Based on the scatter diagram in Question 1, what kind of mathematical relationship would appear to exist between enrollment and operating expenditures per
student? In other words, do operating expenditures per student appear to (i) be
constant (and independent of enrollment), (ii) follow a linear relationship as enrollment increases, or (iii) follow some sort of nonlinear U-shape (possibly quadratic) relationship as enrollment increases?
As part of this study, the following cost function was developed:
C = f(Q, X1, X2, X3, X4, X5)
where C = operating expenditures per student in average daily attendance
ðmeasured in dollarsÞ
Q = enrollment ðnumber of students in average daily attendanceÞ
X1 = average teacher salary
X2 = number of credit units ð“courses”Þ offered
X3 = average number of courses taught per teacher
X4 = change in enrollment between 1957 and 1960
X5 = percentage of classrooms built after 1950
Variables X1, X2, and X3 were considered measures of teacher qualifications,
breadth of curriculum, and the degree of specialization in instruction, respectively. Variable X4 measured changes in demand for school services that could
cause some lagging adjustments in cost. Variable X5 was used to reflect any
differentials in the costs of maintenance and operation due to the varying ages of
school properties. Statistical data on 109 selected high schools yielded the following regression equation:
Notes: The numbers in parentheses are the t-scores of each of the respective
(b) coefficients. An asterisk (*) indicates that the result is statistically significant
at the 0.01 level.