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 the following results:
_____________________________________________________________________
| ROOT MSE | 0.700 | R-SQUARE | 0.211 |
DEP MEAN
4.635
ADJ R-SQ
0.193
Interpret the value under the column heading PROB > F.
◦ Accept
H0 (at
α = .01); at least one of the
β-coefficients in the first-order model is equal to 0.
◦ Over 99% of the variation in GPAs can be explained by the model.
◦ There is sufficient evidence (at
α = .01) to conclude that the first-order model is statistically useful for predicting GPA.
◦ There is insufficient evidence (at
α = .01) to conclude that the first-order model is statistically useful for predicting GPA.
Lake position in the landscape and proportion of water received as groundwater (data from Webster et
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