Which of the following statements are not true?
A) $R _ { k} ^ { 2 }$

, the coefficient of multiple determination for a k-predictor model, will virtually always increase as k does, and can never decrease.
B) We are not interested in the number of predictors k that maximizes $R _ { k} ^ { 2 }$

, the coefficient of multiple determination for a k-predictor model. Instead, we wish to identify a small k for which $R _ {k } ^ { 2 }$

Is nearly as large as $R ^ { 2 }$
For all predictors in the model.
C) $M S E _ { k } = S S E / ( n - k )$

Is the mean squared error for a k-predictor model.
D) All of the above statements are true.
E) None of the above statements are true.

Question

Which of the following statements are not true?
A) $R _ { k} ^ { 2 }$

, the coefficient of multiple determination for a k-predictor model, will virtually always increase as k does, and can never decrease.
B) We are not interested in the number of predictors k that maximizes $R _ { k} ^ { 2 }$

, the coefficient of multiple determination for a k-predictor model. Instead, we wish to identify a small k for which $R _ {k } ^ { 2 }$

Is nearly as large as $R ^ { 2 }$
For all predictors in the model.
C) $M S E _ { k } = S S E / ( n - k )$

Is the mean squared error for a k-predictor model.
D) All of the above statements are true.
E) None of the above statements are true.

Quizplus · Accepted Answer

Statement C is not true because the formula for the mean squared error (MSE) of a k-predictor model should be $MSE_k = SSE / (n - k - 1)$, not $SSE / (n - k)$. The denominator should subtract an additional 1 to account for the degrees of freedom used by the intercept term.

Which of the Following Statements Are Not True? A) Rk2R _ { k} ^ { 2 }Rk2​

Which of the Following Statements Are Not True?
A) $R _ { k} ^ { 2 }$