Question

The iq scores and english test scores of fifth grade students is given by the line of best fit Å· = -26.7 + 0.9346s, where Å· is the predicted english score and s is the iq score. An actual english test score for a student is 65.7 with an iq of 96. Find and interpret the residual.

1) -2.68; the line of best fit underpredicts the student's english test score.
2) 2.68; the line of best fit overpredicts the student's english test score.
3) -2.68; the line of best fit overpredicts the student's english test score.
4) 2.68; the line of best fit underpredicts the student's english test score.

Answer 1

The residual for the student's English test score is 2.68, indicating that the actual score was higher than the predicted value by this amount, meaning that the line of best fit underpredicts the student's English test score.

Step-by-step explanation:

The residual is the difference between an actual observed value and the predicted value given by a line of best fit. In this scenario, the student's actual English test score is 65.7 and the predicted English test score using the provided line of best fit equation Å· = -26.7 + 0.9346s, based on an IQ (s) of 96, would be Å· = -26.7 + 0.9346(96) = 63.0216. Calculating the residual for the student's English test score involves subtracting the predicted score from the actual score: 65.7 - 63.0216 = 2.6784, which rounds to 2.68.

Therefore, the residual is 2.68, meaning that the line of best fit underpredicts the student's English test score by 2.68 points. This answers option 4. When a residual is positive, it indicates that the actual observed value was higher than the predicted value. In context, this suggests that the relationship captured by the line of best fit underestimated this particular student's English achievement based on their IQ score.