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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.