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.

For each 1 unit decrease in the percentage of high school graduates taking the test, the predicted average math test score decreases 1.11 pointsIf no high school seniors in a particular state take the exam, the average math score is expected to be 575 points    For each 1 unit increase in the percentage of high school graduates taking the test, the predicted average math test decreases 1.11 pointsFor each 1.11 point decrease in average math test scores, the predicted percentage of high school graduates taking the test increases by 1If 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 5% 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 575 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. Here regression equation is Average math=575-1.11(Percent took)

Hence slope is -1.11

So interpretation is  For each 1 unit increase in the percentage of high school graduates taking the test, the predicted average math test decreases 1.11

b. For 5%

Average Math=575-(1.11*5)=569.45

c. Residual=y-y'=575-569.45=5.55

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