I have a dataset, and i have to predict the flow of users at a certain city given some information like the day of the week, the month, the distance of the city of origin ecc..

First i decided to plot the heatmap of correlation, to see if there are correlations between the features, and this is the result: As we can see there's no much correlations between the features.

I have done Linear regression obtaining very bad results (R^2 = 0.1).

I have done Lasso Regression in order to drop the bad features but the best result for Lasso is given by lambda=0, so the best result is using all the features.

My question is, is it possibile that the dataset is very bad and it's not a problem of linear regression tool? Are there other techniques in order to understand if there is a better model? I'm trying to understand why Linear Regression performs so bad.

OK i plotted the features with respect to the label and i think that the problem is the dataset. The plot with the green X are the features i decided to drop, obtaining an average training error of 4200 (against the 22000 of before). Honestly i don't know what to do now.

• of course it is possible that a simple linear regression is a bad model to describe whats going on; this has not necessarily to be a data problem but could instead be a modelling problem. – BloXX Feb 21 '19 at 17:03
• I'm afraid I'm unable to see "there's no much correlations" because the meanings of the colors are undefined. I would expect the darkest purple would be close to $-1,$ in which case evidently some features are strongly correlated. However, this has nothing whatsoever to do with $R^2,$ which is a measure of how these features are related to the response. For a better understanding, consider drawing scatterplots of the response against the regressors so you can see how they might be related. – whuber Feb 21 '19 at 17:07

Also, before throwing away the model on the basis of $$R^2$$ (which is generally not a good thing to do) you should perform the usual regression diagnostics such as inspecting residual plots.