In a standard linear regression model, let R 2 and R̅ 2 denote the coefficient of determination and the adjusted coefficient of determination, respectively. Which of the following statements is always true?

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Mathematics · Regression Analysis

In a standard linear regression model, let R 2 and R̅ 2 denote the coefficient of determination and the adjusted coefficient of determination, respectively. Which of the following statements is always true?

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R 2 increases or remains constant as the number of independent variables increases

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Answer 1

R̅ 2 always decreases as the number of independent variables increases

Answer 2

R̅ 2 is always greater than R 2

Answer 3

R 2 increases or remains constant as the number of independent variables increases

Answer 4

R̅ 2 is always strictly greater than 0

In a standard linear regression model, let R 2 and R̅ 2 denote the coefficient of determination and the adjusted coefficient of determination, respectively. Which of the following statements is always true?

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In a standard linear regression model, let R 2 and R&#773; 2 denote the coefficient of determination and the adjusted coefficient of determination, respectively. Which of the following statements is always true?

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In a standard linear regression model, let R 2 and R̅ 2 denote the coefficient of determination and the adjusted coefficient of determination, respectively. Which of the following statements is always true?