I scraped a real estate website and would like to impute missing data on total area (about 40% missing) using linear regression. I achieve the best results using price, number of rooms, bedrooms, bathrooms, and powder rooms.

Correlation matrix

Adding price to the room information makes a significant difference. This makes sense, since the number of rooms alone don't give you any information on how large those rooms may be. Price can reduce some of that uncertainty. There is a 20 point difference between the R^2 scores of the model that includes and the one that excludes price (0.62 vs 0.82).

The problem that I see, is that my final model would likely also be a liner regression with price as the target. With this, it seems wrong to include price in predicting total area for imputation. In essence, I'm using the target to predict a feature and then use that feature to predict the target again. That's circular and seems problematic to me but I could be wrong. My final model will look better as a consequence but I will have engineered a synthetic correlation. This seems especially critical since about 40% of values need to be replaced.

Does anyone disagree with this? Should I keep price as a predictor to impute missing values even though it will be the target of my final model?

  • 2
    $\begingroup$ Are you doing multiple imputation or single imputation? With MI it is usually recommended to include the outcome for the final analysis model as part of the imputation model. With single imputation, you shouldn't be doing it in the first place. $\endgroup$ Commented Aug 15, 2020 at 17:46
  • $\begingroup$ Do you know a reference for the second claim? $\endgroup$
    – Michael M
    Commented Aug 15, 2020 at 21:27

1 Answer 1


As Robert Long says in a comment, "With single imputation, you shouldn't be doing it in the first place."

There is a well respected way to deal with missing data, by doing multiple imputations. The idea is to acknowledge and incorporate variability in the imputation process by producing probabilistically several different imputed data sets. You then perform your analysis separately on each of the imputed sets, and combine the information in a way that takes both within-set and between-set variability into account. That gets around the inherent circularity that you rightly fear with the single-imputation approach.

Functions implementing the imputation and analysis process are available in many statistical software systems. This online book is a helpful introduction. And yes, including the outcomes (prices in your case) is an important part of the multiple imputation process.

  • $\begingroup$ Thank you for the book link, I will keep that as a future reference. Skimming through the material I realized that for this data set, imputation is probably not a good approach. Values are not missing at random. Total area is available for all condos but for non of the houses/duplexes/etc. This way I fear that I will introduce massive bias without being able to detect it in the future model. I will try and pivot my strategy. Thank you again for the link, it is a great resource. I would give you an up-vote but my current rank doesn't allow for it. Cheers! $\endgroup$ Commented Aug 16, 2020 at 17:27
  • $\begingroup$ @JahnicBeck "missing at random" (MAR) isn't necessarily so restrictive as you seem to be inferring. It's not the same as "missing completely at random" (MCAR). All that matters for MAR is that information about the missingness pattern is present in the data that you have. So a higher probability of having area data for condos than for other dwelling types could in principle still be compatible with the MAR assumption and suitable for imputation. Also, if this answers your question I believe that you can accept the answer even if you can't up-vote it. $\endgroup$
    – EdM
    Commented Aug 16, 2020 at 17:37
  • $\begingroup$ Even in the extreme case that all condo area values are present and all of the other housing types are missing? I will read the link further that you supplied and check this answer as accepted. $\endgroup$ Commented Aug 16, 2020 at 17:56

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