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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 mat
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.
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Mathematics
3 years
2021-08-14T15:57:05+00:00
2021-08-14T15:57:05+00:00 1 Answers
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Answer: 3.13; The regression line underpredicts the student’s math test score.
Step-by-step 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