Question

The iq scores and math test scores of third grade students is given by the line of best fit ���� = -23.5 + 0.8534s, where ���� 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 underpredicts the student's math test score.
2) 3.13; the line of best fit overpredicts the student's math test score.
3) 3.13; the line of best fit underpredicts the student's math test score.
4) -3.13; the line of best fit overpredicts the student's math test score.

Answer 1

The residual for the student with an actual math score of 73.5 and an IQ of 110 is approximately 3.13. This means that the line of best fit slightly underestimates the student's math test score by this margin.

Step-by-step explanation:

The given line of best fit is ŷ = -23.5 + 0.8534s, where ŷ is the predicted math score and s is the IQ score. To find the residual for a student with an actual math test score of 73.5 and an IQ of 110, we first calculate their predicted math score using the line of best fit:

Predicted math score = -23.5 + 0.8534(110) = 70.374.

Next, we determine the residual, which is the difference between the actual score and the predicted score:

Residual = Actual score - Predicted score = 73.5 - 70.374 = 3.126.

The residual is approximately 3.13, which means that the line of best fit underpredicts the student's math test score by approximately 3.13 points. Therefore, the correct answer is option 3: 3.13; the line of best fit underpredicts the student's math test score.