Question

The IQ scores and math test scores of third-grade students are given by the line of best fit ŷ = −23.5 + 0.8534s, where ŷ 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.

a. −3.13; the line of best fit underpredicts the student's math test score.
b. 3.13; the line of best fit overpredicts the student's math test score.
c. 3.13; the line of best fit underpredicts the student's math test score.
d. −3.13; the line of best fit overpredicts the student's math test score.

Answer 1

The residual for the student's math test score is 3.13, indicating the line of best fit underpredicts the student's actual math test score.

Step-by-step explanation:

To find and interpret the residual, we first use the line of best fit equation to calculate the predicted math score for the student with an IQ of 110:

â = -23.5 + 0.8534 * s
â = -23.5 + 0.8534 * 110
â = -23.5 + 93.874
â = 70.374

Now we calculate the residual, which is the difference between the actual score and the predicted score:

residual = actual score - predicted score
residual = 73.5 - 70.374
residual = 3.126

Since the residual is positive, the line of best fit underpredicts the student's math test score. Therefore, the correct answer is:

c. 3.13; the line of best fit underpredicts the student's math test score.