As part of a study at a large university, data were collected on n = 224 freshmen
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):
x 1 = average high school grade in mathematics (HSM)
x 2 = average high school grade in science (HSS)
x 3 = average high school grade in English (HSE)
x 4 = SAT mathematics score (SATM)
x 5 = SAT verbal score (SAW)
A first-order model was fit to data with R 2 = 0.211.
What is the correct interpretation of R 2 , the coefficient of determination for the model?
- We are 79% confident that the model is useful for predicting y.
- Approximately 79% of the sample variation in GPAs can be explained by the first-order model.
- We expect to predict GPA to within approximately .21 of its true value.
- Approximately 21 % of the sample variation in GPAs can be explained by the first-order model.
An Introduction to Statistical Methods and Data Analysis
ISBN: 978-1305269477
7th edition
Authors: R. Lyman Ott, Micheal T. Longnecker