The figure for this exercise is a scatterplot of average math test score versus
ID: 3158473 • 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) From the choices below, the best interpretation of the slope estimator is: 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-percent decrease in the percentage of high school graduates taking the test, the average math test score decreases 1.11 points For each 1.11 point decrease in average with test scores, the percentage of high school graduates taking the test increases by 1% If all high school seniors in a particular state take the exam, the average math score is expected to be 575 points In a certain state, only 5% of graduates take the test. What is the predicted average math test score for this state? (careful here: note that, for the predictor variable, the units are already in percentage. You do not need to move the decimal place.) (Round the answer to two decimal places.) Suppose that the average math test score was 579 for the state in part (b). What is the residual (prediction error) for this state? (Round the answer to two decimal places.)Explanation / Answer
The equatuin of the regression is
Average math=575-1.11 *Percent took
B. Answer
Threfore, The predicted average mark math test score for the state when 5% of the graduate take the test is
Average math=575-1.11 *5 =575 -5.55= 569.45
The predicted average mark math test score for the state when 5% of the graduate take the test is 569.45.
C. Answer
Residual =Average math test score - predicted average mark math test score
= 579 - 569.45
= 9.55
The residua for the state when the test score and predicted test score 579 and 569.45 respectively is 9.55.