# Using linear regression for bias correction

I have a predictor and the ground truth. I have found that I can use linear regression for bias correction, so instead of using the predictor's estimate directly, we can use the one obtained from the LR between the ground truth and the predictor.

I am actually finding it confusing what bias correction actually means. Any pointers?

• My friend's wife constantly nags him to do chores: "Honey, it will only take ten minutes!" From experience he has discovered that a "ten minute" chore will take an hour and an "hour" chore will take up most of the day. So now when she asks him to do something that will only take $x$ minutes, he figures it'll really be $x/10$ hours: that's the bias correction. They're both happier now that they're in agreement :-). (In many fields, this is called calibration.) – whuber Aug 20 '12 at 19:49
• @whuber thanks for the analogy. I wanted to know how bias is calculated. I mean by linear regression as you said I can find a model that can give me the calibrated value as you mentioned. But I wanted to know how can I know about the bias from the scatter plot. Actually I wanted to know how it actually looks like given some data – user31820 Aug 20 '12 at 21:56
• My comment included actual data :-). Seriously, the procedure is no different than the intuitively obvious approach taken by my friend: he found a way to predict real experience ($y$) from estimated values ($x$) and used that relationship to adjust future estimates. Are you asking how to apply OLS to such situations? If so, then what have you learned about OLS so far and where are you stuck? – whuber Aug 20 '12 at 22:10

An estimate is biased if its expected value is not equal to the true parameter value. The magnitude of the difference between the expected or average value of the estimator and the parameter is the absolute bias of the estimator. Bias correction means that you take a biased estimate and add a constant to it to obtain an estimator with less or possibly (and ideally) zero bias.

• In my case how does it apply. Like I have predictions and their corresponding ground truths. So by expectation you mean taking the average of both the predictions and the ground truths and to see if they match? – user31820 Aug 20 '12 at 21:54
• Well I found this paper cawcr.gov.au/projects/verification/Stanski_et_al/…. And it has explained everything nicely. Thanks everyone for sharing – user31820 Aug 20 '12 at 23:02

If you know that your prediction is always 10 too high, then if your model says that the predicted Y is 100-- you would "correct" this and say the answer is actually 90.

You don't keep making the same mistake over and over again - if you know your model is always too high, then you fix it by adjusting the prediction aka correcting the bias.