Question 5. Correlation & Regression Here is a scatterplot and least squares regression line. Closing the school achievement gap with attendance: Low-income students tend to have lower attendance rates and lower math test scores than their middle/upper income peers. Would raising their attendance close the achievement gap? To explore this possibility, a random sample was collected of students in Texas. For each student, data was collected on their attendance rate (percent of school days attended) and raw test scores on the Algebra 1 state exam. 1. Interpret the slope of the regression line (y^ = -7.69 + 0.57x) in a sentence. 2. Suggest some possible values for r, the correlation coefficient. 3. Does attendance cause test scores to go up? 4. Predict the test score for a student who attends 85% of the school days. 5. In general, are the residuals small or large? 6. Which variable is the response variable? Is it discrete or continuous? 7. Suppose that the coefficient of determination is 0.85. Interpret the coefficient of determination in a sentence. Attendance and Math Assessment Scores 55 50 45 STAAR Algebra 1 Score (Texas Exam) 40 35 30 65 70 75 80 85 90 95 100 Percent of School Days Attended