The figure for this exercise is a scatterplot of average math test score versus
ID: 3363233 • 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 575 500 475 20304030007080” Average math = 575-1.11 (Percent took) a. From the choices below, the best interpretation of the estimated slope is... (there is just one correct answer; you have 2 attempts) O 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 unit decrease in the percentage of high school graduates taking the test, the predicted average math test score decreases 1.11 points O 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 predicted percentage of high school graduates taking the test increases by 1 For each 1 unit increase in the percentage of high school graduates taking the test, the predicted average math test decreases 1.11 points b. In a certain state, only 9% of graduates take the test. what is the predicted average math test score for this state? (careful here: note that, for the 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.) c.Suppose that the average math test score was 572 for the state in part b. What is the residual (prediction error) for this state? Round the answer to to two decimal places.)Explanation / Answer
(a) Besst interpretation of slope is
Here option E is correct, for each 1 unit of increase in the percentage of high school graduate taking the test,the predcicted average math test decreases 1.11 points.
(b) Here percentage of test givers = 9%
Predicted average math test score = 575 - 1.11 * percent took test
= 575 - 1.11 * 9 = 565.01
(C) Residual for this state when the real marks where percentage took the test = 572
residual = 572 - 565.01 = 6.99