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Explanation:
COMPLETE QUESTION: Standardized test scores are often used as part of an application to college. Test scores in math and verbal are between 200 and 800 but have no units.These verbal scores averaged 470.8, with a standard deviation of 175.7, and the math scores averaged 465.4, with a standard deviation of 172.9. Students who score one standard deviation above the mean in verbal are expected to score 0.623 standard deviations above the mean in math. Also, 38.8% of the variability in math score is explained by variability in verbal score.
Every year some student scored a perfect 1600 (combined math and verbal score). Based on this model, what would that student's residual be for her math score?
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SOLUTION:
The first thing to do is to find the equation of the regression line, then use the equation to find student's residual score for math score. This can be done as below;
From the question, we are given that the verbal mean score = 0.623 l, the standard deviation of math score= 172.9, the standard deviation of verbal score= 175.7.
Therefore, (mean verbal score × standard deviation of math score)÷ standard deviation of verbal scores.
That is; a°° = (0.623 × 172.9)/175.7.
= 0.613.
Next, we are given from the question the math score average to be 465.4 and verbal score average to be 470.8. Then;
==> Average score in math - (average verbal score × 0.613).
a°= 465.4 - (470.8 × 0.613).
= 176.8.
====> Therefore, the equation of the regression line is given below;
(a° + a°°x===> the equation of the regression line is in this form).
===> 176.8 + 0.613x.
The atudent's residual for her math score= 176.8 + 0.613x. where X = test score for verbal= 800.
Then, 176.7 + 0.613(800) = 667.1.
===> 176.8 + 0.613× (1600).
= 1157.6.
