Question

The article "Examined Life: What Stanley H. Kaplan Taught Us About the SAT" (The New Yorker [December 17,2001\(]: 86-92\) ) included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 16 percent of the variance in first-year college grades. GPA was second at \(15.4\) percent, and SAT I was last at \(13.3\) percent." a. If the data from this study were used to fit a leastsquares line with \(y=\) first-year college GPA and \(x=\) high school GPA, what would the value of \(r^{2}\) have been? b. The article stated that SAT II was the best predictor of first-year college grades. Do you think that predictions based on a least-squares line with \(y=\) first-year college GPA and \(x=\) SAT II score would have been very accurate? Explain why or why not.

Short answer

a) The value of \(r^{2}\) would have been 0.154. b) No, predictions based only on SAT II score would not be very accurate because it still leaves 84% of the variation in first-year college grades unexplained.

Step-by-step solution

Understand Coefficient of Determination

Coefficient of Determination, represented as \(r^{2}\), shows the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In this given scenario, the dependent variable is first-year college GPA and the independent variable is high school GPA. As per the exercise, the GPA explains 15.4 percent of the variance in first-year college grades. Therefore, \(r^{2}\) would be \(0.154\).

Analyze SAT II score as predictor

In the article, it is mentioned that SAT II scores are the best predictor, explaining 16 percent of the variance in first-year college grades. However, this does not necessarily mean the predictions would be very accurate. While it explains more variation than GPA or SAT I, it still leaves a vast majority (84%) of variation unexplained. Factors other than SAT II scores also play a significant role in determining first-year college success, which needs to be considered.

Key concepts

Understanding SAT II Scores

SAT II scores, also known as SAT Subject Test scores, offer colleges a more subject-specific evaluation of a student's academic abilities. Unlike the general SAT I, which assesses mathematical and verbal reasoning, SAT II tests measure knowledge in specific subjects such as Biology, Chemistry, Mathematics, and Foreign Languages. Students often take SAT II tests to showcase their strengths in particular areas, which can be a significant part of their college applications.

According to the article from The New Yorker, among SAT I scores, SAT II scores, and high school GPA, the SAT II scores were found to be the best predictor of first-year college GPA. Although with an explanatory power of only 16 percent, indicating that SAT II scores are somewhat effective at anticipating college performance, it's crucial to recognize that the vast majority of the variance is due to other factors not captured by these tests. Hence, while helpful, relying on SAT II scores alone for college success predictions is not sufficient as they account for a relatively small proportion of the factors influencing academic performance in college.

As educators and colleges evaluate the predictive validity of SAT II scores, it is significant to understand both the strengths and limitations of these exams. They reflect a student's ability in specific subject areas, but they may not fully represent a student's overall academic potential or the diverse factors that contribute to college success.

First-Year College GPA

First-year college GPA is an important indicator of a student's initial success in higher education. It reflects not only a student's cognitive abilities but also their adaptability to the college environment, work ethic, and time management skills. Colleges and universities often look at a student's GPA as a better approximator for success, as it is an amalgamation of all the academic efforts a student has put forth.

Because first-year college GPA is an aggregate measure, it may be influenced by a wide range of factors including the level of high school preparation, the rigor of college courses taken, and the quality of instruction, among others. The exercise reveals that high school GPA explained approximately 15.4 percent of the variance in first-year college GPA. This suggests that high school performance is a significant predictor of college success, yet there is still a large portion of variance unaccounted for. This gap indicates the presence of other influential elements such as personal determination, extracurricular involvement, or even socioeconomic status.

It's important for students and advisors to recognize that while GPA is a vital component of the academic narrative, comprehensive success strategies should incorporate support areas outside of the academic purview. Building study habits, seeking mentorship, and engaging in campus life are just as vital for transitioning and succeeding in the first year of college.

High School GPA as a Predictor

High school GPA is often used as a benchmark for predicting academic success in college because it is a cumulative measure of a student's performance throughout their high school years. It provides a broad view of a student's consistency, perseverance, and ability to meet academic requirements over an extended period. In the context of the exercise, the high school GPA came in just slightly behind SAT II scores at explaining variance in first-year college GPA.

Despite its slight inferiority to SAT II scores in the predictive scope (15.4 percent versus 16 percent), high school GPA remains a cornerstone of most college admissions processes. This metric is valued for its longitudinal perspective on a student's effort and achievement. Nonetheless, like SAT II scores, high school GPA is not the sole factor in forecasting college performance, and a significant amount of variance is left unexplained. This implies that while a high GPA may correlate with college readiness, it doesn't guarantee success without considering other qualitative factors such as motivation, extracurricular activities, and personal characteristics.

Ultimately, high school GPA should be seen as part of a complex array of metrics and experiences that prepare a student for the rigors of higher education. When students understand that their GPA is just one piece of the puzzle, they can focus on strengthening other areas that contribute to academic and personal development.