediction. Option B goes beyond what is required for a model to be considered statistically useful; a model only needs to be better than the sample mean at prediction. Option C introduces the term "practical," which is not necessarily related to statistical usefulness. "Statistically" useful means that the model provides more accurate predictions than simply using the sample mean. Choice D states that the model is a better predictor of Y than the sample mean, therefore it is statistically useful. Choices A, B, and C do not necessarily indicate statistical usefulness.

What Do We Mean When We Say That a Simple