or if a lower score in one measure were compensated by higher performance
in the other measure.
Details of this particular standard are described below.
Performance data from the fall, 1998, class were used to evaluate the
potential impact of increasing admission standards at UHH.
First semester performance at UHH (F98GPA) was positively and
statistically significantly correlated with each of the three high school
performance measures, HSGPA (r=0.50, p<0.001), SATV (r=0.29, p<0.001),
and SATM (r=0.22, p<0.001).
Scatter plots for these pairs of variables are
shown in Figures 1-3.
When run in a multiple regression analysis, an equation
can be generated using high school performance variables to predict college
GPA.
This predicted grade point index (PGI) equation has the form: PGI=
a(HSGPA) + b(SATV) + c(SATM) + d, where a, b, c, and d are constants.
The
multiple regression equation for these fall, 1998 data was PGI = 1.036(HSGPA)
+ 0.00126(SATV) + 0.00101(SATM) - 1.966.
In this analysis, HSGPA was the
most powerful predictor (p<0.001) followed, although not statistically
significantly, by SATV (p<0.06), and SATM (p<0.16).
The SAT scores lose
apparent importance in the multiple regression analysis, because SAT scores
are already highly correlated with HSGPA and with each other; thus they add
little additional explanation of variation in UHH GPA.
For example, Figure 4
shows a scatter plot of SATV vs SATM for which the correlation coefficient, r =
0.61, P<0.001.
It is also possible that the first semester course load at UHH
may not draw as much on mathematics skills as later semesters with the
result that SATM has a diminished predictive power for early college GPA.
These results are essentially the same as the results of Susan Brown's earlier
analysis of student performance data from the class of fall, 1996.
Once established from an earlier base of data, the predicted grade point
index could potentially be used to evaluate and determine admission status of
future UHH applicants.
To examine the impacts of this possibility, Figure 5

7
shows actual GPA performance of students plotted against predicted GPA
index from the multiple regression on high school performance measures.
Two
points must be recognized at the onset of interpreting these data.
1) The data
set is necessarily restricted to students who were admitted; there is no

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- Summer '20
- Regression Analysis, HSGPA