# How to detect and exclude outliers from linear regression?

 [Just to follow-up on this question]: I'm doing linear regression tests with SQL Anywhere's builtin OLAP functions. Say, for a very simplified example, I would assume a linear correlation between the columns x and y in a table MyTable. So I would generate a linear function with ```select REGR_COUNT(y, x) as cnt, round(REGR_SLOPE(y, x), 4) as slope, round(REGR_INTERCEPT(y, x), 4) as yIntercept, round(REGR_R2(my, x), 4) as fitness from MyTable where x > 0 and y > 0; ``` This works well generally. However, what would be a senseful method to exclude outliers? A simple test for maximum/minimum values (or a ranking) seems inadequate as outliers would be defined as based on their value pairs, not just on the y value. Currently, Im trying to use the above query as common table expression and then to check for those pairs that have a bigger deviation compared to the generated linear function: ```with CTE_LR as (select REGR_COUNT(y, x) as cnt, round(REGR_SLOPE(y, x), 4) as slope, round(REGR_INTERCEPT(y, x), 4) as yIntercept, round(REGR_R2(my, x), 4) as fitness from MyTable where x > 0 and y > 0) select x, y, round(slope * x + yIntercept, 4) as yCalc, abs(yCalc - y) as absDiff, abs(yCalc - y) / y as relDiff from MyTable M, CTE_LR where x > 0 and y > 0 order by relDiff desc, x, y; ``` However, this helps to detect outliers post-mortem, but obviously they have already influenced the linear regression. I could then build another regression without these outliers (say, those with a certain relative deviation) but that again might exclude the "wrong outliers" based on them being part of the previous regression. Therefore I would like a way to exclude them beforehand. Is there a (not too complicated) way to do so? asked 08 Jun '11, 12:26 Volker Barth 39.2k●354●537●806 accept rate: 33%

 The word percentile comes to my mind, exclude the <5% and the >95% percentile of the data range. See the PERCENT_RANK function and select the set for your regression based on the PERCENT_RANK. answered 08 Jun '11, 12:55 Martin 8.8k●126●162●249 accept rate: 14% That seems helpful (and I haven't been aware of that variation of RANK()), but... ...the problem is I'm not looking for absolute values but maximum/minimum y values w.r.t. the according x values. So basically it's a question how to do a "partition" (or a group by) over a continuous range of double values - and unfortunately not a range which is evenly filled with x values. (09 Jun '11, 04:20) Volker Barth you order by y and then use the Percent_Rank to skip the areas which you define as outliers (09 Jun '11, 06:14) Martin
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question asked: 08 Jun '11, 12:26

question was seen: 3,559 times

last updated: 09 Jun '11, 06:14