Question

The IQ scores and English test scores of fifth grade students are given by the line of best fit ���� = -26.7 + 0.9346s, where ���� 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 approximately 2.68, which indicates that the line of best fit underpredicts the student's English test score.

Step-by-step explanation:

To find the residual for the student with an actual English test score of 65.7 and an IQ score of 96, we first calculate the predicted English score using the given line of best fit equation:

ÿ = -26.7 + 0.9346s

Where ÿ is the predicted English score and s is the student's IQ score.

Substituting the IQ score (s = 96) into the equation gives us the predicted score:

ÿ = -26.7 + 0.9346(96)

ÿ = -26.7 + 89.7216

ÿ = 63.0216

Now, we calculate the residual:

Residual = Actual score - Predicted score

Residual = 65.7 - 63.0216

Residual = 2.6784

The residual is approximately 2.68 which means that the actual score is 2.68 points higher than the predicted score. Therefore, the correct statement is:

2) 2.68; the line of best fit underpredicts the student's English test score.