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.

A) From the choices below, the best interpretation of the slope estimator is:

() For each 1.11 point decrease in average math test scores, the percentage of high school graduates taking the test increases by 1%

() 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 increase in the percentage of high school graduates taking the test, the average math test decreases 1.11 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 all 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 6% of graduates take the test. What is the predicted average math test score for this state?
  (Round the answer to two decimal places.)
   

C) Suppose that the average math test score was 578 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)

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

b) predicted average math test score for this state=575-1.11*6=568.34

c)

residual =actual-predicted=578-568.34=9.66

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