As Part of a Study at a Large University, Data

question 67

Essay

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): $\begin{array}{l}x_{1}=\text { average high school grade in mathematics (HSM) } \\x_{2}=\text { average high school grade in science (HSS) } \\x_{3}=\text { average high school grade in English (HSE) } \\x_{4}=\text { SAT mathematics score (SATM) } \\x_{5}=\text { SAT verbal score (SATV) }\end{array}$

$\text { A first-order model was fit to the data with the following results: }$

$\begin{array}{llllll}\hline \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F VALUE } & \text { PROB }>\text { F }\\\\\text { MODEL } & 5 & 28.64 & 5.73 & 11.69 & .0001 \\\text { ERROR } & 218 & 106.82 & 0.49 & \\\text { TOTAL } & 223 & 135.46 & & \end{array}$

$\begin{array}{llll}\text { ROOT MSE } & 0.700 & \text { R-SQUARE } & 0.211 \\\text { DEP MEAN } & 4.635 & \text { ADJ R-SQ } & 0.193\end{array}$

$\begin{array}{lrrrr}&\text { PARAMETER}&\text { STANDARD}&\text { TFOR O: }\\\text { VARIABLE } & \text { ESTIMATE }&\text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\\\text { INTERCEPT } & 2.327 & 0.039 & 5.817 & 0.0001 \\\text { X1 (HSM) } & 0.146 & 0.037 & 3.718 & 0.0003 \\\text { X2 (HSS) } & 0.036 & 0.038 & 0.950 & 0.3432 \\\text { X3 (HSE) } & 0.055 & 0.040 & 1.397 & 0.1637 \\\text { X4 (SATM) } & 0.00094 & 0.00068 & 1.376 & 0.1702 \\\text { X5 (SATV) } & -0.00041 & 0.0059 & -0.689 & 0.4915\\\hline \end{array}$

$\text { Test to determine if the model is adequate for predicting GPA. Use } \alpha=.01 \text {. }$

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