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I have a doubt about the multiple lieìnear regression I wanna run.

My dataset is of more than 16000 obs about videogames (kaggle one).

  • The target variable is Global sales,
  • The regressors are all factors (genre, publisher and platform of videogames).
  • The other regressor I'd like to use is the variable NA_Sales (total sales in North America), which is a part of the target variable (Global Sales is the sum of this last variable and other 3 geographical area of the world).

As expected, by adding NA_Sales the $R^2$ jumps to more than 80%, while considering only the 3 factors is only of about 11%. Is it right to use as regressor NA_Sales which is a component of the target variable?

If not, is it right to use only FACTORS variables as regressors?

Can anyone recommend an other model?

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    $\begingroup$ What does it mean to predict total using one of its parts as a predictor? Using all categorical predictors is fine. $\endgroup$
    – mdewey
    Dec 17, 2016 at 18:26
  • $\begingroup$ Sorry maybe it wasn't clear, i mean that Global sales is the sum of other 3 variables in the dataset, namely Na sales, JApan sales and eu sales $\endgroup$
    – Giuseppe Marzano
    Dec 17, 2016 at 19:55

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Your suspicion is correct, you cannot predict Sales using NA_Sales. The general term for this situation, when one of the predictors contains direct information about the response, is "data leakage". This is a particularly clear cut case, but it can be much more subtle.

One thing you could do is fit seperate models for NA_Sales and non_NA_Sales, and then sum the predictions of those two models. It's possible that this kind of procedure would improve the predictive power of your model if there is a structural difference between what is associated with NA_Sales vs non_NA_Sales. On the other hand, doing so means estimating more parameters, increasing the variance of your model. There is no way to know how this bias and variance balances for your specific data set without experimentation and model validation.

On your final point, there is no trouble at all with a model that has only categorical predictors. This is relatively common.

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  • $\begingroup$ Thank you! The problem is that all the other sales available (JP, EU and others sales are a part of global sales... so which model do you suggest? Linear regression with only that 3 factors is not very performative, the r^2 is about 11%... maybe PLS from PCA? Ridge and lasso? Random forest? $\endgroup$
    – Giuseppe Marzano
    Dec 18, 2016 at 7:47
  • $\begingroup$ @GiuseppeMarzano Instead of going too deep into the models, think about what it is you want to model! If you want to predict the regional decomposition of sales, you can use something like a multinomial regression, but there's no regional data. If you want to predict sales using only other variables, you probably don't have enough data or interesting variables either. $\endgroup$
    – Maximilian Aigner
    Dec 19, 2016 at 11:48
  • $\begingroup$ Yes the first aim was to predict global sales... but I think I can use multinomial regression as you suggested for "geographical areas" I mean Japan, North America and EU, no? Thank you for the answer $\endgroup$
    – Giuseppe Marzano
    Dec 19, 2016 at 18:29

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