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

Question

Quizplus · Accepted Answer

When we say that a simple linear regression model is 'statistically' useful, it means that it is a better predictor of Y than the sample mean. This is because the model takes into account the relationship between the independent variable and the dependent variable, and can therefore make more accurate predictions. Option A is not correct because 'practical' usefulness depends on the context and the specific problem being solved. Option B is not correct because no model can be an excellent predictor of Y in all cases, and it is important to assess the model's predictive power using appropriate metrics. Option C is not correct because the fact that statistics computed from the sample make sense does not necessarily imply that the model is useful for prediction.

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What Do We Mean When We Say That a Simple $\bar { Y }$