A professor is interested in understanding the factors on which the grades a student obtains in her final exam depends.

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A Professor Is Interested In Understanding The Factors On Which The Grades A Student Obtains In Her Final Exam Depends 1 (152.09 KiB) Viewed 10 times

A professor is interested in understanding the factors on which the grades a student obtains in her final exam depends. She chooses the student's intelligence quotient (X₁), the grades obtained in the mid-term exam (X₂), the number of days the student was present in the class in the whole semester (X3) as regressors. She randomly selects 120 students and estimates the following regression function: ¡= 56 +0.98X₁¡ +0.45X2¡ +0.98X3¡ + Uj, where Ρ, X₁₁, X2₁, and X3, denote the predicted value of grades obtained by the th student, her intellegence quotient, the grades obtained by her in the mid-term exam, and the number of days she was present in the class in the whole semester, respectively. She calculates the value of the regression R² to be 0.54. The value of the adjusted R² (R²) will be (Round your answer to two decimal places). Which of the following statements is not true about the R²? (Check all that apply.) A. The value of R² is always greater than the R² given that the number of regressors remains the same in the regression equation. B. The value of R² increases when a new regressor is added to the regression equation. C. The value of R² can be negative. D. The value of R² always lies between 0 and 1.