The figure for this exercise is a scatterplot of average math test score versus
ID: 3230694 • Letter: T
Question
The figure for this exercise is a scatterplot of average math test score versus percent of graduating seniors who took the test for the 50 states. The regression line for these data is expressed with the following formula. Average math = 575-1.11 (Percent took) a) From the choices below, the best interpretation of the slope estimator is: If all high school seniors in a particular state take the exam, the average math score is expected to be 575 points For each 1-percent decrease in the percentage of high school graduates taking the test, the average math test score decreases 1.11 points For each 1-percent increase in the percentage of high school graduates taking the test, the average math test decreases 1.11 points If no high school seniors in a particular state take the exam, the average math score is expected to be 575 points For each 1.11 point decrease in average math test scores, the percentage of high school graduates taking the test increases by 1% b) In a certain state, only 4% of graduates take the test. What is the predicted average math test score for this state? (Do NOT convert the percentage into a decimal, i.e. if 27% use 27 instead of .27 in the equation. Use two decimal places in your answer.) c) Suppose that the (observed) average math test score was 580 for the state in part (b). What is the residual for this state? (use two decimal places in your answer)Explanation / Answer
a) option (c) is correct
For each 1-percent increase in the percentage of high school graduates taking the test, the average math test decreases 1.11 points.
b )) Y=575-1.11(Percent took)
Where prediction percent X=4% given
Predicted Average math Y=575-1.11(4 )
=570.56
c)Residual = Average Math(actual) - Average Math(predicted)
=575 -570.56
=4.44