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, $\bar{Y}$
.

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, $\bar{Y}$
 .

Quizplus · Accepted Answer

A simple linear regression model is considered statistically useful when it is a better predictor of Y than the sample mean, which is represented by the formula Ŷ = b0 + b1X. In other words, the model has a lower standard error of the estimate and a higher coefficient of determination (R-squared), indicating that it explains a larger proportion of the variance in Y. While the other options (A, B, and C) may also be desirable, they do not necessarily indicate that the model is statistically useful, which is based on the model's ability to explain the relationship between X and Y.

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

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