Machine Learning Regression To Support Multi Variable Regression
Have you considered simply performing separate linear regressions for each dependent variable?
Also, you need to decide which inputs are theoretically significant (in terms of explaining the variation in the output) and then test for statistical significance to determine which ones should be retained in the model.
Additionally, test for multicollinearity to determine if you have variables which are statistically related and inadvertently influencing the output. Then, test in turn for serial correlation (if the data is a time series) and heteroscedasticity.
The approach you are describing of "garbage in, garbage out" risks overfitting - since you don't seem to be screening the inputs themselves for their relevance in predicting the output.
I have a data set of ~150 samples where for each sample I have 11 inputs and 3 outputs. I tried to build a full regression model to take in 11 inputs to be trained to predict the 3 outputs The issue is with so few samples training a full model is almost impossible. For this reason I am experimenting with regression such as linear regression in pythons sklearn. From what I can find most regression models either support one input to predict one output (after regression is complete) or many inputs to predict one output.
Question: Are there any types of regression that support many inputs to predict many outputs. Or perhaps any regression types at all that may be better suited for my needs.
Thank you for any help!