The figure for this exercise is a scatterplot of average math test score versus
ID: 3222609 • 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.
I) From the choices below, the best interpretation of the slope estimator is:
a. For each 1-percent decrease in the percentage of high school graduates taking the test, the average math test score decreases 1.11 points
b. If all high school seniors in a particular state take the exam, the average math score is expected to be 575 points
c. If no high school seniors in a particular state take the exam, the average math score is expected to be 575 points
d. For each 1.11 point decrease in average math test scores, the percentage of high school graduates taking the test increases by 1%
e. For each 1-percent increase in the percentage of high school graduates taking the test, the average math test decreases 1.11 points
II) In a certain state, only 7% of graduates take the test. What is the predicted average math test score for this state?
(Round the answer to two decimal places.)
III) Suppose that the average math test score was 574 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
(I)The given regression model is
Average Math = 575 - 1.11( percent took)
so in simple term, by increasing one percent took , there is 1.11 unit decrease in Average math score which is given in option (e). so option (e) is correct.
Option (a) say 1.11 increasein Average math score so itis wrong.
Option (b) talk about intercept and which is also wrong.
Option (c) talks about intercept correctly but how it is possible that is nobody takes the exam, an average math score is calculated. It is also about intercept not about slope.
Option (d) it is inverse on point (a), so it is also wrong
(II) when Only 7% took the test
predicted average math test score = 575 - 1.11 * 7 = 567.23 marks
(III) but average math score is 574
so residual or prediction error = raw score - predicted score = 574 - 567.23 = 6.77