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 (X,), 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 180 students and estimates the following regression function: Ý = 49 + 1.85X, + 0.98X,+0.98Xy, + u. where Y, X. X2, and X, denote the predicted value of grades obtained by the " student, her intellegence quotient, the grades obtained by her in the mid-term exam, and the number of days she was preseont in the class in the whole semester, respectively. She calculates the value of the regression R to be 0.45. The value of the adjusted R R)wil be (Round your answer to two decimal places). Which of the following statements is not true about the R? (Check all that apply.)

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter4A: Problems In Applying The Linear Regression Model
Section: Chapter Questions
Problem 2E
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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 (X,), 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 180 students and estimates the following regression function:
Ý = 49 + 1.85X, + 0.98X2 + 0.98X3, + u,.
where Y,, X, X2j, and X3, denote the predicted value of grades obtained by the " 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 R to be 0.45.
The value of the adjusted R (R) will be
(Round your answer to two docimal places).
Which of the following statements is not true about the R? (Chock all that apply.)
DA The value of R is always greater than the R given that the number of regressors remains the same in the regression equation,
B. The value of R always lies between O and 1.
O C. The value of R increases when a new regressor is added to the regression equation.
O D. The value of R can be negative.
Transcribed Image Text: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 (X,), 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 180 students and estimates the following regression function: Ý = 49 + 1.85X, + 0.98X2 + 0.98X3, + u,. where Y,, X, X2j, and X3, denote the predicted value of grades obtained by the " 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 R to be 0.45. The value of the adjusted R (R) will be (Round your answer to two docimal places). Which of the following statements is not true about the R? (Chock all that apply.) DA The value of R is always greater than the R given that the number of regressors remains the same in the regression equation, B. The value of R always lies between O and 1. O C. The value of R increases when a new regressor is added to the regression equation. O D. The value of R can be negative.
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