Which of the following statements are not true?
A) The predicted value $\hat { y } _ { i }$
Is the value of y that we would predict or expect when using the estimated regression line with $x = x _ { i }$
B) The predicted value $\hat { y } _ {i}$
Is the height of the estimated regression line above the value $x _ {i }$
For which the $i ^ { t h }$
Observation was made.
C) The residual $y _ { i } - \hat { y } _ { i }$
Is the difference between the observed $y _ { i }$
And the predicted $\hat { y } _ { i }$
D) If the residuals are all large in magnitude, then much of the variability in observed y values appears to be due to the linear relationship between x and y, whereas many small residuals suggest quite a bit of inherent variability in y relative to the amount due to the linear relation.
E) All of the above statements are true.

Question

Quizplus · Accepted Answer

Statement D is incorrect because it misinterprets the meaning of residuals in regression analysis. Large residuals indicate that the linear model does not fit the data well, suggesting that much of the variability in observed y values is not explained by the linear relationship between x and y. Conversely, small residuals indicate that the linear model provides a good fit to the data, meaning that much of the variability in observed y values can be attributed to the linear relationship between x and y.

Which of the Following Statements Are Not True? A) the Predicted

Which of the Following Statements Are Not True?
A) the Predicted