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

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):
$x _ { 1 } =$ 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 the data with the following results:

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


$\begin{array}{llll}\text { ROOT MSE } & 0.700 & \text { R-SQUARE } & 0.211 \\\text { DEP MEAN } & 4.635 & \text { ADJ R-SQ } & 0.193\end{array}$
$$\begin{array}{l}\begin{array} { l r r r r } & \text { PARAMETER } & \text { STANDARD } & \text { T FOR 0: } & \\\text { VARIABLE } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER = 0 } & \text { PROB > |T| } \\\text { INTERCEPT } & 2.327 & 0.039 & 5.817 & 0.0001 \\\text { X1 (HSM) } & 0.146 & 0.037 & 3.718 & 0.0003 \\\text { X2 (HSS) } & 0.036 & 0.038 & 0.950 & 0.3432 \\\text { X3 (HSE) } & 0.055 & 0.040 & 1.397 & 0.1637 \\\text { X4 (SATM) } & 0.00094 & 0.00068 & 1.376 & 0.1702 \\\text { X5 (SATV) } & - 0.00041 & 0.0059 & - 0.689 & 0.4915 \\\hline\end{array}\\\text { Test to determine if the model is adequate for predicting GPA. Use } \alpha = .01 \text {. }\end{array}$$