Question

The IQ scores and math test scores of third grade students is given by the regression line 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.

−3.13; The regression line underpredicts the student's math test score.
3.13; The regression line overpredicts the student's math test score.
3.13; The regression line underpredicts the student's math test score.
−3.13; The regression line overpredicts the student's math test score.
82.9; The regression line overpredicts the student's math test score.

Answer 1

Answer: 3.13; The regression line underpredicts the student's math test score.

Explanation:

Given the equation of a regression model:

ŷ = −23.5 + 0.8534s,

where ŷ = predicted math score

s = IQ score

An actual math test score for a student is 73.5 with an IQ of 110.

Using the model to predict the score is f the student above ;

ŷ = −23.5 + 0.8534(110)

ŷ = −23.5 + 93.874

y = 70.374

Actual score = 73.5

Hence, since the actual score is greater Than the predicted score, then the model underpredicted the score by

Residual = actual - predicted = (73.5 - 70.374) = 3.126 = 3.13