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

Question

Quizplus · Accepted Answer

A simple linear regression model is considered statistically useful if it can provide better predictions of the dependent variable (Y) than simply using the sample mean of Y. Therefore, option B is the correct answer. Option A is not always true since the effectiveness of the model as a predictor can vary depending on the data. Option C is not relevant to the statistical usefulness of the model. Option D may be important for assessing the appropriateness of the model assumptions, but it does not capture the concept of statistical usefulness.

What Do We Mean When We Say That a Simple