Refer to the scatterplot for given Exercise showing the relationship between the average math SAT score and the percentage of high school graduates taking the test for the 50 states and District of Columbia. (The data are from the sats98 dataset on the companion website.) The regression line for these data is
Average math = 575 - 1.11 (percent took)
a. The slope of the equation is 21.11. Interpret this value in the context of how average math SAT changes when the percent of graduates taking the test changes.
b. In Missouri, only 8% of graduates took the SAT test. What is the predicted average math SAT score for Missouri?
c. In 1998, the average math SAT score for Missouri was 573. What is the residual (prediction error) for Missouri?
Exercise
The figure for this exercise is a scatterplot of y = average math SAT score in 1998 versus x = percent of graduating seniors who took the test that year for the 50 states and the District of Columbia. The data are from the sats98 dataset on the companion website.
a. Does the plot show a positive association, a negative association, or no association between the two variables? Explain.
b. Explain whether you think the pattern of the plot is linear or curvilinear.
c. About what was the highest average math SAT for the 50 states and District of Columbia? Approximately, what percent of graduates took the test in that state?
d. About what was the lowest average math SAT for the 50 states and District of Columbia? Approximately what percent of graduates took the test in that state?