Question

The IQ scores and math test scores of third grade students is given by the line of best fit Å· = -23.5 + 0.8534s, where Å· is the predicted math score and s is the IQ score. An actual math test score for a student is 73.5 with an IQ of 110. Find and interpret the residual.

1) -3.13; the line of best fit overpredicts the student's math test score.
2) 3.13; the line of best fit underpredicts the student's math test score.
3) 3.13; the line of best fit overpredicts the student's math test score.
4) -3.13; the line of best fit underpredicts the student's math test score.

Answer 1

The correct residual is 3.13, indicating that the line of best fit underpredicts the student’s math test score. The predicted score was 70.374 whereas the actual score was 73.5.

Step-by-step explanation:

The residual is the difference between the actual score and the predicted score from the line of best fit. In this case, the predicted math score for an IQ of 110 using the line ŷ = -23.5 + 0.8534s is calculated as follows:

ŷ = -23.5 + 0.8534(110)
ŷ = -23.5 + 93.874
ŷ = 70.374

The actual math test score is 73.5, so the residual is:

Residual = Actual score - Predicted score
Residual = 73.5 - 70.374
Residual = 3.13

The positive sign of the residual indicates that the actual score was higher than the predicted score. Therefore, the line of best fit underpredicts the student's math test score. Option 2 is correct: 3.13; the line of best fit underpredicts the student's math test score.