As part of a study at a large university, data were collected on n = 224 freshme
ID: 3229569 • Letter: A
Question
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
x1 = average high school grade in mathematics (HSM)
x2 = average high school grade in science (HSS)
x3 = average high school grade in English (HSE)
x4 = SAT mathematics score (SATM)
x5 = SAT verbal score (SATV)
A first-order model was fit to data with R2 = 0.211.
What is the correct interpretation of R2, the coefficient of determination for the model?
We expect to predict GPA to within approximately .21 of its true value.
We are 79% confident that the model is useful for predicting y.
Approximately 21% of the sample variation in GPAs can be explained by the first-order model.
Approximately 79% of the sample variation in GPAs can be explained by the first-order model.
pt. 2
Give the null hypothesis for testing the overall adequacy of the model.
H0: 0 = 1 = 2 = 3 = 4 = 5 = 0
H0: 1 = 0
H0: 1 = 2 = 3 = 4 = 5 = 0
H0: 0 + 1x1 + 2x2 + 3x3 + 4x4 + 5x5 = 0
We expect to predict GPA to within approximately .21 of its true value.
We are 79% confident that the model is useful for predicting y.
Approximately 21% of the sample variation in GPAs can be explained by the first-order model.
Approximately 79% of the sample variation in GPAs can be explained by the first-order model.
pt. 2
Give the null hypothesis for testing the overall adequacy of the model.
H0: 0 = 1 = 2 = 3 = 4 = 5 = 0
H0: 1 = 0
H0: 1 = 2 = 3 = 4 = 5 = 0
H0: 0 + 1x1 + 2x2 + 3x3 + 4x4 + 5x5 = 0
Explanation / Answer
R2 = 0.211 ,Measures the proportion of total variation in y within is explained by regressor
the correct interpretation of R2:-
ANS:- Approximately 21% of the sample variation in GPAs can be explained by the first-order model.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.