Recently, I came across this situation wherein the value of Rsquare found to be 1 with the lower RMSE. What does it mean (in the practical sense)? Will it have any different consequences than normal regression model's outcomes? Please share your expert opinions and suggestions.
Hi @Shaktiyavesh Nandan Pratap Singh
In regression-based models, the RMSE criterion means the square root of the mean square error. The lower the value of this criterion, the better the situation.
This type of minimization is very common in data mining and classification. In it, we calculate the total errors of each point relative to the constructed model, and this in itself is a measure of the goodness of the model constructed by the algorithm.
Good luck
Thank you@Majid Jangizehi.
Could you please comment about the value of R^2(coefficient of determinants) of the model?
R^2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R^2 coefficient of determination is a statistical measure of how well the regression predictions approximate the real data points. An R^ 2 of 1 indicates that the regression predictions perfectly fit the data. , which is also evdident from the low RMSE value. All the best!
Shaktiyavesh Nandan Pratap Singh:
To answer your first question R^2 has an inverse relation with RMSE. Please check the answer in this Stack Exchange blog for detailed understanding. https://stats.stackexchange.com/questions/142248/difference-between-r-square-and-rmse-in-linear-regression
What do you exactly mean "Will it have any different consequences than the normal regression model's outcomes?" by this question? Usually, a Multiple Linear Regression (including linear regression), where we consider error is additive and Gaussian in nature. Can you please be more specific?
Aside, ML or statistics, if you have an R^2 =1for the training dataset, that might imply overfitting. We usually don't encourage to train a model up to an R^2 =1. Check the following blogs:
1. https://statisticsbyjim.com/regression/r-squared-too-high/
2. https://statisticsbyjim.com/regression/overfitting-regression-models/
Thank you so much@Shibaji Chakrabarty, for exploring more into this question. Further I would like to clarify my question in the following ways:
1. By the different consequences, I want to ask about: Will the predictive model generate any error? Will it sense some noise from new data and deviate from actual prediction?
2. The general understanding of R2 is considered better if the value falls close to 1.
3. For overfitting of model may have some other cause factors like many independent variables to predict, or variances of test data found more as compared to training data..etc.
That's why I raised this issue.
Regards..
The best way to confirm that what you observed with your original data set is real is to replicate using a different data set if at all available. If you get the same result consistently with high Rsquare and low RMSE then the model can be considered reliable in terms of it's predictability.
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