The figure for this exercise is a scatterplot of average math test score versus

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 575 550 525 500 475 10 20 30 40 50 60 80 90 Percent taking test Average math = 575-1.11 (Percent took) A) 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 For each 1.11 point decrease in average math 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 For each 1-percent decrease in the percentage of high school graduates taking the test, the average math test score 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 B) In a certain state, only 9% of graduates take the test, what is the predicted average math test score for this state? (Round the answer to two decimal places.)

Explanation / Answer

Solution

(a) Slope = -1.11

So, For each 1% increase in the percentage of high school graduates taking the test, the average math test decreases 1.11 points

(b) Percent took = 9%

Average maths = 575 - 1.11 (9) = 565.01

(c) Residual = 572 - 565.01 = 6.99

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