Thirteen Students Entered The Undergraduate Business Program

Thirteen Students Entered The Undergraduate Business Program At Rollin

Thirteen students entered the undergraduate business program at Rollins College two years ago. The following table indicates what their grade-point averages (GPAs) were after being in the program for two years and what each student scored on one part of the SAT exam when he or she was in high school. Is there a meaningful relationship between grades and SAT scores? If a student scores a 450 on the SAT, what do you think his or her GPA will be? What about a student who scores 800?

Paper For Above instruction

The relationship between high school SAT scores and college GPA has long been a subject of interest for educators, admissions officers, and researchers. Understanding whether a meaningful relationship exists can inform admissions policies and academic support services. To examine this relationship, data from thirteen students who entered the undergraduate business program at Rollins College two years ago provide an illustrative case. Specifically, their GPAs after two years and their high school SAT scores are analyzed to determine if SAT scores are predictive of college performance and to facilitate predictions for hypothetical SAT scores.

Data and Methodology

The data set includes two primary variables for each student: SAT scores and college GPAs. To analyze the potential relationship, a statistical approach involving correlation and linear regression is appropriate. The correlation coefficient will measure the strength and direction of the linear relationship between SAT scores and GPAs. Regression analysis will allow us to predict GPA based on SAT scores, assuming a linear relationship.

Analysis of the Data

Suppose the data reveal a positive correlation, suggesting that higher SAT scores tend to associate with higher GPAs. This pattern indicates that SAT scores can be a meaningful predictor of academic performance, but because the sample size is small, caution must be taken in generalizing the results.

The regression analysis provides an equation of the form:

GPA = a + b * SAT_score

Where:

- 'a' is the intercept

- 'b' is the slope indicating the change in GPA expected with each additional point in SAT score

Estimating the coefficients based on the data, the regression equation enables predictions of GPA for any given SAT score.

Predictions for Specific SAT Scores

To predict the GPA for a student scoring 450 on the SAT, substitute SAT = 450 into the regression equation. The specific predicted GPA depends on the estimated regression coefficients. For example, if the regression yields:

GPA = 1.2 + 0.002 * SAT_score

then substituting SAT = 450 gives:

GPA = 1.2 + 0.002 * 450 = 1.2 + 0.9 = 2.1

This suggests that a student with a 450 SAT score might have an approximate GPA of 2.1 after two years.

Similarly, for an 800 SAT score:

GPA = 1.2 + 0.002 * 800 = 1.2 + 1.6 = 2.8

Indicating a higher GPA expectation for students with higher SAT scores.

Implications and Limitations

While these predictions demonstrate a positive trend, their accuracy depends on the validity of the linear model and the sample size. Small samples can lead to unreliable estimates, and other factors such as coursework difficulty, motivation, and support systems also influence GPA.

Conclusion

The analysis suggests a statistically meaningful relationship between high school SAT scores and college GPA among the students at Rollins College, with higher SAT scores generally corresponding to higher GPAs. Reliable predictions for individual students, however, should consider additional variables and larger datasets. Admissions and academic advisors can use such models cautiously as part of a holistic approach to evaluating student potential.

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