SAT scores are often used as a proxy for how well a state educates the students who reside in that state. However, not all students in a state actually take the SAT, and SAT participation rates vary across states. For example, some states require the SAT as an assessment test in high school. Those states will have higher participation rates than states that do not require the test in high school. If a student attends a high school that does not require the SAT, but the student plans to apply to a college that requires the SAT for admission, then that student willchoose to take the exam. Regression results from a regression using Y = state average SAT and X = state SAT participation are shown below.

(a) What do these regression results tell you about the relationship between state average SAT score and state SAT participation?

(b) Do you consider this a strong relationship? Explain.

(c) Can you suggest reasons why this relationship might exist?

Transcribed Image Text:

Regression Statistics R Square Standard Error 0.8419 59.94 Observations 51 Variables Coefficients Std Error I Stat p-value Lower 95% Upper 95% 1752.44 -388.08 12.916 135.683 8.77E-65 24.024 - 16.154 2.91E-21 Intercept Participation 1726.49 -436.36 1778.40 -339.80