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This seems should be a common question, but I couldn't find the answer after search around.

Let's say we want to calculate student adjusted math test score after controlling on family income. And based on the regression model and the data we have:

Math test score = Intercept + a * family income

Let's assume:

Math test score = 50 + 1 * family income (in 10 thousands)

As an example, we have a student whose test score is 60 and family income is 50 thousands. So his predicted score should be 55 and his residual is 5. This means he is doing 5 points better than the peers with same family income.

What should be his adjusted test score after controlling on family income? I guess it should not be his predicted score. I am thinking the adjusted score should be the average predicted score + the residual. Am I right?

I intend to use the adjusted score within the dataset, so that I can compare and visualize test scores of different groups of students based on the adjusted score.

kjetil b halvorsen
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Feng Jiang
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  • What do you mean by "average predicted score"? – whuber Jul 25 '16 at 18:19
  • In this case, should be predication based on average family income . – Feng Jiang Jul 25 '16 at 18:20
  • I get that. But you supply a proposed formula. Could you explain how one would compute "average predicted score"? That might show us what you really mean by that phrase. It's unclear what set of data or population you are averaging the score over. – whuber Jul 25 '16 at 18:21
  • Can I just say "average predicted score" is the average of predicted score across all observations in the dataset? Is this clear? – Feng Jiang Jul 25 '16 at 18:23
  • It is, thank you. But it raises questions about what you are trying to accomplish. Often "adjusted" scores are intended to be universal: they can be applied to different datasets to enable comparison between them. If you are going to base your adjusted score on averages of individuals within datasets, then you must have some other kind of objective in mind. That suggests you make an effort to edit your post to explain what you intend to achieve with the score adjustment. – whuber Jul 25 '16 at 18:25
  • Thanks for your explanation. Your question makes sense. What if I just want to use the adjust score within the dataset. Let's say I want to compare students in school A and school B based on this adjusted score? – Feng Jiang Jul 25 '16 at 18:29
  • Then you just "take out" the effect of income (which would be the residual in the ordinary regression of score on income). See http://stats.stackexchange.com/questions/17336 or http://stats.stackexchange.com/questions/46185, for instance. – whuber Jul 25 '16 at 20:08
  • Sorry. I can't see how to calculated the adjusted score in the two links. – Feng Jiang Jul 25 '16 at 20:34
  • @whuber can you be more explicit about "'take out' the effect of income"? Is my "average predicted score + the residual" approach correct? – Feng Jiang Jul 26 '16 at 02:46

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