I am using linear regression to do inference and know how much each predictor affects sales. In have data for several stores with features and sales during a certain time frame.

There is not much variation in sales in each individual store across time (as sales and all features are quite stable per store). There is a lot of variation across different stores (orders of magnitude).

My objective is to know how much each feature affect sales but to enrich the model i added past sales of the stores, the problem is that while the mse is highly reduced the model only focuses in this feature and the others become unimportant. If I don´t include it the model perfomrs much worse, as I don´t have data for size or prime location which highly influences the output.

I suspect it might be because there is not enough variation across time and what I am doing is adding a co-linear feature (If I could theoretically predict sales with the features I can more or less estimate past sales).

Does it makes sense in this case to dampen the past sales predictor? for example rounding the numbers, converting it to a category like gold, silver, bronze so it is not so much correlated? What other approaches could i take?



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