1
$\begingroup$

I'm doing a personal project on regression and I hope I can get some advice from you on several problems. The dataset I'm having is about cuisine, shape is 180x9, and the 2 continuous variables are "prep_time" and "cook_time". I want to predict cook_time based on other variables. I one hot encoded other categorical variables and get a total of ~30 features in the end (and only prep_time is continuous). This is the dataset before processing:

enter image description here

The baseline model with linear regression, SVR and Random forest doesn't perform really well (The absolute r2 scores are <0.1 for all 3 models). But when I added a feature total_time = prep_time+cook_time, and used MinMaxscale on prep_time and total_time, the RF model improves to r2 of ~0.3. However, LinReg results in ~0 mse and 1.0 r2 on the test set, surprisingly.

Thus, I tried to analyze this LR model more. I used sklearn.feature_selection.SelectFromModel function to get the important features from this Linear Regression model, and it shows that only the prep_time and total_time are important for the model. In fact, the model trained using only these 2 variables perform just as well. VIF of these 2 variables are ~7.0, which implies multicollinearity. However, if I remove either of these 2 variables, and train on only the other feature, the model doesn't perform that well.

My question is, is this still a good model? What could explain/potentially be a problem with this LinReg model when it has such a low mse and high r2? Should I use another algorithm instead?

Thank you!

$\endgroup$
3
  • $\begingroup$ Something is weird if you get $R^2=0$ in the out-of-sample data. $\text{//}$ $R^2$ loses its "proportion of variance explained" in nonlinear models like random forest and support vector regression, so it is just a reformulation of mean squared error that does not give the desired answer to the "Is this good enough?" question. $\endgroup$
    – Dave
    Jul 21 at 15:07
  • $\begingroup$ @Dave so in this case what are the metrics we can use? Is it just mse? $\endgroup$ Jul 21 at 15:25
  • 1
    $\begingroup$ $MSE$ and $MAE$ are completely viable metrics for this. $R^2$ is not a wrong metric, but keep in mind that it is just a function of the $MSE$. Any model that performs better on $MSE$ (on the same data!) will perform better on $R^2$, and any model that performs better on $R^2$ will perform better on $MSE$. The danger I see with $R^2$ is that it gets us thinking like grades in school. A useful model might have $R^2 = 0.2$, but that runs the risk of getting us to think that we got a $20\%$ and an F grade. Likewise, $R^2 > 0.9$ might looks like an A grade, but such performance might be pedestrian. $\endgroup$
    – Dave
    Jul 21 at 15:28
3
$\begingroup$

I suspect the issue is:

But when I added a feature total_time = prep_time + cook_time

Your response variable is cook_time. So it is nonsense to include it as a predictor. Suppose your model is something like:

$$y = x_1 + x_2 + x_3 + x_4$$

where $y$ is cook time, and $x_1$ is prep time.

So let us introduce another variable to represent total time: $z = y + x_1$, or $x_1 = z - y$. Now we substitute this into the model and we get:

$$y = z - y + x_2 + x_3 + x_4$$

So now we have $y$ on both sides of the model equation. This is going to lead to a perfect fit, which means that $R^2$ will be 1.0) and there will be no residuals (so that $MSE$ will be zero).

Moreover, let's just say that you did proceed with such a model. Now, when it comes to making predictions on new (out of sample) data, for which you obviously don't know what the cook time is, how can you form the total_time feature to predict on the new data ?

$\endgroup$
2
  • $\begingroup$ This makes sense, thank you so much! $\endgroup$ Jul 21 at 15:26
  • $\begingroup$ You're very welcome. Glad it could help :) $\endgroup$ Jul 21 at 15:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.