Retention of students is one of the largest problems facing colleges and universities today. Loss of students impacts revenues not only from tuition but from state and federal funding programs. If a university can understand what factors impact student retention, it can form strategic plans aimed at keeping student enrolled. Academic performance is often cited as one reason that students leave. Data were collected from 20 colleges in the Midwest on the freshman retention rate (% of freshmen who stay for a second year) and the 25th percentile score on the American college testing (ACT) examination. (The ACT test is a college entrance examination similar to the Scholastic Assessment Test, SAT). The data are given In Table 1:
a) Which variable is the independent variable? Which is the dependent variable?
b) Create a scatter plot of the data (Make sure to label your axis). Does it appear that freshman retention rate is related to the 25th percentile on the ACT exam?
c) Determine the coefficient of correlation. Interpret your answer.
d) Determine the coefficient of determination. Interpret your answer.
e) Determine the regression equation for this data.
f) Plot the regression line on the scatter plot. Do you think that the line does a good job of predicting freshman retention at a college or university? Why or Why not?
g) Estimate the retention rate when the ACT 25th percentile equal to 24.
Table 1
College ACT 25th Percentile Freshman Retention Rate
1 21 0.82
2 25 0.86
3 22 0.78
4 22 0.82
5 22 0.82
6 23 0.87
7 23 0.90
8 21 0.85
9 23 0.84
10 20 0.80
11 21 0.84
12 23 0.82
13 21 0.82
14 23 0.83
15 26 0.78
16 21 0.79
17 22 0.83
18 20 0.78
19 22 0.78
20 21 0.61