As Part of a Study at a Large University, Data $x _ { 1 } =$

question 71

Short Answer

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

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

---

Definitions:

Okazaki Fragments

Short fragments of DNA that are synthesized on the lagging strand during DNA replication.

Semiconservative Replication

The method by which DNA is duplicated in all known cells, where each of the two strands of the DNA molecule serve as a template for the production of the complementary strand.

Double Helix

The spiral structure forming the shape of DNA molecules, consisting of two strands wound around each other.

New Strands

Refers typically to the newly synthesized strands of DNA or RNA following replication or transcription processes.