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As Part of a Study at a Large University, Data n=224n = 224

Question 99

Multiple Choice

As part of a study at a large university, data were collected on n=224n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling yy , 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=x _ { 1 } = average high school grade in mathematics (HSM)
x2=x _ { 2 } = average high school grade in science (HSS)
x3=x _ { 3 } = average high school grade in English (HSE)
x4=x _ { 4 } = SAT mathematics score (SATM)
x5=x _ { 5 } = SAT verbal score (SATV)
A first-order model was fit to data with R2=0.211R ^ { 2 } = 0.211 .
What is the correct interpretation of R2R ^ { 2 } , the coefficient of determination for the model?


A) Approximately 21%21 \% of the sample variation in GPAs can be explained by the first-order model.
B) Approximately 79%79 \% of the sample variation in GPAs can be explained by the first-order model.
C) We are 79%79 \% confident that the model is useful for predicting yy .
D) We expect to predict GPA to within approximately .21.21 of its true value.

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