Which of the following statements are true?
A) The kth-degree polynomial model $Y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \cdots \cdots + \beta _ {k } x ^ { k} + \varepsilon$

With K large is quite unrealistic in virtually all applications, and in most applications k =2 (quadratic) or k =3 (cubic) is appropriate.
B) The objective of regression analysis is to find a model that is both simple (relatively few parameters) and provides a good fit to the data.
C) A higher-degree polynomial may not specify a better model than a lower-degree model despite its higher coefficient of multiple determination $R ^ { 2 }$
Value.
D) All of the above statements are true.
E) None of the above statements are true.

Question

Which of the following statements are true?
A) The kth-degree polynomial model $Y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \cdots \cdots + \beta _ {k } x ^ { k} + \varepsilon$

With K large is quite unrealistic in virtually all applications, and in most applications k =2 (quadratic) or k =3 (cubic) is appropriate.
B) The objective of regression analysis is to find a model that is both simple (relatively few parameters) and provides a good fit to the data.
C) A higher-degree polynomial may not specify a better model than a lower-degree model despite its higher coefficient of multiple determination $R ^ { 2 }$
Value.
D) All of the above statements are true.
E) None of the above statements are true.

Quizplus · Accepted Answer

A) True, because in practice, very high-degree polynomials are rarely used due to overfitting and complexity issues. B) True, as the goal is to balance simplicity and fit to avoid overfitting and underfitting. C) True, because a higher $R^2$ value does not necessarily mean a better model if it leads to overfitting or lacks generalizability.

Which of the Following Statements Are True? A) the Kth-Degree Y=β0+β1x+β2x2+⋯⋯+βkxk+εY = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \cdots \cdots + \beta _ {k } x ^ { k} + \varepsilonY=β0​+β1​x+β2​x2+⋯⋯+βk​xk+ε

Which of the Following Statements Are True?
A) the Kth-Degree $Y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \cdots \cdots + \beta _ {k } x ^ { k} + \varepsilon$